Results of Elementary Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 4.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genlog{a}@@{z} = \ifrac{\ln@@{z}}{\ln@@{a}}} | log[a](z)=(ln(z))/(ln(a)) |
Log[a,z]=Divide[Log[z],Log[a]] |
Successful | Successful | - | - |
| 4.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genlog{a}@@{z} = \frac{\genlog{b}@@{z}}{\genlog{b}@@{a}}} | log[a](z)=(log[b](z))/(log[b](a)) |
Log[a,z]=Divide[Log[b,z],Log[b,a]] |
Successful | Successful | - | - |
| 4.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genlog{a}@@{b} = \frac{1}{\genlog{b}@@{a}}} | log[a](b)=(1)/(log[b](a)) |
Log[a,b]=Divide[1,Log[b,a]] |
Successful | Successful | - | - |
| 4.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{e} = 1} | ln(exp(1))= 1 |
Log[E]= 1 |
Successful | Successful | - | - |
| 4.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{1}^{e}\frac{\diff{t}}{t} = 1} | int((1)/(t), t = 1..exp(1))= 1 |
Integrate[Divide[1,t], {t, 1, E}]= 1 |
Successful | Successful | - | - |
| 4.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genlog{e}@@{z} = \ln@@{z}} | log[exp(1)](z)= ln(z) |
Log[E,z]= Log[z] |
Successful | Successful | - | - |
| 4.2.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genlog{10}@@{z} = \ifrac{(\ln@@{z})}{(\ln@@{10})}} | log[10](z)=(ln(z))/(ln(10)) |
Log[10,z]=Divide[Log[z],Log[10]] |
Successful | Successful | - | - |
| 4.2.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ifrac{(\ln@@{z})}{(\ln@@{10})} = (\genlog{10}@@{e})\ln@@{z}} | (ln(z))/(ln(10))=(log[10](exp(1)))* ln(z) |
Divide[Log[z],Log[10]]=(Log[10,E])* Log[z] |
Successful | Successful | - | - |
| 4.2.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{z} = (\ln@@{10})\genlog{10}@@{z}} | ln(z)=(ln(10))* log[10](z) |
Log[z]=(Log[10])* Log[10,z] |
Successful | Successful | - | - |
| 4.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@{z+2\pi i} = \exp@@{z}} | exp(z + 2*Pi*I)= exp(z) |
Exp[z + 2*Pi*I]= Exp[z] |
Successful | Successful | - | - |
| 4.2.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@{-z} = 1/\exp@{z}} | exp(- z)= 1/ exp(z) |
Exp[- z]= 1/ Exp[z] |
Successful | Successful | - | - |
| 4.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\exp@@{z}| = \exp@{\realpart@@{z}}} | abs(exp(z))= exp(Re(z)) |
Abs[Exp[z]]= Exp[Re[z]] |
Successful | Successful | - | - |
| 4.2.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{\exp@@{z}} = \imagpart@@{z}+2k\pi} | argument(exp(z))= Im(z)+ 2*k*Pi |
Arg[Exp[z]]= Im[z]+ 2*k*Pi |
Failure | Failure | Fail -18.84955592 <- {z = 2^(1/2)+I*2^(1/2), k = 3}-18.84955592 <- {z = 2^(1/2)-I*2^(1/2), k = 3}-18.84955592 <- {z = -2^(1/2)-I*2^(1/2), k = 3}-18.84955592 <- {z = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
-18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-18.84955592153876 <- {Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.2.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@@{z} = e^{x}\cos@@{y}+ie^{x}\sin@@{y}} | exp(z)= exp(x)*cos(y)+ I*exp(x)*sin(y) |
Exp[z]= Exp[x]*Cos[y]+ I*Exp[x]*Sin[y] |
Failure | Failure | Fail -.8272584772+1.775573363*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}1.772639846+1.591201978*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}3.332514076+3.679324696*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-3.350888586-2.154747662*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[-0.8272584783533998, 1.7755733643246545] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.7726398453192989, 1.591201979498678] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.332514075382279, 3.679324697962366] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.3508885868787868, -2.154747660864471] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.2.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{a} = \exp@{a\Ln@@{z}}} | (z)^(a)= exp(a*ln(z)) |
(z)^(a)= Exp[a*Log[z]] |
Successful | Failure | - | Successful |
| 4.2.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{a} = \exp@{a\ln@@{z}}} | (z)^(a)= exp(a*ln(z)) |
(z)^(a)= Exp[a*Log[z]] |
Successful | Successful | - | - |
| 4.2.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z^{a}| = |z|^{\realpart@@{a}}\exp@{-(\imagpart@@{a})\phase@@{z}}} | abs((z)^(a))=(abs(z))^(Re(a))* exp(-(Im(a))* argument(z)) |
Abs[(z)^(a)]=(Abs[z])^(Re[a])* Exp[-(Im[a])* Arg[z]] |
Failure | Failure | Successful | Successful |
| 4.2.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{z^{a}} = (\realpart@@{a})\phase@@{z}+(\imagpart@@{a})\ln@@{|z|}} | argument((z)^(a))=(Re(a))* argument(z)+(Im(a))* ln(abs(z)) |
Arg[(z)^(a)]=(Re[a])* Arg[z]+(Im[a])* Log[Abs[z]] |
Failure | Failure | Fail -6.283185309 <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}6.283185309 <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}6.283185309 <- {a = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-6.283185309 <- {a = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} |
Fail
-6.283185307179586 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}6.283185307179586 <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}6.283185307179586 <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-6.283185307179586 <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} |
| 4.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{z^{a}} = a\phase@@{z}} | argument((z)^(a))= a*argument(z) |
Arg[(z)^(a)]= a*Arg[z] |
Failure | Failure | Fail .980258143-1.110720734*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.9802581426+1.110720734*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}.980258144+3.332162204*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.302927166-3.332162204*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.9802581434685473, -1.1107207345395915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9802581434685472, 1.1107207345395915] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.9802581434685469, 3.332162203618774] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.302927163711039, -3.332162203618774] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.2.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z} = \exp@@{z}} | exp(z)= exp(z) |
Exp[z]= Exp[z] |
Successful | Successful | - | - |
| 4.2.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z} = (\exp@@{z})\exp@{2kz\pi\iunit}} | exp(z)=(exp(z))* exp(2*k*z*Pi*I) |
Exp[z]=(Exp[z])* Exp[2*k*z*Pi*I] |
Failure | Failure | Fail .6414354628+4.062928650*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}-.1544020768e13-.1710664597e12*I <- {z = 2^(1/2)-I*2^(1/2), k = 3}.8993679173e11+.1849553851e11*I <- {z = -2^(1/2)-I*2^(1/2), k = 3}.3791252193e-1+.2401424313*I <- {z = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
Complex[0.6414354615731531, 4.062928651501303] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5440207807554412*^12, -1.710664745395911*^11] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.993679264986926*^10, 1.8495537828408436*^10] <- {Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.03791252182632387, 0.24014243117514714] <- {Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.2.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi <= \imagpart@@{\left(\frac{1}{a}\Ln@@{w}\right)}} | - Pi < = Im((1)/(a)*ln(w)) |
- Pi < = Im[Divide[1,a]*Log[w]] |
Failure | Failure | Successful | Successful |
| 4.2.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{\left(\frac{1}{a}\Ln@@{w}\right)} <= \pi} | Im((1)/(a)*ln(w))< = Pi |
Im[Divide[1,a]*Log[w]]< = Pi |
Failure | Failure | Successful | Successful |
| 4.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{1} = 0} | ln(1)= 0 |
Log[1]= 0 |
Successful | Successful | - | - |
| 4.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{-1+\iunit 0} = +\pi\iunit} | ln(- 1 + I*0)= + Pi*I |
Log[- 1 + I*0]= + Pi*I |
Successful | Successful | - | - |
| 4.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{-1-\iunit 0} = -\pi\iunit} | ln(- 1 - I*0)= - Pi*I |
Log[- 1 - I*0]= - Pi*I |
Failure | Failure | Fail 6.283185308*I <- {} |
Fail
Complex[0.0, 6.283185307179586] <- {} |
| 4.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{+\iunit} = +\tfrac{1}{2}\pi\iunit} | ln(+ I)= +(1)/(2)*Pi*I |
Log[+ I]= +Divide[1,2]*Pi*I |
Successful | Successful | - | - |
| 4.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{-\iunit} = -\tfrac{1}{2}\pi\iunit} | ln(- I)= -(1)/(2)*Pi*I |
Log[- I]= -Divide[1,2]*Pi*I |
Successful | Successful | - | - |
| 4.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+\pi\iunit} = -1} | exp(+ Pi*I)= - 1 |
Exp[+ Pi*I]= - 1 |
Successful | Successful | - | - |
| 4.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\pi\iunit} = -1} | exp(- Pi*I)= - 1 |
Exp[- Pi*I]= - 1 |
Successful | Successful | - | - |
| 4.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+\pi\iunit/2} = +\iunit} | exp(+ Pi*I/ 2)= + I |
Exp[+ Pi*I/ 2]= + I |
Successful | Successful | - | - |
| 4.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\pi\iunit/2} = -\iunit} | exp(- Pi*I/ 2)= - I |
Exp[- Pi*I/ 2]= - I |
Successful | Successful | - | - |
| 4.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{2\pi k\iunit} = 1} | exp(2*Pi*k*I)= 1 |
Exp[2*Pi*k*I]= 1 |
Successful | Failure | - | Successful |
| 4.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+\pi\iunit/3} = \frac{1}{2}+\iunit\frac{\sqrt{3}}{2}} | exp(+ Pi*I/ 3)=(1)/(2)+ I*(sqrt(3))/(2) |
Exp[+ Pi*I/ 3]=Divide[1,2]+ I*Divide[Sqrt[3],2] |
Successful | Successful | - | - |
| 4.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\pi\iunit/3} = \frac{1}{2}-\iunit\frac{\sqrt{3}}{2}} | exp(- Pi*I/ 3)=(1)/(2)- I*(sqrt(3))/(2) |
Exp[- Pi*I/ 3]=Divide[1,2]- I*Divide[Sqrt[3],2] |
Successful | Successful | - | - |
| 4.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+ 2\pi\iunit/3} = -\frac{1}{2}+\iunit\frac{\sqrt{3}}{2}} | exp(+ 2*Pi*I/ 3)= -(1)/(2)+ I*(sqrt(3))/(2) |
Exp[+ 2*Pi*I/ 3]= -Divide[1,2]+ I*Divide[Sqrt[3],2] |
Successful | Successful | - | - |
| 4.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{- 2\pi\iunit/3} = -\frac{1}{2}-\iunit\frac{\sqrt{3}}{2}} | exp(- 2*Pi*I/ 3)= -(1)/(2)- I*(sqrt(3))/(2) |
Exp[- 2*Pi*I/ 3]= -Divide[1,2]- I*Divide[Sqrt[3],2] |
Successful | Successful | - | - |
| 4.4.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+\pi\iunit/4} = \frac{1}{\sqrt{2}}+\iunit\frac{1}{\sqrt{2}}} | exp(+ Pi*I/ 4)=(1)/(sqrt(2))+ I*(1)/(sqrt(2)) |
Exp[+ Pi*I/ 4]=Divide[1,Sqrt[2]]+ I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - |
| 4.4.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\pi\iunit/4} = \frac{1}{\sqrt{2}}-\iunit\frac{1}{\sqrt{2}}} | exp(- Pi*I/ 4)=(1)/(sqrt(2))- I*(1)/(sqrt(2)) |
Exp[- Pi*I/ 4]=Divide[1,Sqrt[2]]- I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - |
| 4.4.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+ 3\pi\iunit/4} = -\frac{1}{\sqrt{2}}+\iunit\frac{1}{\sqrt{2}}} | exp(+ 3*Pi*I/ 4)= -(1)/(sqrt(2))+ I*(1)/(sqrt(2)) |
Exp[+ 3*Pi*I/ 4]= -Divide[1,Sqrt[2]]+ I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - |
| 4.4.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{- 3\pi\iunit/4} = -\frac{1}{\sqrt{2}}-\iunit\frac{1}{\sqrt{2}}} | exp(- 3*Pi*I/ 4)= -(1)/(sqrt(2))- I*(1)/(sqrt(2)) |
Exp[- 3*Pi*I/ 4]= -Divide[1,Sqrt[2]]- I*Divide[1,Sqrt[2]] |
Successful | Successful | - | - |
| 4.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit^{+\iunit} = e^{-\pi/2}} | (I)^(+ I)= exp(- Pi/ 2) |
(I)^(+ I)= Exp[- Pi/ 2] |
Successful | Successful | - | - |
| 4.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit^{-\iunit} = e^{+\pi/2}} | (I)^(- I)= exp(+ Pi/ 2) |
(I)^(- I)= Exp[+ Pi/ 2] |
Successful | Successful | - | - |
| 4.4.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to\infty}x^{-a}\ln@@{x} = 0} | limit((x)^(- a)* ln(x), x = infinity)= 0 |
Limit[(x)^(- a)* Log[x], x -> Infinity]= 0 |
Successful | Failure | - | Successful |
| 4.4.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to 0}x^{a}\ln@@{x} = 0} | limit((x)^(a)* ln(x), x = 0)= 0 |
Limit[(x)^(a)* Log[x], x -> 0]= 0 |
Failure | Failure | Skip | Successful |
| 4.4.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\left(\left(\sum^{n}_{k=1}\frac{1}{k}\right)-\ln@@{n}\right) = \EulerConstant} | limit((sum((1)/(k), k = 1..n))- ln(n), n = infinity)= gamma |
Limit[(Sum[Divide[1,k], {k, 1, n}])- Log[n], n -> Infinity]= EulerGamma |
Successful | Successful | - | - |
| 4.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x}{1+x} < \ln@{1+x}} | (x)/(1 + x)< ln(1 + x) |
Divide[x,1 + x]< Log[1 + x] |
Failure | Failure | Skip | Successful |
| 4.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{1+x} < x} | ln(1 + x)< x |
Log[1 + x]< x |
Failure | Failure | Skip | Successful |
| 4.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x < -\ln@{1-x}} | x < - ln(1 - x) |
x < - Log[1 - x] |
Failure | Failure | Skip | Successful |
| 4.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\ln@{1-x} < \frac{x}{1-x}} | - ln(1 - x)<(x)/(1 - x) |
- Log[1 - x]<Divide[x,1 - x] |
Failure | Failure | Skip | Successful |
| 4.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\ln@{1-x}| < \tfrac{3}{2}x} | abs(ln(1 - x))<(3)/(2)*x |
Abs[Log[1 - x]]<Divide[3,2]*x |
Failure | Failure | Error | Successful |
| 4.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{x} <= x-1} | ln(x)< = x - 1 |
Log[x]< = x - 1 |
Failure | Failure | Successful | Successful |
| 4.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{x} <= a(x^{1/a}-1)} | ln(x)< = a*((x)^(1/ a)- 1) |
Log[x]< = a*((x)^(1/ a)- 1) |
Failure | Failure | Successful | Successful |
| 4.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\ln@{1+z}| <= -\ln@{1-|z|}} | abs(ln(1 + z))< = - ln(1 -abs(z)) |
Abs[Log[1 + z]]< = - Log[1 -Abs[z]] |
Failure | Failure | Successful | Successful |
| 4.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\ln@@{z} = \frac{1}{z}} | diff(ln(z), z)=(1)/(z) |
D[Log[z], z]=Divide[1,z] |
Successful | Successful | - | - |
| 4.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\Ln@@{z} = \frac{1}{z}} | diff(ln(z), z)=(1)/(z) |
D[Log[z], z]=Divide[1,z] |
Successful | Successful | - | - |
| 4.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}} | diff(ln(z), [z$(n)])=(- 1)^(n - 1)*factorial(n - 1)*(z)^(- n) |
D[Log[z], {z, n}]=(- 1)^(n - 1)*(n - 1)!*(z)^(- n) |
Failure | Failure | Successful | Successful |
| 4.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\Ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}} | diff(ln(z), [z$(n)])=(- 1)^(n - 1)*factorial(n - 1)*(z)^(- n) |
D[Log[z], {z, n}]=(- 1)^(n - 1)*(n - 1)!*(z)^(- n) |
Failure | Failure | Successful | Successful |
| 4.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}e^{z} = e^{z}} | diff(exp(z), z)= exp(z) |
D[Exp[z], z]= Exp[z] |
Successful | Successful | - | - |
| 4.7.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}e^{az} = ae^{az}} | diff(exp(a*z), z)= a*exp(a*z) |
D[Exp[a*z], z]= a*Exp[a*z] |
Successful | Successful | - | - |
| 4.7.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}a^{z} = a^{z}\ln@@{a}} | diff((a)^(z), z)= (a)^(z)* ln(a) |
D[(a)^(z), z]= (a)^(z)* Log[a] |
Successful | Failure | - | Successful |
| 4.7.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}z^{a} = az^{a-1}} | diff((z)^(a), z)= a*(z)^(a - 1) |
D[(z)^(a), z]= a*(z)^(a - 1) |
Successful | Successful | - | - |
| 4.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = aw} | diff(w, [z$(2)])= a*w |
D[w, {z, 2}]= a*w |
Failure | Failure | Skip | Successful |
| 4.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@{z_{1}z_{2}} = \Ln@@{z_{1}}+\Ln@@{z_{2}}} | ln(z[1]*z[2])= ln(z[1])+ ln(z[2]) |
Log[Subscript[z, 1]*Subscript[z, 2]]= Log[Subscript[z, 1]]+ Log[Subscript[z, 2]] |
Failure | Failure | Fail .4e-9+6.283185307*I <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}.4e-9+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2)}0.+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}0.-6.283185307*I <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{z_{1}z_{2}} = \ln@@{z_{1}}+\ln@@{z_{2}}} | ln(z[1]*z[2])= ln(z[1])+ ln(z[2]) |
Log[Subscript[z, 1]*Subscript[z, 2]]= Log[Subscript[z, 1]]+ Log[Subscript[z, 2]] |
Failure | Failure | Skip | Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 4.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@@{\frac{z_{1}}{z_{2}}} = \Ln@@{z_{1}}-\Ln@@{z_{2}}} | ln((z[1])/(z[2]))= ln(z[1])- ln(z[2]) |
Log[Divide[Subscript[z, 1],Subscript[z, 2]]]= Log[Subscript[z, 1]]- Log[Subscript[z, 2]] |
Failure | Failure | Fail 0.+6.283185307*I <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}0.+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2)}0.+6.283185307*I <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}0.-6.283185307*I <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)} |
Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} |
| 4.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\frac{z_{1}}{z_{2}}} = \ln@@{z_{1}}-\ln@@{z_{2}}} | ln((z[1])/(z[2]))= ln(z[1])- ln(z[2]) |
Log[Divide[Subscript[z, 1],Subscript[z, 2]]]= Log[Subscript[z, 1]]- Log[Subscript[z, 2]] |
Failure | Failure | Skip | Fail
Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.283185307179586] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} |
| 4.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@{z^{n}} = n\Ln@@{z}} | ln((z)^(n))= n*ln(z) |
Log[(z)^(n)]= n*Log[z] |
Failure | Failure | Fail 0.+6.283185307*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}0.-6.283185307*I <- {z = -2^(1/2)+I*2^(1/2), n = 3} |
Fail
Complex[0.0, 6.283185307179586] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -6.283185307179586] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{z^{n}} = n\ln@@{z}} | ln((z)^(n))= n*ln(z) |
Log[(z)^(n)]= n*Log[z] |
Failure | Failure | Skip | Successful |
| 4.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\frac{1}{z}} = -\ln@@{z}} | ln((1)/(z))= - ln(z) |
Log[Divide[1,z]]= - Log[z] |
Failure | Failure | Skip | Successful |
| 4.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@{\exp@@{z}} = z+2k\pi\iunit} | ln(exp(z))= z + 2*k*Pi*I |
Log[Exp[z]]= z + 2*k*Pi*I |
Failure | Failure | Fail 0.-18.84955592*I <- {z = 2^(1/2)+I*2^(1/2), k = 3}0.-18.84955592*I <- {z = 2^(1/2)-I*2^(1/2), k = 3}0.-18.84955592*I <- {z = -2^(1/2)-I*2^(1/2), k = 3}0.-18.84955592*I <- {z = -2^(1/2)+I*2^(1/2), k = 3} |
Fail
Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -18.84955592153876] <- {Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{\exp@@{z}} = z} | ln(exp(z))= z |
Log[Exp[z]]= z |
Failure | Failure | Skip | Successful |
| 4.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@{\ln@@{z}} = \exp@{\Ln@@{z}}} | exp(ln(z))= exp(ln(z)) |
Exp[Log[z]]= Exp[Log[z]] |
Successful | Successful | - | - |
| 4.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@{\Ln@@{z}} = z} | exp(ln(z))= z |
Exp[Log[z]]= z |
Successful | Successful | - | - |
| 4.8.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Ln@{a^{z}} = z\Ln@@{a}+2k\pi\iunit} | ln((a)^(z))= z*ln(a)+ 2*k*Pi*I |
Log[(a)^(z)]= z*Log[a]+ 2*k*Pi*I |
Failure | Failure | Fail 0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 3}0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), k = 3}0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), k = 3}... skip entries to safe data |
Fail
Complex[1.1102230246251565*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.3877787807814457*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.440892098500626*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.8.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{a^{z}} = z\ln@@{a}+2k\pi\iunit} | ln((a)^(z))= z*ln(a)+ 2*k*Pi*I |
Log[(a)^(z)]= z*Log[a]+ 2*k*Pi*I |
Failure | Failure | Fail 0.-6.283185308*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}0.-12.56637062*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}0.-18.84955592*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}0.-6.283185308*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[1.1102230246251565*^-16, -6.283185307179586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1102230246251565*^-16, -12.566370614359172] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1102230246251565*^-16, -18.84955592153876] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -6.283185307179586] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{a^{x}} = x\ln@@{a}} | ln((a)^(x))= x*ln(a) |
Log[(a)^(x)]= x*Log[a] |
Failure | Failure | Successful | Successful |
| 4.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{z}}{z} = \ln@@{z}} | int((1)/(z), z)= ln(z) |
Integrate[Divide[1,z], z]= Log[z] |
Successful | Successful | - | - |
| 4.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\ln@@{z}\diff{z} = z\ln@@{z}-z} | int(ln(z), z)= z*ln(z)- z |
Integrate[Log[z], z]= z*Log[z]- z |
Successful | Successful | - | - |
| 4.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int z^{n}\ln@@{z}\diff{z} = \frac{z^{n+1}}{n+1}\ln@@{z}-\frac{z^{n+1}}{(n+1)^{2}}} | int((z)^(n)* ln(z), z)=((z)^(n + 1))/(n + 1)*ln(z)-((z)^(n + 1))/((n + 1)^(2)) |
Integrate[(z)^(n)* Log[z], z]=Divide[(z)^(n + 1),n + 1]*Log[z]-Divide[(z)^(n + 1),(n + 1)^(2)] |
Successful | Successful | - | - |
| 4.10.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{z}}{z\ln@@{z}} = \ln@{\ln@@{z}}} | int((1)/(z*ln(z)), z)= ln(ln(z)) |
Integrate[Divide[1,z*Log[z]], z]= Log[Log[z]] |
Successful | Successful | - | - |
| 4.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{\ln@@{t}}{1-t}\diff{t} = -\frac{\pi^{2}}{6}} | int((ln(t))/(1 - t), t = 0..1)= -((Pi)^(2))/(6) |
Integrate[Divide[Log[t],1 - t], {t, 0, 1}]= -Divide[(Pi)^(2),6] |
Successful | Successful | - | - |
| 4.10.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{\ln@@{t}}{1+t}\diff{t} = -\frac{\pi^{2}}{12}} | int((ln(t))/(1 + t), t = 0..1)= -((Pi)^(2))/(12) |
Integrate[Divide[Log[t],1 + t], {t, 0, 1}]= -Divide[(Pi)^(2),12] |
Successful | Successful | - | - |
| 4.10.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int e^{az}\diff{z} = \frac{e^{az}}{a}} | int(exp(a*z), z)=(exp(a*z))/(a) |
Integrate[Exp[a*z], z]=Divide[Exp[a*z],a] |
Successful | Successful | - | - |
| 4.10.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{z}}{e^{az}+b} = \frac{1}{ab}(az-\ln@{e^{az}+b})} | int((1)/(exp(a*z)+ b), z)=(1)/(a*b)*(a*z - ln(exp(a*z)+ b)) |
Integrate[Divide[1,Exp[a*z]+ b], z]=Divide[1,a*b]*(a*z - Log[Exp[a*z]+ b]) |
Failure | Successful | Skip | - |
| 4.10.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{e^{az}-1}{e^{az}+1}\diff{z} = \frac{2}{a}\ln@{e^{az/2}+e^{-az/2}}} | int((exp(a*z)- 1)/(exp(a*z)+ 1), z)=(2)/(a)*ln(exp(a*z/ 2)+ exp(- a*z/ 2)) |
Integrate[Divide[Exp[a*z]- 1,Exp[a*z]+ 1], z]=Divide[2,a]*Log[Exp[a*z/ 2]+ Exp[- a*z/ 2]] |
Failure | Failure | Skip | Fail
Complex[-4.442882938158366, -4.442882938158366] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.442882938158366, -4.442882938158366] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.442882938158366, 4.442882938158366] <- {Rule[a, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.442882938158366, 4.442882938158366] <- {Rule[a, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 4.10.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}e^{-cx^{2}}\diff{x} = \sqrt{\frac{\pi}{c}}} | int(exp(- c*(x)^(2)), x = - infinity..infinity)=sqrt((Pi)/(c)) |
Integrate[Exp[- c*(x)^(2)], {x, - Infinity, Infinity}]=Sqrt[Divide[Pi,c]] |
Successful | Failure | - | Skip |
| 4.10.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\ln@@{2}}\frac{xe^{x}}{e^{x}-1}\diff{x} = \frac{\pi^{2}}{12}} | int((x*exp(x))/(exp(x)- 1), x = 0..ln(2))=((Pi)^(2))/(12) |
Integrate[Divide[x*Exp[x],Exp[x]- 1], {x, 0, Log[2]}]=Divide[(Pi)^(2),12] |
Successful | Successful | - | - |
| 4.10.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\diff{x}}{e^{x}+1} = \ln@@{2}} | int((1)/(exp(x)+ 1), x = 0..infinity)= ln(2) |
Integrate[Divide[1,Exp[x]+ 1], {x, 0, Infinity}]= Log[2] |
Successful | Successful | - | - |
| 4.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = \ln@{x+1}} | phi*(x)= ln(x + 1) |
\[Phi]*(x)= Log[x + 1] |
Failure | Failure | Skip | Successful |
| 4.12.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi(x) = \ell+\ln^{(\ell)}@@{x}} | psi*(x)= ell + subs( temp=x, diff( ln(temp), temp$(ell) ) ) |
\[Psi]*(x)= \[ScriptL]+ (D[Log[temp], {temp, \[ScriptL]}]/.temp-> x) |
Failure | Failure | Fail .454653676+2.121320343*I <- {psi = 2^(1/2)+I*2^(1/2), ell = 1, x = 3/2}.565764787+2.121320343*I <- {psi = 2^(1/2)+I*2^(1/2), ell = 2, x = 3/2}-1.471272250+2.121320343*I <- {psi = 2^(1/2)+I*2^(1/2), ell = 3, x = 3/2}.454653676-2.121320343*I <- {psi = 2^(1/2)-I*2^(1/2), ell = 1, x = 3/2}... skip entries to safe data |
Fail
Complex[0.45465367689297564, 2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 1], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.5657647880040868, 2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 2], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4712722490329502, 2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 3], Rule[ψ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.45465367689297564, -2.1213203435596424] <- {Rule[x, Rational[3, 2]], Rule[ℓ, 1], Rule[ψ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle We^{W} = x} | W*exp(W)= x |
W*Exp[W]= x |
Failure | Failure | Fail -5.838722068+6.652975529*I <- {W = 2^(1/2)+I*2^(1/2), x = 1}-6.838722068+6.652975529*I <- {W = 2^(1/2)+I*2^(1/2), x = 2}-7.838722068+6.652975529*I <- {W = 2^(1/2)+I*2^(1/2), x = 3}-5.838722068-6.652975529*I <- {W = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[-5.838722072781763, 6.652975531039188] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[-6.838722072781763, 6.652975531039188] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-7.838722072781763, 6.652975531039188] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-5.838722072781763, -6.652975531039188] <- {Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 4.13#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LambertWp@{-1/e} = \LambertWm@{-1/e}} | LambertW(0, - 1/ exp(1))= LambertW(-1, - 1/ exp(1)) |
ProductLog[0, - 1/ E]= ProductLog[-1, - 1/ E] |
Successful | Successful | - | - |
| 4.13#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LambertWm@{-1/e} = -1} | LambertW(-1, - 1/ exp(1))= - 1 |
ProductLog[-1, - 1/ E]= - 1 |
Successful | Successful | - | - |
| 4.13#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LambertWp@{0} = 0} | LambertW(0, 0)= 0 |
ProductLog[0, 0]= 0 |
Successful | Successful | - | - |
| 4.13#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LambertWp@{e} = 1} | LambertW(0, exp(1))= 1 |
ProductLog[0, E]= 1 |
Successful | Successful | - | - |
| 4.13#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U+\ln@@{U} = x} | U + ln(U)= x |
U + Log[U]= x |
Failure | Failure | Fail 1.107360742+2.199611725*I <- {U = 2^(1/2)+I*2^(1/2), x = 1}.107360742+2.199611725*I <- {U = 2^(1/2)+I*2^(1/2), x = 2}-.892639258+2.199611725*I <- {U = 2^(1/2)+I*2^(1/2), x = 3}1.107360742-2.199611725*I <- {U = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[1.1073607429330403, 2.199611725770543] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.10736074293304043, 2.199611725770543] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-0.8926392570669596, 2.199611725770543] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[1.1073607429330403, -2.199611725770543] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 4.13#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U = U(x)} | U = U*(x) |
U = U*(x) |
Failure | Failure | Fail -1.414213562-1.414213562*I <- {U = 2^(1/2)+I*2^(1/2), x = 2}-2.828427124-2.828427124*I <- {U = 2^(1/2)+I*2^(1/2), x = 3}-1.414213562+1.414213562*I <- {U = 2^(1/2)-I*2^(1/2), x = 2}-2.828427124+2.828427124*I <- {U = 2^(1/2)-I*2^(1/2), x = 3}... skip entries to safe data |
Fail
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}... skip entries to safe data |
| 4.13#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U(x) = \LambertW@{e^{x}}} | U*(x)= LambertW(exp(x)) |
U*(x)= ProductLog[Exp[x]] |
Failure | Failure | Fail .414213562+1.414213562*I <- {U = 2^(1/2)+I*2^(1/2), x = 1}1.271281525+2.828427124*I <- {U = 2^(1/2)+I*2^(1/2), x = 2}2.034700655+4.242640686*I <- {U = 2^(1/2)+I*2^(1/2), x = 3}.414213562-1.414213562*I <- {U = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[1.2712815257485788, 2.8284271247461903] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[2.0347006555499627, 4.242640687119286] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}... skip entries to safe data |
| 4.13.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\LambertW}{x} = \frac{e^{-\LambertW}}{1+\LambertW}} | diff(LambertW(x), =)*(exp(- LambertW($0)))/(1 + LambertW($0)) |
D[ProductLog[x], =]*Divide[Exp[- ProductLog[$0]],1 + ProductLog[$0]] |
Error | Error | - | - |
| 4.13.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LambertWp@{x} = \sum_{n=1}^{\infty}(-1)^{n-1}\frac{n^{n-2}}{(n-1)!}x^{n}} | LambertW(0, x)= sum((- 1)^(n - 1)*((n)^(n - 2))/(factorial(n - 1))*(x)^(n), n = 1..infinity) |
ProductLog[0, x]= Sum[(- 1)^(n - 1)*Divide[(n)^(n - 2),(n - 1)!]*(x)^(n), {n, 1, Infinity}] |
Failure | Successful | Skip | - |
| 4.13.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LambertW@{-e^{-1-(t^{2}/2)}} = \sum_{n=0}^{\infty}(-1)^{n-1}c_{n}t^{n}} | LambertW(- exp(- 1 -((t)^(2)/ 2)))= sum((- 1)^(n - 1)* c[n]*(t)^(n), n = 0..infinity) |
ProductLog[- Exp[- 1 -((t)^(2)/ 2)]]= Sum[(- 1)^(n - 1)* Subscript[c, n]*(t)^(n), {n, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 4.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}} | sin(z)=(exp(I*z)- exp(- I*z))/(2*I) |
Sin[z]=Divide[Exp[I*z]- Exp[- I*z],2*I] |
Successful | Successful | - | - |
| 4.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}} | cos(z)=(exp(I*z)+ exp(- I*z))/(2) |
Cos[z]=Divide[Exp[I*z]+ Exp[- I*z],2] |
Successful | Successful | - | - |
| 4.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z}+ i\sin@@{z} = e^{+ iz}} | cos(z)+ I*sin(z)= exp(+ I*z) |
Cos[z]+ I*Sin[z]= Exp[+ I*z] |
Successful | Successful | - | - |
| 4.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z}- i\sin@@{z} = e^{- iz}} | cos(z)- I*sin(z)= exp(- I*z) |
Cos[z]- I*Sin[z]= Exp[- I*z] |
Successful | Successful | - | - |
| 4.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}} | tan(z)=(sin(z))/(cos(z)) |
Tan[z]=Divide[Sin[z],Cos[z]] |
Successful | Successful | - | - |
| 4.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@@{z} = \frac{1}{\sin@@{z}}} | csc(z)=(1)/(sin(z)) |
Csc[z]=Divide[1,Sin[z]] |
Successful | Successful | - | - |
| 4.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@@{z} = \frac{1}{\cos@@{z}}} | sec(z)=(1)/(cos(z)) |
Sec[z]=Divide[1,Cos[z]] |
Successful | Successful | - | - |
| 4.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}} | cot(z)=(cos(z))/(sin(z)) |
Cot[z]=Divide[Cos[z],Sin[z]] |
Successful | Successful | - | - |
| 4.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}} | (cos(z))/(sin(z))=(1)/(tan(z)) |
Divide[Cos[z],Sin[z]]=Divide[1,Tan[z]] |
Successful | Successful | - | - |
| 4.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z+2k\pi} = \sin@@{z}} | sin(z + 2*k*Pi)= sin(z) |
Sin[z + 2*k*Pi]= Sin[z] |
Failure | Failure | Successful | Successful |
| 4.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z+2k\pi} = \cos@@{z}} | cos(z + 2*k*Pi)= cos(z) |
Cos[z + 2*k*Pi]= Cos[z] |
Failure | Failure | Successful | Successful |
| 4.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{z+k\pi} = \tan@@{z}} | tan(z + k*Pi)= tan(z) |
Tan[z + k*Pi]= Tan[z] |
Failure | Failure | Successful | Successful |
| 4.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{x+iy} = \sin@{x+\tfrac{1}{2}\pi+iy}} | cos(x + I*y)= sin(x +(1)/(2)*Pi + I*y) |
Cos[x + I*y]= Sin[x +Divide[1,2]*Pi + I*y] |
Successful | Successful | - | - |
| 4.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@{x+iy} = -\tan@{x+\tfrac{1}{2}\pi+iy}} | cot(x + I*y)= - tan(x +(1)/(2)*Pi + I*y) |
Cot[x + I*y]= - Tan[x +Divide[1,2]*Pi + I*y] |
Successful | Successful | - | - |
| 4.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{x+iy} = \csc@{x+\tfrac{1}{2}\pi+iy}} | sec(x + I*y)= csc(x +(1)/(2)*Pi + I*y) |
Sec[x + I*y]= Csc[x +Divide[1,2]*Pi + I*y] |
Successful | Successful | - | - |
| 4.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 0}\frac{\sin@@{z}}{z} = 1} | limit((sin(z))/(z), z = 0)= 1 |
Limit[Divide[Sin[z],z], z -> 0]= 1 |
Successful | Successful | - | - |
| 4.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 0}\frac{\tan@@{z}}{z} = 1} | limit((tan(z))/(z), z = 0)= 1 |
Limit[Divide[Tan[z],z], z -> 0]= 1 |
Successful | Successful | - | - |
| 4.17.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 0}\frac{1-\cos@@{z}}{z^{2}} = \frac{1}{2}} | limit((1 - cos(z))/((z)^(2)), z = 0)=(1)/(2) |
Limit[Divide[1 - Cos[z],(z)^(2)], z -> 0]=Divide[1,2] |
Successful | Successful | - | - |
| 4.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2x}{\pi} <= \sin@@{x}} | (2*x)/(Pi)< = sin(x) |
Divide[2*x,Pi]< = Sin[x] |
Failure | Failure | Skip | Successful |
| 4.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{x} <= x} | sin(x)< = x |
Sin[x]< = x |
Failure | Failure | Skip | Successful |
| 4.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x <= \tan@@{x}} | x < = tan(x) |
x < = Tan[x] |
Failure | Failure | Skip | Successful |
| 4.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{x} <= \frac{\sin@@{x}}{x}} | cos(x)< =(sin(x))/(x) |
Cos[x]< =Divide[Sin[x],x] |
Failure | Failure | Skip | Successful |
| 4.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{x}}{x} <= 1} | (sin(x))/(x)< = 1 |
Divide[Sin[x],x]< = 1 |
Failure | Failure | Skip | Successful |
| 4.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi < \frac{\sin@{\pi x}}{x(1-x)}} | Pi <(sin(Pi*x))/(x*(1 - x)) |
Pi <Divide[Sin[Pi*x],x*(1 - x)] |
Failure | Failure | Successful | Successful |
| 4.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@{\pi x}}{x(1-x)} <= 4} | (sin(Pi*x))/(x*(1 - x))< = 4 |
Divide[Sin[Pi*x],x*(1 - x)]< = 4 |
Failure | Failure | Successful | Successful |
| 4.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sinh@@{y}| <= |\sin@@{z}|\leq\cosh@@{y}} | abs(sinh(y))< =abs(sin(z))<= cosh(y) |
Abs[Sinh[y]]< =Abs[Sin[z]]<= Cosh[y] |
Failure | Failure | Error | Successful |
| 4.18.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sinh@@{y}| <= |\cos@@{z}|\leq\cosh@@{y}} | abs(sinh(y))< =abs(cos(z))<= cosh(y) |
Abs[Sinh[y]]< =Abs[Cos[z]]<= Cosh[y] |
Failure | Failure | Error | Successful |
| 4.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\csc@@{z}| <= \csch@@{|y|}} | abs(csc(z))< = csch(abs(y)) |
Abs[Csc[z]]< = Csch[Abs[y]] |
Failure | Failure | Fail .4602792559 <= .2757205648 <- {z = 2^(1/2)+I*2^(1/2), y = 2}.4602792559 <= .9982156967e-1 <- {z = 2^(1/2)+I*2^(1/2), y = 3}.4602792559 <= .2757205648 <- {z = 2^(1/2)-I*2^(1/2), y = 2}.4602792559 <= .9982156967e-1 <- {z = 2^(1/2)-I*2^(1/2), y = 3}... skip entries to safe data |
Successful |
| 4.18.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cos@@{z}| <= \cosh@@{|z|}} | abs(cos(z))< = cosh(abs(z)) |
Abs[Cos[z]]< = Cosh[Abs[z]] |
Failure | Failure | Successful | Successful |
| 4.18.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sin@@{z}| <= \sinh@@{|z|}} | abs(sin(z))< = sinh(abs(z)) |
Abs[Sin[z]]< = Sinh[Abs[z]] |
Failure | Failure | Successful | Successful |
| 4.18#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cos@@{z}| < 2} | abs(cos(z))< 2 |
Abs[Cos[z]]< 2 |
Failure | Failure | Successful | Successful |
| 4.18#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sin@@{z}| <= \tfrac{6}{5}|z|} | abs(sin(z))< =(6)/(5)*abs(z) |
Abs[Sin[z]]< =Divide[6,5]*Abs[z] |
Failure | Failure | Successful | Successful |
| 4.19.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{\frac{\sin@@{z}}{z}} = \sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}\BernoullinumberB{2n}}{n(2n)!}z^{2n}} | ln((sin(z))/(z))= sum(((- 1)^(n)* (2)^(2*n - 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity) |
Log[Divide[Sin[z],z]]= Sum[Divide[(- 1)^(n)* (2)^(2*n - 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}] |
Failure | Failure | Skip | Successful |
| 4.19.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{\cos@@{z}} = \sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}(2^{2n}-1)\BernoullinumberB{2n}}{n(2n)!}z^{2n}} | ln(cos(z))= sum(((- 1)^(n)* (2)^(2*n - 1)*((2)^(2*n)- 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity) |
Log[Cos[z]]= Sum[Divide[(- 1)^(n)* (2)^(2*n - 1)*((2)^(2*n)- 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}] |
Failure | Failure | Skip | Successful |
| 4.19.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{\frac{\tan@@{z}}{z}} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}2^{2n}(2^{2n-1}-1)\BernoullinumberB{2n}}{n(2n)!}z^{2n}} | ln((tan(z))/(z))= sum(((- 1)^(n - 1)* (2)^(2*n)*((2)^(2*n - 1)- 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity) |
Log[Divide[Tan[z],z]]= Sum[Divide[(- 1)^(n - 1)* (2)^(2*n)*((2)^(2*n - 1)- 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}] |
Failure | Failure | Skip | Successful |
| 4.20.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\sin@@{z} = \cos@@{z}} | diff(sin(z), z)= cos(z) |
D[Sin[z], z]= Cos[z] |
Successful | Successful | - | - |
| 4.20.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\cos@@{z} = -\sin@@{z}} | diff(cos(z), z)= - sin(z) |
D[Cos[z], z]= - Sin[z] |
Successful | Successful | - | - |
| 4.20.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\tan@@{z} = \sec^{2}@@{z}} | diff(tan(z), z)= (sec(z))^(2) |
D[Tan[z], z]= (Sec[z])^(2) |
Successful | Successful | - | - |
| 4.20.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\csc@@{z} = -\csc@@{z}\cot@@{z}} | diff(csc(z), z)= - csc(z)*cot(z) |
D[Csc[z], z]= - Csc[z]*Cot[z] |
Successful | Successful | - | - |
| 4.20.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\sec@@{z} = \sec@@{z}\tan@@{z}} | diff(sec(z), z)= sec(z)*tan(z) |
D[Sec[z], z]= Sec[z]*Tan[z] |
Successful | Successful | - | - |
| 4.20.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\cot@@{z} = -\csc^{2}@@{z}} | diff(cot(z), z)= - (csc(z))^(2) |
D[Cot[z], z]= - (Csc[z])^(2) |
Successful | Successful | - | - |
| 4.20.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\sin@@{z} = \sin@{z+\tfrac{1}{2}n\pi}} | diff(sin(z), [z$(n)])= sin(z +(1)/(2)*n*Pi) |
D[Sin[z], {z, n}]= Sin[z +Divide[1,2]*n*Pi] |
Successful | Successful | - | - |
| 4.20.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\cos@@{z} = \cos@{z+\tfrac{1}{2}n\pi}} | diff(cos(z), [z$(n)])= cos(z +(1)/(2)*n*Pi) |
D[Cos[z], {z, n}]= Cos[z +Divide[1,2]*n*Pi] |
Successful | Successful | - | - |
| 4.20.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+a^{2}w = 0} | diff(w, [z$(2)])+ (a)^(2)* w = 0 |
D[w, {z, 2}]+ (a)^(2)* w = 0 |
Failure | Failure | Fail -5.656854245+5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.20.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{w}{z}\right)^{2}+a^{2}w^{2} = 1} | (diff(w, z))^(2)+ (a)^(2)* (w)^(2)= 1 |
(D[w, z])^(2)+ (a)^(2)* (w)^(2)= 1 |
Failure | Failure | Fail -16.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}14.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}-16.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}14.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.20.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{w}{z}-a^{2}w^{2} = 1} | diff(w, z)- (a)^(2)* (w)^(2)= 1 |
D[w, z]- (a)^(2)* (w)^(2)= 1 |
Failure | Failure | Fail 14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}-16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.20.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = A\cos@{az}+B\sin@{az}} | w = A*cos(a*z)+ B*sin(a*z) |
w = A*Cos[a*z]+ B*Sin[a*z] |
Failure | Failure | Skip | Skip |
| 4.20.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = (1/a)\sin@{az+c}} | w =(1/ a)* sin(a*z + c) |
w =(1/ a)* Sin[a*z + c] |
Failure | Failure | Fail -43.99146068+34.43827298*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.560620374+.384416402*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-.552876601+4.108989171*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}2.401710418+1.589052846*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-43.991460739515965, 34.43827305491785] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.5606203716754656, 0.38441640190707305] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5528766038746884, 4.1089891749071095] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.4017104180648507, 1.5890528479992119] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.20.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = (1/a)\tan@{az+c}} | w =(1/ a)* tan(a*z + c) |
w =(1/ a)* Tan[a*z + c] |
Failure | Failure | Fail 1.060642513+1.060651152*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.097992560+1.014214371*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.770353735+1.772853405*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.045061232+1.116024928*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.0606425136739976, 1.0606511525471942] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0979925605963208, 1.0142143722877455] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7703537351803704, 1.7728534052480869] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0450612330665354, 1.11602492841073] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{u}+\cos@@{u} = \sqrt{2}\sin@{u+\tfrac{1}{4}\pi}} | sin(u)+ cos(u)=sqrt(2)*sin(u +(1)/(4)*Pi) |
Sin[u]+ Cos[u]=Sqrt[2]*Sin[u +Divide[1,4]*Pi] |
Successful | Successful | - | - |
| 4.21.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{u}-\cos@@{u} = \sqrt{2}\sin@{u-\tfrac{1}{4}\pi}} | sin(u)- cos(u)=sqrt(2)*sin(u -(1)/(4)*Pi) |
Sin[u]- Cos[u]=Sqrt[2]*Sin[u -Divide[1,4]*Pi] |
Successful | Successful | - | - |
| 4.21.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\sin@{u+\tfrac{1}{4}\pi} = +\sqrt{2}\cos@{u-\tfrac{1}{4}\pi}} | sqrt(2)*sin(u +(1)/(4)*Pi)= +sqrt(2)*cos(u -(1)/(4)*Pi) |
Sqrt[2]*Sin[u +Divide[1,4]*Pi]= +Sqrt[2]*Cos[u -Divide[1,4]*Pi] |
Successful | Successful | - | - |
| 4.21.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\sin@{u-\tfrac{1}{4}\pi} = -\sqrt{2}\cos@{u+\tfrac{1}{4}\pi}} | sqrt(2)*sin(u -(1)/(4)*Pi)= -sqrt(2)*cos(u +(1)/(4)*Pi) |
Sqrt[2]*Sin[u -Divide[1,4]*Pi]= -Sqrt[2]*Cos[u +Divide[1,4]*Pi] |
Successful | Successful | - | - |
| 4.21.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{u+ v} = \sin@@{u}\cos@@{v}+\cos@@{u}\sin@@{v}} | sin(u + v)= sin(u)*cos(v)+ cos(u)*sin(v) |
Sin[u + v]= Sin[u]*Cos[v]+ Cos[u]*Sin[v] |
Successful | Successful | - | - |
| 4.21.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{u- v} = \sin@@{u}\cos@@{v}-\cos@@{u}\sin@@{v}} | sin(u - v)= sin(u)*cos(v)- cos(u)*sin(v) |
Sin[u - v]= Sin[u]*Cos[v]- Cos[u]*Sin[v] |
Successful | Successful | - | - |
| 4.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{u+ v} = \cos@@{u}\cos@@{v}-\sin@@{u}\sin@@{v}} | cos(u + v)= cos(u)*cos(v)- sin(u)*sin(v) |
Cos[u + v]= Cos[u]*Cos[v]- Sin[u]*Sin[v] |
Successful | Successful | - | - |
| 4.21.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{u- v} = \cos@@{u}\cos@@{v}+\sin@@{u}\sin@@{v}} | cos(u - v)= cos(u)*cos(v)+ sin(u)*sin(v) |
Cos[u - v]= Cos[u]*Cos[v]+ Sin[u]*Sin[v] |
Successful | Successful | - | - |
| 4.21.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{u+ v} = \frac{\tan@@{u}+\tan@@{v}}{1-\tan@@{u}\tan@@{v}}} | tan(u + v)=(tan(u)+ tan(v))/(1 - tan(u)*tan(v)) |
Tan[u + v]=Divide[Tan[u]+ Tan[v],1 - Tan[u]*Tan[v]] |
Successful | Successful | - | - |
| 4.21.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{u- v} = \frac{\tan@@{u}-\tan@@{v}}{1+\tan@@{u}\tan@@{v}}} | tan(u - v)=(tan(u)- tan(v))/(1 + tan(u)*tan(v)) |
Tan[u - v]=Divide[Tan[u]- Tan[v],1 + Tan[u]*Tan[v]] |
Successful | Successful | - | - |
| 4.21.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@{u+ v} = \frac{+\cot@@{u}\cot@@{v}-1}{\cot@@{u}+\cot@@{v}}} | cot(u + v)=(+ cot(u)*cot(v)- 1)/(cot(u)+ cot(v)) |
Cot[u + v]=Divide[+ Cot[u]*Cot[v]- 1,Cot[u]+ Cot[v]] |
Successful | Successful | - | - |
| 4.21.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@{u- v} = \frac{-\cot@@{u}\cot@@{v}-1}{\cot@@{u}-\cot@@{v}}} | cot(u - v)=(- cot(u)*cot(v)- 1)/(cot(u)- cot(v)) |
Cot[u - v]=Divide[- Cot[u]*Cot[v]- 1,Cot[u]- Cot[v]] |
Successful | Successful | - | - |
| 4.21.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{u}+\sin@@{v} = 2\sin@{\frac{u+v}{2}}\cos@{\frac{u-v}{2}}} | sin(u)+ sin(v)= 2*sin((u + v)/(2))*cos((u - v)/(2)) |
Sin[u]+ Sin[v]= 2*Sin[Divide[u + v,2]]*Cos[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.21.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{u}-\sin@@{v} = 2\cos@{\frac{u+v}{2}}\sin@{\frac{u-v}{2}}} | sin(u)- sin(v)= 2*cos((u + v)/(2))*sin((u - v)/(2)) |
Sin[u]- Sin[v]= 2*Cos[Divide[u + v,2]]*Sin[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.21.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{u}+\cos@@{v} = 2\cos@{\frac{u+v}{2}}\cos@{\frac{u-v}{2}}} | cos(u)+ cos(v)= 2*cos((u + v)/(2))*cos((u - v)/(2)) |
Cos[u]+ Cos[v]= 2*Cos[Divide[u + v,2]]*Cos[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.21.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{u}-\cos@@{v} = -2\sin@{\frac{u+v}{2}}\sin@{\frac{u-v}{2}}} | cos(u)- cos(v)= - 2*sin((u + v)/(2))*sin((u - v)/(2)) |
Cos[u]- Cos[v]= - 2*Sin[Divide[u + v,2]]*Sin[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.21.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{u}+\tan@@{v} = \frac{\sin@{u+ v}}{\cos@@{u}\cos@@{v}}} | tan(u)+ tan(v)=(sin(u + v))/(cos(u)*cos(v)) |
Tan[u]+ Tan[v]=Divide[Sin[u + v],Cos[u]*Cos[v]] |
Successful | Successful | - | - |
| 4.21.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{u}-\tan@@{v} = \frac{\sin@{u- v}}{\cos@@{u}\cos@@{v}}} | tan(u)- tan(v)=(sin(u - v))/(cos(u)*cos(v)) |
Tan[u]- Tan[v]=Divide[Sin[u - v],Cos[u]*Cos[v]] |
Successful | Successful | - | - |
| 4.21.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{u}+\cot@@{v} = \frac{\sin@{v+ u}}{\sin@@{u}\sin@@{v}}} | cot(u)+ cot(v)=(sin(v + u))/(sin(u)*sin(v)) |
Cot[u]+ Cot[v]=Divide[Sin[v + u],Sin[u]*Sin[v]] |
Successful | Successful | - | - |
| 4.21.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{u}-\cot@@{v} = \frac{\sin@{v- u}}{\sin@@{u}\sin@@{v}}} | cot(u)- cot(v)=(sin(v - u))/(sin(u)*sin(v)) |
Cot[u]- Cot[v]=Divide[Sin[v - u],Sin[u]*Sin[v]] |
Successful | Successful | - | - |
| 4.21.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{z}+\cos^{2}@@{z} = 1} | (sin(z))^(2)+ (cos(z))^(2)= 1 |
(Sin[z])^(2)+ (Cos[z])^(2)= 1 |
Successful | Successful | - | - |
| 4.21.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec^{2}@@{z} = 1+\tan^{2}@@{z}} | (sec(z))^(2)= 1 + (tan(z))^(2) |
(Sec[z])^(2)= 1 + (Tan[z])^(2) |
Successful | Successful | - | - |
| 4.21.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc^{2}@@{z} = 1+\cot^{2}@@{z}} | (csc(z))^(2)= 1 + (cot(z))^(2) |
(Csc[z])^(2)= 1 + (Cot[z])^(2) |
Successful | Successful | - | - |
| 4.21.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sin@@{u}\sin@@{v} = \cos@{u-v}-\cos@{u+v}} | 2*sin(u)*sin(v)= cos(u - v)- cos(u + v) |
2*Sin[u]*Sin[v]= Cos[u - v]- Cos[u + v] |
Successful | Successful | - | - |
| 4.21.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\cos@@{u}\cos@@{v} = \cos@{u-v}+\cos@{u+v}} | 2*cos(u)*cos(v)= cos(u - v)+ cos(u + v) |
2*Cos[u]*Cos[v]= Cos[u - v]+ Cos[u + v] |
Successful | Successful | - | - |
| 4.21.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sin@@{u}\cos@@{v} = \sin@{u-v}+\sin@{u+v}} | 2*sin(u)*cos(v)= sin(u - v)+ sin(u + v) |
2*Sin[u]*Cos[v]= Sin[u - v]+ Sin[u + v] |
Successful | Successful | - | - |
| 4.21.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin^{2}@@{u}-\sin^{2}@@{v} = \sin@{u+v}\sin@{u-v}} | (sin(u))^(2)- (sin(v))^(2)= sin(u + v)*sin(u - v) |
(Sin[u])^(2)- (Sin[v])^(2)= Sin[u + v]*Sin[u - v] |
Successful | Successful | - | - |
| 4.21.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos^{2}@@{u}-\cos^{2}@@{v} = -\sin@{u+v}\sin@{u-v}} | (cos(u))^(2)- (cos(v))^(2)= - sin(u + v)*sin(u - v) |
(Cos[u])^(2)- (Cos[v])^(2)= - Sin[u + v]*Sin[u - v] |
Successful | Successful | - | - |
| 4.21.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos^{2}@@{u}-\sin^{2}@@{v} = \cos@{u+v}\cos@{u-v}} | (cos(u))^(2)- (sin(v))^(2)= cos(u + v)*cos(u - v) |
(Cos[u])^(2)- (Sin[v])^(2)= Cos[u + v]*Cos[u - v] |
Successful | Successful | - | - |
| 4.21.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\frac{z}{2}} = +\left(\frac{1-\cos@@{z}}{2}\right)^{1/2}} | sin((z)/(2))= +((1 - cos(z))/(2))^(1/ 2) |
Sin[Divide[z,2]]= +(Divide[1 - Cos[z],2])^(1/ 2) |
Failure | Failure | Fail -1.637854044-1.167010648*I <- {z = -2^(1/2)-I*2^(1/2)}-1.637854044+1.167010648*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.6378540442140963, -1.1670106484252494] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6378540442140963, 1.1670106484252494] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.21.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\frac{z}{2}} = -\left(\frac{1-\cos@@{z}}{2}\right)^{1/2}} | sin((z)/(2))= -((1 - cos(z))/(2))^(1/ 2) |
Sin[Divide[z,2]]= -(Divide[1 - Cos[z],2])^(1/ 2) |
Failure | Failure | Fail 1.637854044+1.167010648*I <- {z = 2^(1/2)+I*2^(1/2)}1.637854044-1.167010648*I <- {z = 2^(1/2)-I*2^(1/2)} |
Fail
Complex[1.6378540442140963, 1.1670106484252494] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6378540442140963, -1.1670106484252494] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 4.21.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\frac{z}{2}} = +\left(\frac{1+\cos@@{z}}{2}\right)^{1/2}} | cos((z)/(2))= +((1 + cos(z))/(2))^(1/ 2) |
Cos[Divide[z,2]]= +(Divide[1 + Cos[z],2])^(1/ 2) |
Failure | Failure | Successful | Successful |
| 4.21.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\frac{z}{2}} = -\left(\frac{1+\cos@@{z}}{2}\right)^{1/2}} | cos((z)/(2))= -((1 + cos(z))/(2))^(1/ 2) |
Cos[Divide[z,2]]= -(Divide[1 + Cos[z],2])^(1/ 2) |
Failure | Failure | Fail 1.916716266-.9972227728*I <- {z = 2^(1/2)+I*2^(1/2)}1.916716266+.9972227728*I <- {z = 2^(1/2)-I*2^(1/2)}1.916716266-.9972227728*I <- {z = -2^(1/2)-I*2^(1/2)}1.916716266+.9972227728*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.916716265666014, -0.9972227733456656] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.916716265666014, 0.9972227733456656] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.916716265666014, -0.9972227733456656] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.916716265666014, 0.9972227733456656] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.21.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{\frac{z}{2}} = +\left(\frac{1-\cos@@{z}}{1+\cos@@{z}}\right)^{1/2}} | tan((z)/(2))= +((1 - cos(z))/(1 + cos(z)))^(1/ 2) |
Tan[Divide[z,2]]= +(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2) |
Failure | Failure | Fail -.8463685478-1.658064547*I <- {z = -2^(1/2)-I*2^(1/2)}-.8463685478+1.658064547*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.8463685477398917, -1.6580645472823399] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8463685477398917, 1.6580645472823399] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.21.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{\frac{z}{2}} = -\left(\frac{1-\cos@@{z}}{1+\cos@@{z}}\right)^{1/2}} | tan((z)/(2))= -((1 - cos(z))/(1 + cos(z)))^(1/ 2) |
Tan[Divide[z,2]]= -(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2) |
Failure | Failure | Fail .8463685478+1.658064547*I <- {z = 2^(1/2)+I*2^(1/2)}.8463685478-1.658064547*I <- {z = 2^(1/2)-I*2^(1/2)} |
Fail
Complex[0.8463685477398917, 1.6580645472823399] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8463685477398917, -1.6580645472823399] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 4.21.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle +\left(\frac{1-\cos@@{z}}{1+\cos@@{z}}\right)^{1/2} = \frac{1-\cos@@{z}}{\sin@@{z}}} | +((1 - cos(z))/(1 + cos(z)))^(1/ 2)=(1 - cos(z))/(sin(z)) |
+(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2)=Divide[1 - Cos[z],Sin[z]] |
Failure | Failure | Skip | Fail
Complex[0.8463685477398916, 1.6580645472823403] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.8463685477398916, -1.6580645472823403] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.21.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\left(\frac{1-\cos@@{z}}{1+\cos@@{z}}\right)^{1/2} = \frac{1-\cos@@{z}}{\sin@@{z}}} | -((1 - cos(z))/(1 + cos(z)))^(1/ 2)=(1 - cos(z))/(sin(z)) |
-(Divide[1 - Cos[z],1 + Cos[z]])^(1/ 2)=Divide[1 - Cos[z],Sin[z]] |
Failure | Failure | Skip | Fail
Complex[-0.8463685477398916, -1.6580645472823403] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8463685477398916, 1.6580645472823403] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 4.21.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\cos@@{z}}{\sin@@{z}} = \frac{\sin@@{z}}{1+\cos@@{z}}} | (1 - cos(z))/(sin(z))=(sin(z))/(1 + cos(z)) |
Divide[1 - Cos[z],Sin[z]]=Divide[Sin[z],1 + Cos[z]] |
Successful | Successful | - | - |
| 4.21.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{-z} = -\sin@@{z}} | sin(- z)= - sin(z) |
Sin[- z]= - Sin[z] |
Successful | Successful | - | - |
| 4.21.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{-z} = \cos@@{z}} | cos(- z)= cos(z) |
Cos[- z]= Cos[z] |
Successful | Successful | - | - |
| 4.21.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{-z} = -\tan@@{z}} | tan(- z)= - tan(z) |
Tan[- z]= - Tan[z] |
Successful | Successful | - | - |
| 4.21.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{2z} = 2\sin@@{z}\cos@@{z}} | sin(2*z)= 2*sin(z)*cos(z) |
Sin[2*z]= 2*Sin[z]*Cos[z] |
Successful | Successful | - | - |
| 4.21.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sin@@{z}\cos@@{z} = \frac{2\tan@@{z}}{1+\tan^{2}@@{z}}} | 2*sin(z)*cos(z)=(2*tan(z))/(1 + (tan(z))^(2)) |
2*Sin[z]*Cos[z]=Divide[2*Tan[z],1 + (Tan[z])^(2)] |
Successful | Successful | - | - |
| 4.21.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{2z} = 2\cos^{2}@@{z}-1} | cos(2*z)= 2*(cos(z))^(2)- 1 |
Cos[2*z]= 2*(Cos[z])^(2)- 1 |
Successful | Successful | - | - |
| 4.21.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\cos^{2}@@{z}-1 = 1-2\sin^{2}@@{z}} | 2*(cos(z))^(2)- 1 = 1 - 2*(sin(z))^(2) |
2*(Cos[z])^(2)- 1 = 1 - 2*(Sin[z])^(2) |
Successful | Successful | - | - |
| 4.21.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1-2\sin^{2}@@{z} = \cos^{2}@@{z}-\sin^{2}@@{z}} | 1 - 2*(sin(z))^(2)= (cos(z))^(2)- (sin(z))^(2) |
1 - 2*(Sin[z])^(2)= (Cos[z])^(2)- (Sin[z])^(2) |
Successful | Successful | - | - |
| 4.21.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos^{2}@@{z}-\sin^{2}@@{z} = \frac{1-\tan^{2}@@{z}}{1+\tan^{2}@@{z}}} | (cos(z))^(2)- (sin(z))^(2)=(1 - (tan(z))^(2))/(1 + (tan(z))^(2)) |
(Cos[z])^(2)- (Sin[z])^(2)=Divide[1 - (Tan[z])^(2),1 + (Tan[z])^(2)] |
Successful | Successful | - | - |
| 4.21.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{2z} = \frac{2\tan@@{z}}{1-\tan^{2}@@{z}}} | tan(2*z)=(2*tan(z))/(1 - (tan(z))^(2)) |
Tan[2*z]=Divide[2*Tan[z],1 - (Tan[z])^(2)] |
Successful | Successful | - | - |
| 4.21.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2\tan@@{z}}{1-\tan^{2}@@{z}} = \frac{2\cot@@{z}}{\cot^{2}@@{z}-1}} | (2*tan(z))/(1 - (tan(z))^(2))=(2*cot(z))/((cot(z))^(2)- 1) |
Divide[2*Tan[z],1 - (Tan[z])^(2)]=Divide[2*Cot[z],(Cot[z])^(2)- 1] |
Successful | Successful | - | - |
| 4.21.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2\cot@@{z}}{\cot^{2}@@{z}-1} = \frac{2}{\cot@@{z}-\tan@@{z}}} | (2*cot(z))/((cot(z))^(2)- 1)=(2)/(cot(z)- tan(z)) |
Divide[2*Cot[z],(Cot[z])^(2)- 1]=Divide[2,Cot[z]- Tan[z]] |
Successful | Successful | - | - |
| 4.21.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{3z} = 3\sin@@{z}-4\sin^{3}@@{z}} | sin(3*z)= 3*sin(z)- 4*(sin(z))^(3) |
Sin[3*z]= 3*Sin[z]- 4*(Sin[z])^(3) |
Successful | Successful | - | - |
| 4.21.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{3z} = -3\cos@@{z}+4\cos^{3}@@{z}} | cos(3*z)= - 3*cos(z)+ 4*(cos(z))^(3) |
Cos[3*z]= - 3*Cos[z]+ 4*(Cos[z])^(3) |
Successful | Successful | - | - |
| 4.21.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{4z} = 8\cos^{3}@@{z}\sin@@{z}-4\cos@@{z}\sin@@{z}} | sin(4*z)= 8*(cos(z))^(3)* sin(z)- 4*cos(z)*sin(z) |
Sin[4*z]= 8*(Cos[z])^(3)* Sin[z]- 4*Cos[z]*Sin[z] |
Successful | Successful | - | - |
| 4.21.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{4z} = 8\cos^{4}@@{z}-8\cos^{2}@@{z}+1} | cos(4*z)= 8*(cos(z))^(4)- 8*(cos(z))^(2)+ 1 |
Cos[4*z]= 8*(Cos[z])^(4)- 8*(Cos[z])^(2)+ 1 |
Successful | Successful | - | - |
| 4.21.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{nz}+i\sin@{nz} = (\cos@@{z}+i\sin@@{z})^{n}} | cos(n*z)+ I*sin(n*z)=(cos(z)+ I*sin(z))^(n) |
Cos[n*z]+ I*Sin[n*z]=(Cos[z]+ I*Sin[z])^(n) |
Failure | Failure | Successful | Successful |
| 4.21.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{nz} = 2^{n-1}\prod_{k=0}^{n-1}\sin@{z+\frac{k\pi}{n}}} | sin(n*z)= (2)^(n - 1)* product(sin(z +(k*Pi)/(n)), k = 0..n - 1) |
Sin[n*z]= (2)^(n - 1)* Product[Sin[z +Divide[k*Pi,n]], {k, 0, n - 1}] |
Failure | Successful | Skip | - |
| 4.21#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = \frac{2t}{1+t^{2}}} | sin(z)=(2*t)/(1 + (t)^(2)) |
Sin[z]=Divide[2*t,1 + (t)^(2)] |
Failure | Failure | Fail 1.319645209+.8008956689*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.319645209+.1973727279*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-2.983425871+.1973727279*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-2.983425871+.8008956689*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.3196452105315832, 0.8008956683523827] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.3196452105315832, 0.197372728616861] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.9834258721469893, 0.197372728616861] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.9834258721469893, 0.8008956683523827] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \frac{1-t^{2}}{1+t^{2}}} | cos(z)=(1 - (t)^(2))/(1 + (t)^(2)) |
Cos[z]=Divide[1 - (t)^(2),1 + (t)^(2)] |
Failure | Failure | Fail 1.222026934-1.440804874*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.222026934+2.381981344*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.222026934-1.440804874*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.222026934+2.381981344*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.222026932871195, -1.4408048748700928] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.222026932871195, 2.381981345458328] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.222026932871195, -1.4408048748700928] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.222026932871195, 2.381981345458328] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = \sin@@{x}\cosh@@{y}+\iunit\cos@@{x}\sinh@@{y}} | sin(z)= sin(x)*cosh(y)+ I*cos(x)*sinh(y) |
Sin[z]= Sin[x]*Cosh[y]+ I*Cos[x]*Sinh[y] |
Failure | Failure | Fail .853077958-.3332024445*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-1.014242973-1.657839572*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-6.320109918-5.110919454*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.748416289+.7908177296*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[0.8530779599233089, -0.33320244491697526] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.014242971876882, -1.6578395715538454] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.320109912960862, -5.110919453310433] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7484162907172458, 0.7908177289090546] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \cos@@{x}\cosh@@{y}-\iunit\sin@@{x}\sinh@@{y}} | cos(z)= cos(x)*cosh(y)- I*sin(x)*sinh(y) |
Cos[z]= Cos[x]*Cosh[y]- I*Sin[x]*Sinh[y] |
Failure | Failure | Fail -.4940560329-.9224954029*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-1.693049015+1.140504690*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-5.099907002+6.518357974*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.9818221171-.842785687*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[-0.49405603343642457, -0.9224954044013453] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6930490153249411, 1.1405046889875898] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.099906999325039, 6.518357970685734] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9818221164102445, -0.842785688781432] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{z} = \frac{\sin@{2x}+\iunit\sinh@{2y}}{\cos@{2x}+\cosh@{2y}}} | tan(z)=(sin(2*x)+ I*sinh(2*y))/(cos(2*x)+ cosh(2*y)) |
Tan[z]=Divide[Sin[2*x]+ I*Sinh[2*y],Cos[2*x]+ Cosh[2*y]] |
Failure | Failure | Fail -.2308812766+.34450810e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.705848261e-2+.103580521*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.3635417141e-1+.116319149*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.2843295099-.48362120e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[-0.23088127675619197, 0.03445081006213968] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.007058482483423091, 0.1035805212542007] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.03635417128666136, 0.1163191491550224] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.28432950974904503, -0.04836211984008565] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{z} = \frac{\sin@{2x}-\iunit\sinh@{2y}}{\cosh@{2y}-\cos@{2x}}} | cot(z)=(sin(2*x)- I*sinh(2*y))/(cosh(2*y)- cos(2*x)) |
Cot[z]=Divide[Sin[2*x]- I*Sinh[2*y],Cosh[2*y]- Cos[2*x]] |
Failure | Failure | Fail -.1849879852-.249484083e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-.16417892e-3+.913666750e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.2813503899e-1+.1049663965*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.2040171895-.716327538e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[-0.18498798535387256, -0.024948408389711685] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6417903322245991*^-4, 0.09136667517255426] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.02813503889543659, 0.10496639594574086] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.20401718940971514, -0.07163275379178491] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sin@@{z}| = (\sin^{2}@@{x}+\sinh^{2}@@{y})^{1/2}} | abs(sin(z))=((sin(x))^(2)+ (sinh(y))^(2))^(1/ 2) |
Abs[Sin[z]]=((Sin[x])^(2)+ (Sinh[y])^(2))^(1/ 2) |
Failure | Failure | Fail .727197533 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-1.550602076 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-7.880559200 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.686687095 <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
0.7271975341555692 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-1.5506020747613944 <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-7.880559199441702 <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.6866870962353082 <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sin^{2}@@{x}+\sinh^{2}@@{y})^{1/2} = \left(\tfrac{1}{2}\left(\cosh@{2y}-\cos@{2x}\right)\right)^{1/2}} | ((sin(x))^(2)+ (sinh(y))^(2))^(1/ 2)=((1)/(2)*(cosh(2*y)- cos(2*x)))^(1/ 2) |
((Sin[x])^(2)+ (Sinh[y])^(2))^(1/ 2)=(Divide[1,2]*(Cosh[2*y]- Cos[2*x]))^(1/ 2) |
Successful | Successful | - | - |
| 4.21.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cos@@{z}| = (\cos^{2}@@{x}+\sinh^{2}@@{y})^{1/2}} | abs(cos(z))=((cos(x))^(2)+ (sinh(y))^(2))^(1/ 2) |
Abs[Cos[z]]=((Cos[x])^(2)+ (Sinh[y])^(2))^(1/ 2) |
Failure | Failure | Fail .647885813 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-1.725544377 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-8.091094362 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.694634194 <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
0.6478858145183544 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-1.7255443754392632 <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-8.091094362320007 <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.694634195495673 <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.21.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\cos^{2}@@{x}+\sinh^{2}@@{y})^{1/2} = \left(\tfrac{1}{2}(\cosh@{2y}+\cos@{2x})\right)^{1/2}} | ((cos(x))^(2)+ (sinh(y))^(2))^(1/ 2)=((1)/(2)*(cosh(2*y)+ cos(2*x)))^(1/ 2) |
((Cos[x])^(2)+ (Sinh[y])^(2))^(1/ 2)=(Divide[1,2]*(Cosh[2*y]+ Cos[2*x]))^(1/ 2) |
Successful | Successful | - | - |
| 4.21.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\tan@@{z}| = \left(\frac{\cosh@{2y}-\cos@{2x}}{\cosh@{2y}+\cos@{2x}}\right)^{1/2}} | abs(tan(z))=((cosh(2*y)- cos(2*x))/(cosh(2*y)+ cos(2*x)))^(1/ 2) |
Abs[Tan[z]]=(Divide[Cosh[2*y]- Cos[2*x],Cosh[2*y]+ Cos[2*x]])^(1/ 2) |
Failure | Failure | Fail .1650695e-2 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.103763936 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.117055546 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-.72745631e-1 <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
0.0016506944407532753 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.10376393520222194 <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.11705554561068499 <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-0.07274563209398122 <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.22.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = z\prod_{n=1}^{\infty}\left(1-\frac{z^{2}}{n^{2}\pi^{2}}\right)} | sin(z)= z*product(1 -((z)^(2))/((n)^(2)* (Pi)^(2)), n = 1..infinity) |
Sin[z]= z*Product[1 -Divide[(z)^(2),(n)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Successful | Successful | - | - |
| 4.22.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \prod_{n=1}^{\infty}\left(1-\frac{4z^{2}}{(2n-1)^{2}\pi^{2}}\right)} | cos(z)= product(1 -(4*(z)^(2))/((2*n - 1)^(2)* (Pi)^(2)), n = 1..infinity) |
Cos[z]= Product[1 -Divide[4*(z)^(2),(2*n - 1)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Successful | Successful | - | - |
| 4.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{z} = \frac{1}{z}+2z\sum_{n=1}^{\infty}\frac{1}{z^{2}-n^{2}\pi^{2}}} | cot(z)=(1)/(z)+ 2*z*sum((1)/((z)^(2)- (n)^(2)* (Pi)^(2)), n = 1..infinity) |
Cot[z]=Divide[1,z]+ 2*z*Sum[Divide[1,(z)^(2)- (n)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Successful | Successful | - | - |
| 4.22.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc^{2}@@{z} = \sum_{n=-\infty}^{\infty}\frac{1}{(z-n\pi)^{2}}} | (csc(z))^(2)= sum((1)/((z - n*Pi)^(2)), n = - infinity..infinity) |
(Csc[z])^(2)= Sum[Divide[1,(z - n*Pi)^(2)], {n, - Infinity, Infinity}] |
Successful | Successful | - | - |
| 4.22.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@@{z} = \frac{1}{z}+2z\sum_{n=1}^{\infty}\frac{(-1)^{n}}{z^{2}-n^{2}\pi^{2}}} | csc(z)=(1)/(z)+ 2*z*sum(((- 1)^(n))/((z)^(2)- (n)^(2)* (Pi)^(2)), n = 1..infinity) |
Csc[z]=Divide[1,z]+ 2*z*Sum[Divide[(- 1)^(n),(z)^(2)- (n)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Successful | Successful | - | - |
| 4.23.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1-t^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, z}]= Integrate[Divide[1,(1 - (t)^(2))^(1/ 2)], {t, 0, z}] |
Error | Failure | - | Successful |
| 4.23.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acos@@{z} = \int_{z}^{1}\frac{\diff{t}}{(1-t^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, z, 1}]= Integrate[Divide[1,(1 - (t)^(2))^(1/ 2)], {t, z, 1}] |
Error | Failure | - | Skip |
| 4.23.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@@{z} = \int_{0}^{z}\frac{\diff{t}}{1+t^{2}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, z}]= Integrate[Divide[1,1 + (t)^(2)], {t, 0, z}] |
Error | Failure | - | Successful |
| 4.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acsc@@{z} = \Asin@{1/z}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, Divide[1,z]}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, 1/ z}] |
Error | Failure | - | Successful |
| 4.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asec@@{z} = \Acos@{1/z}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, Divide[1,z], 1}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 1/ z, 1}] |
Error | Failure | - | Error |
| 4.23.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acot@@{z} = \Atan@{1/z}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, Divide[1,z]}]= Integrate[Divide[1, 1+t^2], {t, 0, 1/ z}] |
Error | Failure | - | Successful |
| 4.23.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsc@@{z} = \asin@{1/z}} | arccsc(z)= arcsin(1/ z) |
ArcCsc[z]= ArcSin[1/ z] |
Failure | Successful | Successful | - |
| 4.23.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asec@@{z} = \acos@{1/z}} | arcsec(z)= arccos(1/ z) |
ArcSec[z]= ArcCos[1/ z] |
Failure | Successful | Successful | - |
| 4.23.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acot@@{z} = \atan@{1/z}} | arccot(z)= arctan(1/ z) |
ArcCot[z]= ArcTan[1/ z] |
Failure | Successful | Successful | - |
| 4.23.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@{-z} = -\asin@@{z}} | arcsin(- z)= - arcsin(z) |
ArcSin[- z]= - ArcSin[z] |
Successful | Successful | - | - |
| 4.23.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@{-z} = \pi-\acos@@{z}} | arccos(- z)= Pi - arccos(z) |
ArcCos[- z]= Pi - ArcCos[z] |
Successful | Successful | - | - |
| 4.23.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@{-z} = -\atan@@{z}} | arctan(- z)= - arctan(z) |
ArcTan[- z]= - ArcTan[z] |
Successful | Successful | - | - |
| 4.23.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsc@{-z} = -\acsc@@{z}} | arccsc(- z)= - arccsc(z) |
ArcCsc[- z]= - ArcCsc[z] |
Successful | Successful | - | - |
| 4.23.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asec@{-z} = \pi-\asec@@{z}} | arcsec(- z)= Pi - arcsec(z) |
ArcSec[- z]= Pi - ArcSec[z] |
Successful | Successful | - | - |
| 4.23.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acot@{-z} = -\acot@@{z}} | arccot(- z)= - arccot(z) |
ArcCot[- z]= - ArcCot[z] |
Failure | Successful | - | - |
| 4.23.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{z} = \tfrac{1}{2}\pi-\asin@@{z}} | arccos(z)=(1)/(2)*Pi - arcsin(z) |
ArcCos[z]=Divide[1,2]*Pi - ArcSin[z] |
Failure | Successful | Successful | - |
| 4.23.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asec@@{z} = \tfrac{1}{2}\pi-\acsc@@{z}} | arcsec(z)=(1)/(2)*Pi - arccsc(z) |
ArcSec[z]=Divide[1,2]*Pi - ArcCsc[z] |
Failure | Successful | Successful | - |
| 4.23.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acot@@{z} = +\tfrac{1}{2}\pi-\atan@@{z}} | arccot(z)= +(1)/(2)*Pi - arctan(z) |
ArcCot[z]= +Divide[1,2]*Pi - ArcTan[z] |
Successful | Failure | - | Successful |
| 4.23.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acot@@{z} = -\tfrac{1}{2}\pi-\atan@@{z}} | arccot(z)= -(1)/(2)*Pi - arctan(z) |
ArcCot[z]= -Divide[1,2]*Pi - ArcTan[z] |
Failure | Failure | Fail 3.141592654 <- {z = 1/2} |
Fail
3.141592653589793 <- {Rule[z, Rational[1, 2]]} |
| 4.23.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{z} = -i\ln@{(1-z^{2})^{1/2}+iz}} | arcsin(z)= - I*ln((1 - (z)^(2))^(1/ 2)+ I*z) |
ArcSin[z]= - I*Log[(1 - (z)^(2))^(1/ 2)+ I*z] |
Failure | Successful | Error | - |
| 4.23.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{x} = \tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}+x}} | arcsin(x)=(1)/(2)*Pi + I*ln(((x)^(2)- 1)^(1/ 2)+ x) |
ArcSin[x]=Divide[1,2]*Pi + I*Log[((x)^(2)- 1)^(1/ 2)+ x] |
Failure | Failure | Error | Error |
| 4.23.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{x} = \tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}+x}} | arcsin(x)=(1)/(2)*Pi - I*ln(((x)^(2)- 1)^(1/ 2)+ x) |
ArcSin[x]=Divide[1,2]*Pi - I*Log[((x)^(2)- 1)^(1/ 2)+ x] |
Failure | Failure | Error | Error |
| 4.23.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{x} = -\tfrac{1}{2}\pi+ i\ln@{(x^{2}-1)^{1/2}-x}} | arcsin(x)= -(1)/(2)*Pi + I*ln(((x)^(2)- 1)^(1/ 2)- x) |
ArcSin[x]= -Divide[1,2]*Pi + I*Log[((x)^(2)- 1)^(1/ 2)- x] |
Failure | Failure | Error | Error |
| 4.23.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{x} = -\tfrac{1}{2}\pi- i\ln@{(x^{2}-1)^{1/2}-x}} | arcsin(x)= -(1)/(2)*Pi - I*ln(((x)^(2)- 1)^(1/ 2)- x) |
ArcSin[x]= -Divide[1,2]*Pi - I*Log[((x)^(2)- 1)^(1/ 2)- x] |
Failure | Failure | Error | Error |
| 4.23.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{z} = \tfrac{1}{2}\pi+i\ln@{(1-z^{2})^{1/2}+iz}} | arccos(z)=(1)/(2)*Pi + I*ln((1 - (z)^(2))^(1/ 2)+ I*z) |
ArcCos[z]=Divide[1,2]*Pi + I*Log[(1 - (z)^(2))^(1/ 2)+ I*z] |
Failure | Successful | Error | - |
| 4.23.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{z} = -2i\ln@{\left(\frac{1+z}{2}\right)^{1/2}+i\left(\frac{1-z}{2}\right)^{1/2}}} | arccos(z)= - 2*I*ln(((1 + z)/(2))^(1/ 2)+ I*((1 - z)/(2))^(1/ 2)) |
ArcCos[z]= - 2*I*Log[(Divide[1 + z,2])^(1/ 2)+ I*(Divide[1 - z,2])^(1/ 2)] |
Failure | Failure | Error | Error |
| 4.23.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{x} = - i\ln@{(x^{2}-1)^{1/2}+x}} | arccos(x)= - I*ln(((x)^(2)- 1)^(1/ 2)+ x) |
ArcCos[x]= - I*Log[((x)^(2)- 1)^(1/ 2)+ x] |
Failure | Failure | Error | Error |
| 4.23.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{x} = + i\ln@{(x^{2}-1)^{1/2}+x}} | arccos(x)= + I*ln(((x)^(2)- 1)^(1/ 2)+ x) |
ArcCos[x]= + I*Log[((x)^(2)- 1)^(1/ 2)+ x] |
Failure | Failure | Error | Error |
| 4.23.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{x} = \pi- i\ln@{(x^{2}-1)^{1/2}-x}} | arccos(x)= Pi - I*ln(((x)^(2)- 1)^(1/ 2)- x) |
ArcCos[x]= Pi - I*Log[((x)^(2)- 1)^(1/ 2)- x] |
Failure | Failure | Error | Error |
| 4.23.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{x} = \pi+ i\ln@{(x^{2}-1)^{1/2}-x}} | arccos(x)= Pi + I*ln(((x)^(2)- 1)^(1/ 2)- x) |
ArcCos[x]= Pi + I*Log[((x)^(2)- 1)^(1/ 2)- x] |
Failure | Failure | Error | Error |
| 4.23.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{z} = \frac{i}{2}\ln@{\frac{i+z}{i-z}}} | arctan(z)=(I)/(2)*ln((I + z)/(I - z)) |
ArcTan[z]=Divide[I,2]*Log[Divide[I + z,I - z]] |
Failure | Failure | Error | Error |
| 4.23.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@{iy} = +\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}} | arctan(I*y)= +(1)/(2)*Pi +(I)/(2)*ln((y + 1)/(y - 1)) |
ArcTan[I*y]= +Divide[1,2]*Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]] |
Failure | Failure | Error | Error |
| 4.23.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@{iy} = -\frac{1}{2}\pi+\frac{i}{2}\ln@{\frac{y+1}{y-1}}} | arctan(I*y)= -(1)/(2)*Pi +(I)/(2)*ln((y + 1)/(y - 1)) |
ArcTan[I*y]= -Divide[1,2]*Pi +Divide[I,2]*Log[Divide[y + 1,y - 1]] |
Failure | Failure | Error | Error |
| 4.23.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \sin@@{w}} | z = sin(w) |
z = Sin[w] |
Failure | Failure | Fail -.737321978+1.112452092*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.737321978-1.715975032*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-3.565749102-1.715975032*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-3.565749102+1.112452092*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.7373219789661911, 1.1124520925053343] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.7373219789661911, -1.715975032240856] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.565749103712381, -1.715975032240856] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.565749103712381, 1.1124520925053343] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \cos@@{w}} | z = cos(w) |
z = Cos[w] |
Failure | Failure | Fail 1.074539570+3.325606671*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.074539570+.497179547*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.753887554+.497179547*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.753887554+3.325606671*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.0745395706783705, 3.3256066725373055] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0745395706783705, 0.4971795477911152] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.7538875540678198, 0.4971795477911152] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.7538875540678198, 3.3256066725373055] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \tan@@{w}} | z = tan(w) |
z = Tan[w] |
Failure | Failure | Fail 1.373342253+.295839425*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.373342253-2.532587699*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.455084871-2.532587699*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.455084871+.295839425*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.3733422538097753, 0.2958394249722609] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.3733422538097753, -2.5325876997739294] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.455084870936415, -2.5325876997739294] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.455084870936415, 0.2958394249722609] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Asin@@{z}} | Error |
w = Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, z}] |
Error | Failure | - | Fail
Complex[0.6905247538249891, 0.022188930362652126] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.6905247538249891, 2.806238194383538] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.1379023709212013, 2.806238194383538] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.1379023709212013, 0.022188930362652126] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@@{z} = (-1)^{k}\asin@@{z}+k\pi} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, z}]=(- 1)^(k)* ArcSin[z]+ k*Pi |
Error | Failure | - | Fail
Complex[-1.694215036493581, 2.784049264020886] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-6.283185307179586 <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-7.9774003436731675, 2.784049264020886] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.694215036493581, -2.784049264020886] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Acos@@{z}} | Error |
w = Integrate[Divide[1, (1-t^2)^(1/2)], {t, z, 1}] |
Error | Failure | - | Successful |
| 4.23.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acos@@{z} = +\acos@@{z}+2k\pi} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, z, 1}]= + ArcCos[z]+ 2*k*Pi |
Error | Failure | - | Successful |
| 4.23.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acos@@{z} = -\acos@@{z}+2k\pi} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, z, 1}]= - ArcCos[z]+ 2*k*Pi |
Error | Failure | - | Successful |
| 4.23.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Atan@@{z}} | Error |
w = Integrate[Divide[1, 1+t^2], {t, 0, z}] |
Error | Failure | - | Fail
Complex[0.950565953372289, 1.4142135623730951] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]}Complex[0.950565953372289, -1.4142135623730951] <- {Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]}Complex[-1.8778611713739013, -1.4142135623730951] <- {Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]}Complex[-1.8778611713739013, 1.4142135623730951] <- {Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]} |
| 4.23.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@@{z} = \atan@@{z}+k\pi} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, z}]= ArcTan[z]+ k*Pi |
Error | Failure | - | Fail
-3.141592653589793 <- {Rule[k, 1], Rule[z, Rational[1, 2]]}-6.283185307179586 <- {Rule[k, 2], Rule[z, Rational[1, 2]]}-9.42477796076938 <- {Rule[k, 3], Rule[z, Rational[1, 2]]} |
| 4.23.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{z} = \asin@@{\beta}+\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}} | arcsin(z)= arcsin(beta)+ I*signum(y)*ln(alpha +((alpha)^(2)- 1)^(1/ 2)) |
ArcSin[z]= ArcSin[\[Beta]]+ I*Sign[y]*Log[\[Alpha]+((\[Alpha])^(2)- 1)^(1/ 2)] |
Failure | Failure | Fail .8471075183-1.392024632*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), y = 1}.8471075183-1.392024632*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), y = 2}.8471075183-1.392024632*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), y = 3}.8471075183-4.176073896*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), y = 1}... skip entries to safe data |
Fail
Complex[0.8471075182467906, -1.3920246320104428] <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8471075182467906, -1.3920246320104428] <- {Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8471075182467906, -1.3920246320104428] <- {Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8471075182467906, 1.3920246320104432] <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{z} = \acos@@{\beta}-\iunit\sign@{y}\ln@{\alpha+(\alpha^{2}-1)^{1/2}}} | arccos(z)= arccos(beta)- I*signum(y)*ln(alpha +((alpha)^(2)- 1)^(1/ 2)) |
ArcCos[z]= ArcCos[\[Beta]]- I*Sign[y]*Log[\[Alpha]+((\[Alpha])^(2)- 1)^(1/ 2)] |
Failure | Failure | Fail -.8471075183+1.392024632*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), y = 1}-.8471075183+1.392024632*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), y = 2}-.8471075183+1.392024632*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), y = 3}-.8471075183+4.176073896*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), y = 1}... skip entries to safe data |
Fail
Complex[-0.8471075182467906, 1.3920246320104428] <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8471075182467906, 1.3920246320104428] <- {Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8471075182467906, 1.3920246320104428] <- {Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8471075182467906, -1.3920246320104432] <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{z} = \tfrac{1}{2}\atan@{\frac{2x}{1-x^{2}-y^{2}}}+\tfrac{1}{4}i\ln@{\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}}} | arctan(z)=(1)/(2)*arctan((2*x)/(1 - (x)^(2)- (y)^(2)))+(1)/(4)*I*ln(((x)^(2)+(y + 1)^(2))/((x)^(2)+(y - 1)^(2))) |
ArcTan[z]=Divide[1,2]*ArcTan[Divide[2*x,1 - (x)^(2)- (y)^(2)]]+Divide[1,4]*I*Log[Divide[(x)^(2)+(y + 1)^(2),(x)^(2)+(y - 1)^(2)]] |
Failure | Failure | Fail 1.746385980-.817820081e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}1.424635426-.817820081e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}1.302146094+.146336119e-1*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}1.585510703+.1472906747*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[1.746385980479988, -0.081782008243384] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4246354260833458, -0.081782008243384] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.3021460945199137, 0.014633611959612158] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.5855107032816669, 0.14729067472515475] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.23.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Gudermannian@{x} = \int_{0}^{x}\sech@@{t}\diff{t}} | arctan(sinh(x))= int(sech(t), t = 0..x) |
Gudermannian[x]= Integrate[Sech[t], {t, 0, x}] |
Successful | Failure | - | Successful |
| 4.23.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ = \asin@{\tanh@@{x}}} | 2*arctan(exp(x))-(1)/(2)*Pi = arcsin(tanh(x)) |
2*ArcTan[Exp[x]]-Divide[1,2]*Pi = ArcSin[Tanh[x]] |
Error | Error | - | - |
| 4.23.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsc@{\coth@@{x}}\\ = \acos@{\sech@@{x}}} | arccsc(coth(x))= arccos(sech(x)) |
ArcCsc[Coth[x]]= ArcCos[Sech[x]] |
Error | Error | - | - |
| 4.23.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asec@{\cosh@@{x}}\\ = \atan@{\sinh@@{x}}} | arcsec(cosh(x))= arctan(sinh(x)) |
ArcSec[Cosh[x]]= ArcTan[Sinh[x]] |
Error | Error | - | - |
| 4.23.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@{\sinh@@{x}} = \acot@{\csch@@{x}}} | arctan(sinh(x))= arccot(csch(x)) |
ArcTan[Sinh[x]]= ArcCot[Csch[x]] |
Failure | Successful | Skip | - |
| 4.23.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aGudermannian@{x} = \int_{0}^{x}\sec@@{t}\diff{t}} | arctanh(sin(x))= int(sec(t), t = 0..x) |
InverseGudermannian[x]= Integrate[Sec[t], {t, 0, x}] |
Successful | Failure | - | Successful |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aGudermannian@{x} = \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}} | arctanh(sin(x))= ln(tan((1)/(2)*x +(1)/(4)*Pi)) |
InverseGudermannian[x]= Log[Tan[Divide[1,2]*x +Divide[1,4]*Pi]] |
Failure | Successful | Fail .2e-8-3.141592654*I <- {x = 2}.9e-9-3.141592654*I <- {x = 3} |
- |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}} = \ln@{\sec@@{x}+\tan@@{x}}} | ln(tan((1)/(2)*x +(1)/(4)*Pi))= ln(sec(x)+ tan(x)) |
Log[Tan[Divide[1,2]*x +Divide[1,4]*Pi]]= Log[Sec[x]+ Tan[x]] |
Successful | Successful | - | - |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{\sec@@{x}+\tan@@{x}} = \asinh@{\tan@@{x}}} | ln(sec(x)+ tan(x))= arcsinh(tan(x)) |
Log[Sec[x]+ Tan[x]]= ArcSinh[Tan[x]] |
Failure | Failure | Skip | Fail
Complex[3.046904887125347, 3.141592653589793] <- {Rule[x, 2]}Complex[0.28413631677879303, 3.141592653589793] <- {Rule[x, 3]} |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{\tan@@{x}} = \acsch@{\cot@@{x}}} | arcsinh(tan(x))= arccsch(cot(x)) |
ArcSinh[Tan[x]]= ArcCsch[Cot[x]] |
Failure | Successful | Skip | - |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsch@{\cot@@{x}} = \acosh@{\sec@@{x}}} | arccsch(cot(x))= arccosh(sec(x)) |
ArcCsch[Cot[x]]= ArcCosh[Sec[x]] |
Failure | Failure | Skip | Fail
Complex[-3.046904887125347, -3.141592653589793] <- {Rule[x, 2]}Complex[-0.2841363167787935, -3.141592653589793] <- {Rule[x, 3]} |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{\sec@@{x}} = \asech@{\cos@@{x}}} | arccosh(sec(x))= arcsech(cos(x)) |
ArcCosh[Sec[x]]= ArcSech[Cos[x]] |
Failure | Successful | Skip | - |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asech@{\cos@@{x}} = \atanh@{\sin@@{x}}} | arcsech(cos(x))= arctanh(sin(x)) |
ArcSech[Cos[x]]= ArcTanh[Sin[x]] |
Failure | Failure | Skip | Fail
Complex[0.0, 3.141592653589793] <- {Rule[x, 2]}Complex[5.273559366969494*^-16, 3.141592653589793] <- {Rule[x, 3]} |
| 4.23.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@{\sin@@{x}} = \acoth@{\csc@@{x}}} | arctanh(sin(x))= arccoth(csc(x)) |
ArcTanh[Sin[x]]= ArcCoth[Csc[x]] |
Failure | Successful | Skip | - |
| 4.24.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\asin@@{z} = (1-z^{2})^{-1/2}} | diff(arcsin(z), z)=(1 - (z)^(2))^(- 1/ 2) |
D[ArcSin[z], z]=(1 - (z)^(2))^(- 1/ 2) |
Successful | Successful | - | - |
| 4.24.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acos@@{z} = -(1-z^{2})^{-1/2}} | diff(arccos(z), z)= -(1 - (z)^(2))^(- 1/ 2) |
D[ArcCos[z], z]= -(1 - (z)^(2))^(- 1/ 2) |
Successful | Successful | - | - |
| 4.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\atan@@{z} = \frac{1}{1+z^{2}}} | diff(arctan(z), z)=(1)/(1 + (z)^(2)) |
D[ArcTan[z], z]=Divide[1,1 + (z)^(2)] |
Successful | Successful | - | - |
| 4.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acsc@@{z} = -\frac{1}{z(z^{2}-1)^{1/2}}} | diff(arccsc(z), z)= -(1)/(z*((z)^(2)- 1)^(1/ 2)) |
D[ArcCsc[z], z]= -Divide[1,z*((z)^(2)- 1)^(1/ 2)] |
Failure | Failure | Successful | Successful |
| 4.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acsc@@{z} = +\frac{1}{z(z^{2}-1)^{1/2}}} | diff(arccsc(z), z)= +(1)/(z*((z)^(2)- 1)^(1/ 2)) |
D[ArcCsc[z], z]= +Divide[1,z*((z)^(2)- 1)^(1/ 2)] |
Failure | Failure | Fail 4.618802153*I <- {z = 1/2} |
Fail
Complex[0.0, 4.618802153517007] <- {Rule[z, Rational[1, 2]]} |
| 4.24.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\asec@@{z} = +\frac{1}{z(z^{2}-1)^{1/2}}} | diff(arcsec(z), z)= +(1)/(z*((z)^(2)- 1)^(1/ 2)) |
D[ArcSec[z], z]= +Divide[1,z*((z)^(2)- 1)^(1/ 2)] |
Failure | Failure | Successful | Successful |
| 4.24.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\asec@@{z} = -\frac{1}{z(z^{2}-1)^{1/2}}} | diff(arcsec(z), z)= -(1)/(z*((z)^(2)- 1)^(1/ 2)) |
D[ArcSec[z], z]= -Divide[1,z*((z)^(2)- 1)^(1/ 2)] |
Failure | Failure | Fail -4.618802153*I <- {z = 1/2} |
Fail
Complex[0.0, -4.618802153517007] <- {Rule[z, Rational[1, 2]]} |
| 4.24.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acot@@{z} = -\frac{1}{1+z^{2}}} | diff(arccot(z), z)= -(1)/(1 + (z)^(2)) |
D[ArcCot[z], z]= -Divide[1,1 + (z)^(2)] |
Successful | Successful | - | - |
| 4.24.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@@{u}+\Asin@@{v} = \Asin@{u(1-v^{2})^{1/2}+ v(1-u^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u}]+ Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, v}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u*(1 - (v)^(2))^(1/ 2)+ v*(1 - (u)^(2))^(1/ 2)}] |
Error | Failure | - | Successful |
| 4.24.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@@{u}-\Asin@@{v} = \Asin@{u(1-v^{2})^{1/2}- v(1-u^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u}]- Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, v}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u*(1 - (v)^(2))^(1/ 2)- v*(1 - (u)^(2))^(1/ 2)}] |
Error | Failure | - | Successful |
| 4.24.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acos@@{u}+\Acos@@{v} = \Acos@{uv-((1-u^{2})(1-v^{2}))^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, u, 1}]+ Integrate[Divide[1, (1-t^2)^(1/2)], {t, v, 1}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, u*v -((1 - (u)^(2))*(1 - (v)^(2)))^(1/ 2), 1}] |
Error | Failure | - | Error |
| 4.24.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acos@@{u}-\Acos@@{v} = \Acos@{uv+((1-u^{2})(1-v^{2}))^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, u, 1}]- Integrate[Divide[1, (1-t^2)^(1/2)], {t, v, 1}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, u*v +((1 - (u)^(2))*(1 - (v)^(2)))^(1/ 2), 1}] |
Error | Failure | - | Error |
| 4.24.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@@{u}+\Atan@@{v} = \Atan@{\frac{u+ v}{1- uv}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, u}]+ Integrate[Divide[1, 1+t^2], {t, 0, v}]= Integrate[Divide[1, 1+t^2], {t, 0, Divide[u + v,1 - u*v]}] |
Error | Failure | - | Fail
Complex[3.141592653589793, 3.3306690738754696*^-16] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.141592653589793, 0.0] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.141592653589793, 0.0] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.141592653589793, -3.3306690738754696*^-16] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.24.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@@{u}-\Atan@@{v} = \Atan@{\frac{u- v}{1+ uv}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, u}]- Integrate[Divide[1, 1+t^2], {t, 0, v}]= Integrate[Divide[1, 1+t^2], {t, 0, Divide[u - v,1 + u*v]}] |
Error | Failure | - | Fail
Complex[3.141592653589793, 3.3306690738754696*^-16] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.141592653589793, 0.0] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.141592653589793, 0.0] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.141592653589793, -3.3306690738754696*^-16] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.24.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@@{u}+\Acos@@{v} = \Asin@{uv+((1-u^{2})(1-v^{2}))^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u}]+ Integrate[Divide[1, (1-t^2)^(1/2)], {t, v, 1}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u*v +((1 - (u)^(2))*(1 - (v)^(2)))^(1/ 2)}] |
Error | Failure | - | Skip |
| 4.24.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@@{u}-\Acos@@{v} = \Asin@{uv-((1-u^{2})(1-v^{2}))^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u}]- Integrate[Divide[1, (1-t^2)^(1/2)], {t, v, 1}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u*v -((1 - (u)^(2))*(1 - (v)^(2)))^(1/ 2)}] |
Error | Failure | - | Skip |
| 4.24.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@{uv+((1-u^{2})(1-v^{2}))^{1/2}} = \Acos@{v(1-u^{2})^{1/2}- u(1-v^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u*v +((1 - (u)^(2))*(1 - (v)^(2)))^(1/ 2)}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, v*(1 - (u)^(2))^(1/ 2)- u*(1 - (v)^(2))^(1/ 2), 1}] |
Error | Failure | - | Successful |
| 4.24.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@{uv-((1-u^{2})(1-v^{2}))^{1/2}} = \Acos@{v(1-u^{2})^{1/2}+ u(1-v^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1-t^2)^(1/2)], {t, 0, u*v -((1 - (u)^(2))*(1 - (v)^(2)))^(1/ 2)}]= Integrate[Divide[1, (1-t^2)^(1/2)], {t, v*(1 - (u)^(2))^(1/ 2)+ u*(1 - (v)^(2))^(1/ 2), 1}] |
Error | Failure | - | Error |
| 4.24.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@@{u}+\Acot@@{v} = \Atan@{\frac{uv+ 1}{v- u}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, u}]+ Integrate[Divide[1, 1+t^2], {t, 0, Divide[1,v]}]= Integrate[Divide[1, 1+t^2], {t, 0, Divide[u*v + 1,v - u]}] |
Error | Failure | - | Successful |
| 4.24.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@@{u}-\Acot@@{v} = \Atan@{\frac{uv- 1}{v+ u}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, u}]- Integrate[Divide[1, 1+t^2], {t, 0, Divide[1,v]}]= Integrate[Divide[1, 1+t^2], {t, 0, Divide[u*v - 1,v + u]}] |
Error | Failure | - | Error |
| 4.24.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@{\frac{uv+ 1}{v- u}} = \Acot@{\frac{v- u}{uv+ 1}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, Divide[u*v + 1,v - u]}]= Integrate[Divide[1, 1+t^2], {t, 0, Divide[1,Divide[v - u,u*v + 1]]}] |
Error | Failure | - | Successful |
| 4.24.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atan@{\frac{uv- 1}{v+ u}} = \Acot@{\frac{v+ u}{uv- 1}}} | Error |
Integrate[Divide[1, 1+t^2], {t, 0, Divide[u*v - 1,v + u]}]= Integrate[Divide[1, 1+t^2], {t, 0, Divide[1,Divide[v + u,u*v - 1]]}] |
Error | Failure | - | Error |
| 4.26.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\sin@@{x}\diff{x} = -\cos@@{x}} | int(sin(x), x)= - cos(x) |
Integrate[Sin[x], x]= - Cos[x] |
Successful | Successful | - | - |
| 4.26.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\cos@@{x}\diff{x} = \sin@@{x}} | int(cos(x), x)= sin(x) |
Integrate[Cos[x], x]= Sin[x] |
Successful | Successful | - | - |
| 4.26.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\tan@@{x}\diff{x} = -\ln@{\cos@@{x}}} | int(tan(x), x)= - ln(cos(x)) |
Integrate[Tan[x], x]= - Log[Cos[x]] |
Successful | Successful | - | - |
| 4.26.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\csc@@{x}\diff{x} = \ln@{\tan@@{\tfrac{1}{2}x}}} | int(csc(x), x)= ln(tan((1)/(2)*x)) |
Integrate[Csc[x], x]= Log[Tan[Divide[1,2]*x]] |
Failure | Successful | Skip | - |
| 4.26.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\sec@@{x}\diff{x} = \aGudermannian@{x}} | int(sec(x), x)= arctanh(sin(x)) |
Integrate[Sec[x], x]= InverseGudermannian[x] |
Failure | Failure | Skip | Successful |
| 4.26.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\cot@@{x}\diff{x} = \ln@{\sin@@{x}}} | int(cot(x), x)= ln(sin(x)) |
Integrate[Cot[x], x]= Log[Sin[x]] |
Successful | Successful | - | - |
| 4.26.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int e^{ax}\sin@{bx}\diff{x} = \frac{e^{ax}}{a^{2}+b^{2}}(a\sin@{bx}-b\cos@{bx})} | int(exp(a*x)*sin(b*x), x)=(exp(a*x))/((a)^(2)+ (b)^(2))*(a*sin(b*x)- b*cos(b*x)) |
Integrate[Exp[a*x]*Sin[b*x], x]=Divide[Exp[a*x],(a)^(2)+ (b)^(2)]*(a*Sin[b*x]- b*Cos[b*x]) |
Successful | Successful | - | - |
| 4.26.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int e^{ax}\cos@{bx}\diff{x} = \frac{e^{ax}}{a^{2}+b^{2}}(a\cos@{bx}+b\sin@{bx})} | int(exp(a*x)*cos(b*x), x)=(exp(a*x))/((a)^(2)+ (b)^(2))*(a*cos(b*x)+ b*sin(b*x)) |
Integrate[Exp[a*x]*Cos[b*x], x]=Divide[Exp[a*x],(a)^(2)+ (b)^(2)]*(a*Cos[b*x]+ b*Sin[b*x]) |
Successful | Successful | - | - |
| 4.26.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\sin@{mt}\sin@{nt}\diff{t} = 0} | int(sin(m*t)*sin(n*t), t = 0..Pi)= 0 |
Integrate[Sin[m*t]*Sin[n*t], {t, 0, Pi}]= 0 |
Failure | Failure | Skip | Successful |
| 4.26.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\cos@{mt}\cos@{nt}\diff{t} = 0} | int(cos(m*t)*cos(n*t), t = 0..Pi)= 0 |
Integrate[Cos[m*t]*Cos[n*t], {t, 0, Pi}]= 0 |
Failure | Failure | Skip | Successful |
| 4.26.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\sin^{2}@{nt}\diff{t} = \int_{0}^{\pi}\cos^{2}@{nt}\diff{t}} | int((sin(n*t))^(2), t = 0..Pi)= int((cos(n*t))^(2), t = 0..Pi) |
Integrate[(Sin[n*t])^(2), {t, 0, Pi}]= Integrate[(Cos[n*t])^(2), {t, 0, Pi}] |
Failure | Failure | Skip | Successful |
| 4.26.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\cos^{2}@{nt}\diff{t} = \tfrac{1}{2}\pi} | int((cos(n*t))^(2), t = 0..Pi)=(1)/(2)*Pi |
Integrate[(Cos[n*t])^(2), {t, 0, Pi}]=Divide[1,2]*Pi |
Failure | Failure | Skip | Successful |
| 4.26.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\sin@{mt}}{t}\diff{t} = \begin{cases}\frac{1}{2}\pi,&m} | int((sin(m*t))/(t), t = 0..infinity)= |
Integrate[Divide[Sin[m*t],t], {t, 0, Infinity}]= |
Error | Failure | - | Error |
| 4.26.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\sin@{t^{2}}\diff{t} = \int_{0}^{\infty}\cos@{t^{2}}\diff{t}} | int(sin((t)^(2)), t = 0..infinity)= int(cos((t)^(2)), t = 0..infinity) |
Integrate[Sin[(t)^(2)], {t, 0, Infinity}]= Integrate[Cos[(t)^(2)], {t, 0, Infinity}] |
Successful | Successful | - | - |
| 4.26.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{t^{2}}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{2}}} | int(cos((t)^(2)), t = 0..infinity)=(1)/(2)*sqrt((Pi)/(2)) |
Integrate[Cos[(t)^(2)], {t, 0, Infinity}]=Divide[1,2]*Sqrt[Divide[Pi,2]] |
Successful | Successful | - | - |
| 4.26.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\asin@@{x}\diff{x} = x\asin@@{x}+(1-x^{2})^{1/2}} | int(arcsin(x), x)= x*arcsin(x)+(1 - (x)^(2))^(1/ 2) |
Integrate[ArcSin[x], x]= x*ArcSin[x]+(1 - (x)^(2))^(1/ 2) |
Successful | Successful | - | - |
| 4.26.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\acos@@{x}\diff{x} = x\acos@@{x}-(1-x^{2})^{1/2}} | int(arccos(x), x)= x*arccos(x)-(1 - (x)^(2))^(1/ 2) |
Integrate[ArcCos[x], x]= x*ArcCos[x]-(1 - (x)^(2))^(1/ 2) |
Successful | Successful | - | - |
| 4.26.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\atan@@{x}\diff{x} = x\atan@@{x}-\tfrac{1}{2}\ln@{1+x^{2}}} | int(arctan(x), x)= x*arctan(x)-(1)/(2)*ln(1 + (x)^(2)) |
Integrate[ArcTan[x], x]= x*ArcTan[x]-Divide[1,2]*Log[1 + (x)^(2)] |
Successful | Successful | - | - |
| 4.26.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\acsc@@{x}\diff{x} = x\acsc@@{x}+\ln@{x+(x^{2}-1)^{1/2}}} | int(arccsc(x), x)= x*arccsc(x)+ ln(x +((x)^(2)- 1)^(1/ 2)) |
Integrate[ArcCsc[x], x]= x*ArcCsc[x]+ Log[x +((x)^(2)- 1)^(1/ 2)] |
Successful | Failure | - | Fail
Complex[-4.440892098500626*^-16, -1.5707963267948966] <- {Rule[x, 2]}Complex[6.661338147750939*^-16, -1.5707963267948966] <- {Rule[x, 3]} |
| 4.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\asec@@{x}\diff{x} = x\asec@@{x}-\ln@{x+(x^{2}-1)^{1/2}}} | int(arcsec(x), x)= x*arcsec(x)- ln(x +((x)^(2)- 1)^(1/ 2)) |
Integrate[ArcSec[x], x]= x*ArcSec[x]- Log[x +((x)^(2)- 1)^(1/ 2)] |
Successful | Failure | - | Fail
Complex[4.440892098500626*^-16, 1.5707963267948966] <- {Rule[x, 2]}Complex[-6.661338147750939*^-16, 1.5707963267948966] <- {Rule[x, 3]} |
| 4.26.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\acot@@{x}\diff{x} = x\acot@@{x}+\tfrac{1}{2}\ln@{1+x^{2}}} | int(arccot(x), x)= x*arccot(x)+(1)/(2)*ln(1 + (x)^(2)) |
Integrate[ArcCot[x], x]= x*ArcCot[x]+Divide[1,2]*Log[1 + (x)^(2)] |
Successful | Successful | - | - |
| 4.26.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x\asin@@{x}\diff{x} = \left(\frac{x^{2}}{2}-\frac{1}{4}\right)\asin@@{x}+\frac{x}{4}(1-x^{2})^{1/2}} | int(x*arcsin(x), x)=(((x)^(2))/(2)-(1)/(4))* arcsin(x)+(x)/(4)*(1 - (x)^(2))^(1/ 2) |
Integrate[x*ArcSin[x], x]=(Divide[(x)^(2),2]-Divide[1,4])* ArcSin[x]+Divide[x,4]*(1 - (x)^(2))^(1/ 2) |
Successful | Successful | - | - |
| 4.26.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x\acos@@{x}\diff{x} = \left(\frac{x^{2}}{2}-\frac{1}{4}\right)\acos@@{x}-\frac{x}{4}(1-x^{2})^{1/2}} | int(x*arccos(x), x)=(((x)^(2))/(2)-(1)/(4))* arccos(x)-(x)/(4)*(1 - (x)^(2))^(1/ 2) |
Integrate[x*ArcCos[x], x]=(Divide[(x)^(2),2]-Divide[1,4])* ArcCos[x]-Divide[x,4]*(1 - (x)^(2))^(1/ 2) |
Failure | Failure | Skip | Fail
0.39269908169872414 <- {Rule[x, Rational[1, 2]]} |
| 4.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{z} = \frac{e^{z}-e^{-z}}{2}} | sinh(z)=(exp(z)- exp(- z))/(2) |
Sinh[z]=Divide[Exp[z]- Exp[- z],2] |
Successful | Successful | - | - |
| 4.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z} = \frac{e^{z}+e^{-z}}{2}} | cosh(z)=(exp(z)+ exp(- z))/(2) |
Cosh[z]=Divide[Exp[z]+ Exp[- z],2] |
Successful | Successful | - | - |
| 4.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z}+\sinh@@{z} = e^{+ z}} | cosh(z)+ sinh(z)= exp(+ z) |
Cosh[z]+ Sinh[z]= Exp[+ z] |
Successful | Successful | - | - |
| 4.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z}-\sinh@@{z} = e^{- z}} | cosh(z)- sinh(z)= exp(- z) |
Cosh[z]- Sinh[z]= Exp[- z] |
Successful | Successful | - | - |
| 4.28.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}}} | tanh(z)=(sinh(z))/(cosh(z)) |
Tanh[z]=Divide[Sinh[z],Cosh[z]] |
Successful | Successful | - | - |
| 4.28.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch@@{z} = \frac{1}{\sinh@@{z}}} | csch(z)=(1)/(sinh(z)) |
Csch[z]=Divide[1,Sinh[z]] |
Successful | Successful | - | - |
| 4.28.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech@@{z} = \frac{1}{\cosh@@{z}}} | sech(z)=(1)/(cosh(z)) |
Sech[z]=Divide[1,Cosh[z]] |
Successful | Successful | - | - |
| 4.28.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{z} = \frac{1}{\tanh@@{z}}} | coth(z)=(1)/(tanh(z)) |
Coth[z]=Divide[1,Tanh[z]] |
Successful | Successful | - | - |
| 4.28.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{iz} = i\sinh@@{z}} | sin(I*z)= I*sinh(z) |
Sin[I*z]= I*Sinh[z] |
Successful | Successful | - | - |
| 4.28.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{iz} = \cosh@@{z}} | cos(I*z)= cosh(z) |
Cos[I*z]= Cosh[z] |
Successful | Successful | - | - |
| 4.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{iz} = i\tanh@@{z}} | tan(I*z)= I*tanh(z) |
Tan[I*z]= I*Tanh[z] |
Successful | Successful | - | - |
| 4.28.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@{iz} = -i\csch@@{z}} | csc(I*z)= - I*csch(z) |
Csc[I*z]= - I*Csch[z] |
Successful | Successful | - | - |
| 4.28.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{iz} = \sech@@{z}} | sec(I*z)= sech(z) |
Sec[I*z]= Sech[z] |
Successful | Successful | - | - |
| 4.28.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@{iz} = -i\coth@@{z}} | cot(I*z)= - I*coth(z) |
Cot[I*z]= - I*Coth[z] |
Successful | Successful | - | - |
| 4.31.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 0}\frac{\sinh@@{z}}{z} = 1} | limit((sinh(z))/(z), z = 0)= 1 |
Limit[Divide[Sinh[z],z], z -> 0]= 1 |
Successful | Successful | - | - |
| 4.31.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 0}\frac{\tanh@@{z}}{z} = 1} | limit((tanh(z))/(z), z = 0)= 1 |
Limit[Divide[Tanh[z],z], z -> 0]= 1 |
Successful | Successful | - | - |
| 4.31.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 0}\frac{\cosh@@{z}-1}{z^{2}} = \frac{1}{2}} | limit((cosh(z)- 1)/((z)^(2)), z = 0)=(1)/(2) |
Limit[Divide[Cosh[z]- 1,(z)^(2)], z -> 0]=Divide[1,2] |
Successful | Successful | - | - |
| 4.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{x} <= \left(\frac{\sinh@@{x}}{x}\right)^{3}} | cosh(x)< =((sinh(x))/(x))^(3) |
Cosh[x]< =(Divide[Sinh[x],x])^(3) |
Failure | Failure | Successful | Successful |
| 4.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{x}\cos@@{x} < \tanh@@{x}} | sin(x)*cos(x)< tanh(x) |
Sin[x]*Cos[x]< Tanh[x] |
Failure | Failure | Successful | Successful |
| 4.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{x} < x} | tanh(x)< x |
Tanh[x]< x |
Failure | Failure | Successful | Successful |
| 4.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cosh@@{x}-\cosh@@{y}| >= |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}} | abs(cosh(x)- cosh(y))> =abs(x - y)*sqrt(sinh(x)*sinh(y)) |
Abs[Cosh[x]- Cosh[y]]> =Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]] |
Failure | Failure | Successful | Successful |
| 4.32.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{x} <= \tfrac{1}{2}\pi\tanh@@{x}} | arctan(x)< =(1)/(2)*Pi*tanh(x) |
ArcTan[x]< =Divide[1,2]*Pi*Tanh[x] |
Failure | Failure | Successful | Successful |
| 4.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\sinh@@{z} = \cosh@@{z}} | diff(sinh(z), z)= cosh(z) |
D[Sinh[z], z]= Cosh[z] |
Successful | Successful | - | - |
| 4.34.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\cosh@@{z} = \sinh@@{z}} | diff(cosh(z), z)= sinh(z) |
D[Cosh[z], z]= Sinh[z] |
Successful | Successful | - | - |
| 4.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\tanh@@{z} = \sech^{2}@@{z}} | diff(tanh(z), z)= (sech(z))^(2) |
D[Tanh[z], z]= (Sech[z])^(2) |
Successful | Successful | - | - |
| 4.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\csch@@{z} = -\csch@@{z}\coth@@{z}} | diff(csch(z), z)= - csch(z)*coth(z) |
D[Csch[z], z]= - Csch[z]*Coth[z] |
Successful | Successful | - | - |
| 4.34.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\sech@@{z} = -\sech@@{z}\tanh@@{z}} | diff(sech(z), z)= - sech(z)*tanh(z) |
D[Sech[z], z]= - Sech[z]*Tanh[z] |
Successful | Successful | - | - |
| 4.34.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\coth@@{z} = -\csch^{2}@@{z}} | diff(coth(z), z)= - (csch(z))^(2) |
D[Coth[z], z]= - (Csch[z])^(2) |
Successful | Successful | - | - |
| 4.34.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}-a^{2}w = 0} | diff(w, [z$(2)])- (a)^(2)* w = 0 |
D[w, {z, 2}]- (a)^(2)* w = 0 |
Failure | Failure | Fail 5.656854245-5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.34.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = 1} | (diff(w, z))^(2)- (a)^(2)* (w)^(2)= 1 |
(D[w, z])^(2)- (a)^(2)* (w)^(2)= 1 |
Failure | Failure | Fail 14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}-16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.34.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{w}{z}\right)^{2}-a^{2}w^{2} = -1} | (diff(w, z))^(2)- (a)^(2)* (w)^(2)= - 1 |
(D[w, z])^(2)- (a)^(2)* (w)^(2)= - 1 |
Failure | Failure | Fail 16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}-14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}16.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-14.99999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.34.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{w}{z}+a^{2}w^{2} = 1} | diff(w, z)+ (a)^(2)* (w)^(2)= 1 |
D[w, z]+ (a)^(2)* (w)^(2)= 1 |
Failure | Failure | Fail -16.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}14.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}-16.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}14.99999998+0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-17.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}15.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.34.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = A\cosh@{az}+B\sinh@{az}} | w = A*cosh(a*z)+ B*sinh(a*z) |
w = A*Cosh[a*z]+ B*Sinh[a*z] |
Failure | Failure | Skip | Skip |
| 4.34.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = (1/a)\sinh@{az+c}} | w =(1/ a)* sinh(a*z + c) |
w =(1/ a)* Sinh[a*z + c] |
Failure | Failure | Fail 1.560620374+2.444010722*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-43.99146068-31.60984586*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}2.401710418+1.239374278*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.552876601-1.280562047*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.5606203716754656, 2.444010722839117] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-43.991460739515965, -31.609845930171662] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.4017104180648507, 1.2393742767469784] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5528766038746884, -1.2805620501609194] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.34.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = (1/a)\cosh@{az+c}} | w =(1/ a)* cosh(a*z + c) |
w =(1/ a)* Cosh[a*z + c] |
Failure | Failure | Fail 1.439486274+2.433863476*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-43.99015111-31.60804529*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}2.429374695+1.121005682*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}3.350840350+4.086833100*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.4394862722813944, 2.433863476686773] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-43.990151188366596, -31.608045369688465] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.4293746952834034, 1.121005681222388] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.350840354280354, 4.086833103365105] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.34.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = (1/a)\coth@{az+c}} | w =(1/ a)* coth(a*z + c) |
w =(1/ a)* Coth[a*z + c] |
Failure | Failure | Fail 1.029591669+1.718277978*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.060677829+1.767757934*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.083172262+1.824036919*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.765190374+1.065683009*I <- {a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.0295916694660097, 1.7182779787395532] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0606778291092909, 1.7677579338582863] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.083172262208037, 1.824036919584044] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7651903746588453, 1.065683009892447] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@{u+ v} = \sinh@@{u}\cosh@@{v}+\cosh@@{u}\sinh@@{v}} | sinh(u + v)= sinh(u)*cosh(v)+ cosh(u)*sinh(v) |
Sinh[u + v]= Sinh[u]*Cosh[v]+ Cosh[u]*Sinh[v] |
Successful | Successful | - | - |
| 4.35.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@{u- v} = \sinh@@{u}\cosh@@{v}-\cosh@@{u}\sinh@@{v}} | sinh(u - v)= sinh(u)*cosh(v)- cosh(u)*sinh(v) |
Sinh[u - v]= Sinh[u]*Cosh[v]- Cosh[u]*Sinh[v] |
Successful | Successful | - | - |
| 4.35.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{u+ v} = \cosh@@{u}\cosh@@{v}+\sinh@@{u}\sinh@@{v}} | cosh(u + v)= cosh(u)*cosh(v)+ sinh(u)*sinh(v) |
Cosh[u + v]= Cosh[u]*Cosh[v]+ Sinh[u]*Sinh[v] |
Successful | Successful | - | - |
| 4.35.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{u- v} = \cosh@@{u}\cosh@@{v}-\sinh@@{u}\sinh@@{v}} | cosh(u - v)= cosh(u)*cosh(v)- sinh(u)*sinh(v) |
Cosh[u - v]= Cosh[u]*Cosh[v]- Sinh[u]*Sinh[v] |
Successful | Successful | - | - |
| 4.35.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@{u+ v} = \frac{\tanh@@{u}+\tanh@@{v}}{1+\tanh@@{u}\tanh@@{v}}} | tanh(u + v)=(tanh(u)+ tanh(v))/(1 + tanh(u)*tanh(v)) |
Tanh[u + v]=Divide[Tanh[u]+ Tanh[v],1 + Tanh[u]*Tanh[v]] |
Successful | Successful | - | - |
| 4.35.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@{u- v} = \frac{\tanh@@{u}-\tanh@@{v}}{1-\tanh@@{u}\tanh@@{v}}} | tanh(u - v)=(tanh(u)- tanh(v))/(1 - tanh(u)*tanh(v)) |
Tanh[u - v]=Divide[Tanh[u]- Tanh[v],1 - Tanh[u]*Tanh[v]] |
Successful | Successful | - | - |
| 4.35.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@{u+ v} = \frac{+\coth@@{u}\coth@@{v}+1}{\coth@@{u}+\coth@@{v}}} | coth(u + v)=(+ coth(u)*coth(v)+ 1)/(coth(u)+ coth(v)) |
Coth[u + v]=Divide[+ Coth[u]*Coth[v]+ 1,Coth[u]+ Coth[v]] |
Successful | Successful | - | - |
| 4.35.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@{u- v} = \frac{-\coth@@{u}\coth@@{v}+1}{\coth@@{u}-\coth@@{v}}} | coth(u - v)=(- coth(u)*coth(v)+ 1)/(coth(u)- coth(v)) |
Coth[u - v]=Divide[- Coth[u]*Coth[v]+ 1,Coth[u]- Coth[v]] |
Successful | Successful | - | - |
| 4.35.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{u}+\sinh@@{v} = 2\sinh@{\frac{u+v}{2}}\cosh@{\frac{u-v}{2}}} | sinh(u)+ sinh(v)= 2*sinh((u + v)/(2))*cosh((u - v)/(2)) |
Sinh[u]+ Sinh[v]= 2*Sinh[Divide[u + v,2]]*Cosh[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.35.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{u}-\sinh@@{v} = 2\cosh@{\frac{u+v}{2}}\sinh@{\frac{u-v}{2}}} | sinh(u)- sinh(v)= 2*cosh((u + v)/(2))*sinh((u - v)/(2)) |
Sinh[u]- Sinh[v]= 2*Cosh[Divide[u + v,2]]*Sinh[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.35.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{u}+\cosh@@{v} = 2\cosh@{\frac{u+v}{2}}\cosh@{\frac{u-v}{2}}} | cosh(u)+ cosh(v)= 2*cosh((u + v)/(2))*cosh((u - v)/(2)) |
Cosh[u]+ Cosh[v]= 2*Cosh[Divide[u + v,2]]*Cosh[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.35.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{u}-\cosh@@{v} = 2\sinh@{\frac{u+v}{2}}\sinh@{\frac{u-v}{2}}} | cosh(u)- cosh(v)= 2*sinh((u + v)/(2))*sinh((u - v)/(2)) |
Cosh[u]- Cosh[v]= 2*Sinh[Divide[u + v,2]]*Sinh[Divide[u - v,2]] |
Successful | Successful | - | - |
| 4.35.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{u}+\tanh@@{v} = \frac{\sinh@{u+ v}}{\cosh@@{u}\cosh@@{v}}} | tanh(u)+ tanh(v)=(sinh(u + v))/(cosh(u)*cosh(v)) |
Tanh[u]+ Tanh[v]=Divide[Sinh[u + v],Cosh[u]*Cosh[v]] |
Successful | Successful | - | - |
| 4.35.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{u}-\tanh@@{v} = \frac{\sinh@{u- v}}{\cosh@@{u}\cosh@@{v}}} | tanh(u)- tanh(v)=(sinh(u - v))/(cosh(u)*cosh(v)) |
Tanh[u]- Tanh[v]=Divide[Sinh[u - v],Cosh[u]*Cosh[v]] |
Successful | Successful | - | - |
| 4.35.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{u}+\coth@@{v} = \frac{\sinh@{v+ u}}{\sinh@@{u}\sinh@@{v}}} | coth(u)+ coth(v)=(sinh(v + u))/(sinh(u)*sinh(v)) |
Coth[u]+ Coth[v]=Divide[Sinh[v + u],Sinh[u]*Sinh[v]] |
Successful | Successful | - | - |
| 4.35.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{u}-\coth@@{v} = \frac{\sinh@{v- u}}{\sinh@@{u}\sinh@@{v}}} | coth(u)- coth(v)=(sinh(v - u))/(sinh(u)*sinh(v)) |
Coth[u]- Coth[v]=Divide[Sinh[v - u],Sinh[u]*Sinh[v]] |
Successful | Successful | - | - |
| 4.35.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh^{2}@@{z}-\sinh^{2}@@{z} = 1} | (cosh(z))^(2)- (sinh(z))^(2)= 1 |
(Cosh[z])^(2)- (Sinh[z])^(2)= 1 |
Successful | Successful | - | - |
| 4.35.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech^{2}@@{z} = 1-\tanh^{2}@@{z}} | (sech(z))^(2)= 1 - (tanh(z))^(2) |
(Sech[z])^(2)= 1 - (Tanh[z])^(2) |
Successful | Successful | - | - |
| 4.35.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch^{2}@@{z} = \coth^{2}@@{z}-1} | (csch(z))^(2)= (coth(z))^(2)- 1 |
(Csch[z])^(2)= (Coth[z])^(2)- 1 |
Successful | Successful | - | - |
| 4.35.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sinh@@{u}\sinh@@{v} = \cosh@{u+v}-\cosh@{u-v}} | 2*sinh(u)*sinh(v)= cosh(u + v)- cosh(u - v) |
2*Sinh[u]*Sinh[v]= Cosh[u + v]- Cosh[u - v] |
Successful | Successful | - | - |
| 4.35.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\cosh@@{u}\cosh@@{v} = \cosh@{u+v}+\cosh@{u-v}} | 2*cosh(u)*cosh(v)= cosh(u + v)+ cosh(u - v) |
2*Cosh[u]*Cosh[v]= Cosh[u + v]+ Cosh[u - v] |
Successful | Successful | - | - |
| 4.35.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sinh@@{u}\cosh@@{v} = \sinh@{u+v}+\sinh@{u-v}} | 2*sinh(u)*cosh(v)= sinh(u + v)+ sinh(u - v) |
2*Sinh[u]*Cosh[v]= Sinh[u + v]+ Sinh[u - v] |
Successful | Successful | - | - |
| 4.35.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh^{2}@@{u}-\sinh^{2}@@{v} = \sinh@{u+v}\sinh@{u-v}} | (sinh(u))^(2)- (sinh(v))^(2)= sinh(u + v)*sinh(u - v) |
(Sinh[u])^(2)- (Sinh[v])^(2)= Sinh[u + v]*Sinh[u - v] |
Successful | Successful | - | - |
| 4.35.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh^{2}@@{u}-\cosh^{2}@@{v} = \sinh@{u+v}\sinh@{u-v}} | (cosh(u))^(2)- (cosh(v))^(2)= sinh(u + v)*sinh(u - v) |
(Cosh[u])^(2)- (Cosh[v])^(2)= Sinh[u + v]*Sinh[u - v] |
Successful | Successful | - | - |
| 4.35.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh^{2}@@{u}+\cosh^{2}@@{v} = \cosh@{u+v}\cosh@{u-v}} | (sinh(u))^(2)+ (cosh(v))^(2)= cosh(u + v)*cosh(u - v) |
(Sinh[u])^(2)+ (Cosh[v])^(2)= Cosh[u + v]*Cosh[u - v] |
Successful | Successful | - | - |
| 4.35.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\frac{z}{2}} = \left(\frac{\cosh@@{z}-1}{2}\right)^{1/2}} | sinh((z)/(2))=((cosh(z)- 1)/(2))^(1/ 2) |
Sinh[Divide[z,2]]=(Divide[Cosh[z]- 1,2])^(1/ 2) |
Failure | Failure | Fail -1.167010648-1.637854044*I <- {z = -2^(1/2)-I*2^(1/2)}-1.167010648+1.637854044*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.1670106484252494, -1.6378540442140963] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1670106484252494, 1.6378540442140963] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.35.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{\frac{z}{2}} = \left(\frac{\cosh@@{z}+1}{2}\right)^{1/2}} | cosh((z)/(2))=((cosh(z)+ 1)/(2))^(1/ 2) |
Cosh[Divide[z,2]]=(Divide[Cosh[z]+ 1,2])^(1/ 2) |
Failure | Failure | Successful | Successful |
| 4.35.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{\frac{z}{2}} = \left(\frac{\cosh@@{z}-1}{\cosh@@{z}+1}\right)^{1/2}} | tanh((z)/(2))=((cosh(z)- 1)/(cosh(z)+ 1))^(1/ 2) |
Tanh[Divide[z,2]]=(Divide[Cosh[z]- 1,Cosh[z]+ 1])^(1/ 2) |
Failure | Failure | Fail -1.658064547-.8463685478*I <- {z = -2^(1/2)-I*2^(1/2)}-1.658064547+.8463685478*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.6580645472823399, -0.8463685477398917] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6580645472823399, 0.8463685477398917] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.35.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{\cosh@@{z}-1}{\cosh@@{z}+1}\right)^{1/2} = \frac{\cosh@@{z}-1}{\sinh@@{z}}} | ((cosh(z)- 1)/(cosh(z)+ 1))^(1/ 2)=(cosh(z)- 1)/(sinh(z)) |
(Divide[Cosh[z]- 1,Cosh[z]+ 1])^(1/ 2)=Divide[Cosh[z]- 1,Sinh[z]] |
Failure | Failure | Fail 1.658064547+.8463685479*I <- {z = -2^(1/2)-I*2^(1/2)}1.658064547-.8463685479*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[1.6580645472823403, 0.8463685477398917] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6580645472823403, -0.8463685477398917] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 4.35.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cosh@@{z}-1}{\sinh@@{z}} = \frac{\sinh@@{z}}{\cosh@@{z}+1}} | (cosh(z)- 1)/(sinh(z))=(sinh(z))/(cosh(z)+ 1) |
Divide[Cosh[z]- 1,Sinh[z]]=Divide[Sinh[z],Cosh[z]+ 1] |
Successful | Successful | - | - |
| 4.35.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@{-z} = -\sinh@@{z}} | sinh(- z)= - sinh(z) |
Sinh[- z]= - Sinh[z] |
Successful | Successful | - | - |
| 4.35.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{-z} = \cosh@@{z}} | cosh(- z)= cosh(z) |
Cosh[- z]= Cosh[z] |
Successful | Successful | - | - |
| 4.35.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@{-z} = -\tanh@@{z}} | tanh(- z)= - tanh(z) |
Tanh[- z]= - Tanh[z] |
Successful | Successful | - | - |
| 4.35.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@{2z} = 2\sinh@@{z}\cosh@@{z}} | sinh(2*z)= 2*sinh(z)*cosh(z) |
Sinh[2*z]= 2*Sinh[z]*Cosh[z] |
Successful | Successful | - | - |
| 4.35.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sinh@@{z}\cosh@@{z} = \frac{2\tanh@@{z}}{1-\tanh^{2}@@{z}}} | 2*sinh(z)*cosh(z)=(2*tanh(z))/(1 - (tanh(z))^(2)) |
2*Sinh[z]*Cosh[z]=Divide[2*Tanh[z],1 - (Tanh[z])^(2)] |
Successful | Successful | - | - |
| 4.35.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{2z} = 2\cosh^{2}@@{z}-1} | cosh(2*z)= 2*(cosh(z))^(2)- 1 |
Cosh[2*z]= 2*(Cosh[z])^(2)- 1 |
Successful | Successful | - | - |
| 4.35.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sinh^{2}@@{z}+1\\ = \cosh^{2}@@{z}+\sinh^{2}@@{z}} | 2*(sinh(z))^(2)+ 1 = (cosh(z))^(2)+ (sinh(z))^(2) |
2*(Sinh[z])^(2)+ 1 = (Cosh[z])^(2)+ (Sinh[z])^(2) |
Error | Error | - | - |
| 4.35.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@{2z} = \frac{2\tanh@@{z}}{1+\tanh^{2}@@{z}}} | tanh(2*z)=(2*tanh(z))/(1 + (tanh(z))^(2)) |
Tanh[2*z]=Divide[2*Tanh[z],1 + (Tanh[z])^(2)] |
Successful | Successful | - | - |
| 4.35.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@{3z} = 3\sinh@@{z}+4\sinh^{3}@@{z}} | sinh(3*z)= 3*sinh(z)+ 4*(sinh(z))^(3) |
Sinh[3*z]= 3*Sinh[z]+ 4*(Sinh[z])^(3) |
Successful | Successful | - | - |
| 4.35.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{3z} = -3\cosh@@{z}+4\cosh^{3}@@{z}} | cosh(3*z)= - 3*cosh(z)+ 4*(cosh(z))^(3) |
Cosh[3*z]= - 3*Cosh[z]+ 4*(Cosh[z])^(3) |
Successful | Successful | - | - |
| 4.35.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@{4z} = 4\sinh^{3}@@{z}\cosh@@{z}+4\cosh^{3}@@{z}\sinh@@{z}} | sinh(4*z)= 4*(sinh(z))^(3)* cosh(z)+ 4*(cosh(z))^(3)* sinh(z) |
Sinh[4*z]= 4*(Sinh[z])^(3)* Cosh[z]+ 4*(Cosh[z])^(3)* Sinh[z] |
Successful | Successful | - | - |
| 4.35.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{4z} = \cosh^{4}@@{z}+6\sinh^{2}@@{z}\cosh^{2}@@{z}+\sinh^{4}@@{z}} | cosh(4*z)= (cosh(z))^(4)+ 6*(sinh(z))^(2)* (cosh(z))^(2)+ (sinh(z))^(4) |
Cosh[4*z]= (Cosh[z])^(4)+ 6*(Sinh[z])^(2)* (Cosh[z])^(2)+ (Sinh[z])^(4) |
Successful | Successful | - | - |
| 4.35.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{nz}+\sinh@{nz} = (\cosh@@{z}+\sinh@@{z})^{n}} | cosh(n*z)+ sinh(n*z)=(cosh(z)+ sinh(z))^(n) |
Cosh[n*z]+ Sinh[n*z]=(Cosh[z]+ Sinh[z])^(n) |
Successful | Failure | - | Successful |
| 4.35.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@{nz}-\sinh@{nz} = (\cosh@@{z}-\sinh@@{z})^{n}} | cosh(n*z)- sinh(n*z)=(cosh(z)- sinh(z))^(n) |
Cosh[n*z]- Sinh[n*z]=(Cosh[z]- Sinh[z])^(n) |
Successful | Failure | - | Successful |
| 4.35.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{z} = \sinh@@{x}\cos@@{y}+i\cosh@@{x}\sin@@{y}} | sinh(z)= sinh(x)*cos(y)+ I*cosh(x)*sin(y) |
Sinh[z]= Sinh[x]*Cos[y]+ I*Cosh[x]*Sin[y] |
Failure | Failure | Fail -.3332024445+.853077958*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.7908177296+.748416289*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}1.465201834+1.933775988*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-1.657839572-1.014242973*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[-0.33320244491697526, 0.8530779599233089] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7908177289090546, 0.7484162907172458] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4652018335710113, 1.933775989717134] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6578395715538454, -1.014242971876882] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z} = \cosh@@{x}\cos@@{y}+i\sinh@@{x}\sin@@{y}} | cosh(z)= cosh(x)*cos(y)+ I*sinh(x)*sin(y) |
Cosh[z]= Cosh[x]*Cos[y]+ I*Sinh[x]*Sin[y] |
Failure | Failure | Fail -.4940560329+.9224954029*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.9818221171+.842785687*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}1.867312242+1.745548707*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-1.693049015-1.140504690*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[-0.49405603343642457, 0.9224954044013453] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.9818221164102445, 0.842785688781432] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.867312241811268, 1.7455487082452315] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6930490153249411, -1.1405046889875898] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{z} = \frac{\sinh@{2x}+i\sin@{2y}}{\cosh@{2x}+\cos@{2y}}} | tanh(z)=(sinh(2*x)+ I*sin(2*y))/(cosh(2*x)+ cos(2*y)) |
Tanh[z]=Divide[Sinh[2*x]+ I*Sin[2*y],Cosh[2*x]+ Cos[2*y]] |
Failure | Failure | Fail .34450810e-1-.2308812766*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-.48362120e-1+.2843295099*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.3503564896+.1000398483*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.103580521+.705848261e-2*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[0.03445081006213968, -0.23088127675619197] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.04836211984008565, 0.28432950974904503] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.3503564901139231, 0.1000398481293705] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.1035805212542007, 0.007058482483423091] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{z} = \frac{\sinh@{2x}-i\sin@{2y}}{\cosh@{2x}-\cos@{2y}}} | coth(z)=(sinh(2*x)- I*sin(2*y))/(cosh(2*x)- cos(2*y)) |
Coth[z]=Divide[Sinh[2*x]- I*Sin[2*y],Cosh[2*x]- Cos[2*y]] |
Failure | Failure | Fail .249484083e-1+.1849879852*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.716327538e-1-.2040171895*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-.4014084428-.1323526933*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-.913666750e-1+.16417892e-3*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
Complex[0.024948408389711685, 0.18498798535387256] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.07163275379178491, -0.20401718940971514] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.401408442677776, -0.1323526931640852] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.09136667517255426, 1.6417903322245991*^-4] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sinh@@{z}| = (\sinh^{2}@@{x}+\sin^{2}@@{y})^{1/2}} | abs(sinh(z))=((sinh(x))^(2)+ (sin(y))^(2))^(1/ 2) |
Abs[Sinh[z]]=((Sinh[x])^(2)+ (Sin[y])^(2))^(1/ 2) |
Failure | Failure | Fail .727197533 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.686687095 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.988950286 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-1.550602076 <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
0.7271975341555692 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.6866870962353082 <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.9889502867617381 <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-1.5506020747613944 <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sinh^{2}@@{x}+\sin^{2}@@{y})^{1/2} = \left(\tfrac{1}{2}(\cosh@{2x}-\cos@{2y})\right)^{1/2}} | ((sinh(x))^(2)+ (sin(y))^(2))^(1/ 2)=((1)/(2)*(cosh(2*x)- cos(2*y)))^(1/ 2) |
((Sinh[x])^(2)+ (Sin[y])^(2))^(1/ 2)=(Divide[1,2]*(Cosh[2*x]- Cos[2*y]))^(1/ 2) |
Successful | Successful | - | - |
| 4.35.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cosh@@{z}| = (\sinh^{2}@@{x}+\cos^{2}@@{y})^{1/2}} | abs(cosh(z))=((sinh(x))^(2)+ (cos(y))^(2))^(1/ 2) |
Abs[Cosh[z]]=((Sinh[x])^(2)+ (Cos[y])^(2))^(1/ 2) |
Failure | Failure | Fail .647885813 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.694634194 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.404726137 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-1.725544377 <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
0.6478858145183544 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.694634195495673 <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.40472613814456393 <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-1.7255443754392632 <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.35.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sinh^{2}@@{x}+\cos^{2}@@{y})^{1/2} = \left(\tfrac{1}{2}(\cosh@{2x}+\cos@{2y})\right)^{1/2}} | ((sinh(x))^(2)+ (cos(y))^(2))^(1/ 2)=((1)/(2)*(cosh(2*x)+ cos(2*y)))^(1/ 2) |
((Sinh[x])^(2)+ (Cos[y])^(2))^(1/ 2)=(Divide[1,2]*(Cosh[2*x]+ Cos[2*y]))^(1/ 2) |
Successful | Successful | - | - |
| 4.35.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\tanh@@{z}| = \left(\frac{\cosh@{2x}-\cos@{2y}}{\cosh@{2x}+\cos@{2y}}\right)^{1/2}} | abs(tanh(z))=((cosh(2*x)- cos(2*y))/(cosh(2*x)+ cos(2*y)))^(1/ 2) |
Abs[Tanh[z]]=(Divide[Cosh[2*x]- Cos[2*y],Cosh[2*x]+ Cos[2*y]])^(1/ 2) |
Failure | Failure | Fail .1650695e-2 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-.72745631e-1 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.3488272508 <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.103763936 <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}... skip entries to safe data |
Fail
0.0016506944407532753 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-0.07274563209398122 <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.3488272498892625 <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.10376393520222194 <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.36.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{z} = z\prod_{n=1}^{\infty}\left(1+\frac{z^{2}}{n^{2}\pi^{2}}\right)} | sinh(z)= z*product(1 +((z)^(2))/((n)^(2)* (Pi)^(2)), n = 1..infinity) |
Sinh[z]= z*Product[1 +Divide[(z)^(2),(n)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Failure | Successful | Skip | - |
| 4.36.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z} = \prod_{n=1}^{\infty}\left(1+\frac{4z^{2}}{(2n-1)^{2}\pi^{2}}\right)} | cosh(z)= product(1 +(4*(z)^(2))/((2*n - 1)^(2)* (Pi)^(2)), n = 1..infinity) |
Cosh[z]= Product[1 +Divide[4*(z)^(2),(2*n - 1)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Failure | Successful | Skip | - |
| 4.36.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{z} = \frac{1}{z}+2z\sum_{n=1}^{\infty}\frac{1}{z^{2}+n^{2}\pi^{2}}} | coth(z)=(1)/(z)+ 2*z*sum((1)/((z)^(2)+ (n)^(2)* (Pi)^(2)), n = 1..infinity) |
Coth[z]=Divide[1,z]+ 2*z*Sum[Divide[1,(z)^(2)+ (n)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Successful | Successful | - | - |
| 4.36.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch^{2}@@{z} = \sum_{n=-\infty}^{\infty}\frac{1}{(z-n\pi i)^{2}}} | (csch(z))^(2)= sum((1)/((z - n*Pi*I)^(2)), n = - infinity..infinity) |
(Csch[z])^(2)= Sum[Divide[1,(z - n*Pi*I)^(2)], {n, - Infinity, Infinity}] |
Successful | Successful | - | - |
| 4.36.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch@@{z} = \frac{1}{z}+2z\sum_{n=1}^{\infty}\frac{(-1)^{n}}{z^{2}+n^{2}\pi^{2}}} | csch(z)=(1)/(z)+ 2*z*sum(((- 1)^(n))/((z)^(2)+ (n)^(2)* (Pi)^(2)), n = 1..infinity) |
Csch[z]=Divide[1,z]+ 2*z*Sum[Divide[(- 1)^(n),(z)^(2)+ (n)^(2)* (Pi)^(2)], {n, 1, Infinity}] |
Successful | Successful | - | - |
| 4.37.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@@{z} = \int_{0}^{z}\frac{\diff{t}}{(1+t^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, z}]= Integrate[Divide[1,(1 + (t)^(2))^(1/ 2)], {t, 0, z}] |
Error | Failure | - | Successful |
| 4.37.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acosh@@{z} = \int_{1}^{z}\frac{\diff{t}}{(t^{2}-1)^{1/2}}} | Error |
Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, z}]= Integrate[Divide[1,((t)^(2)- 1)^(1/ 2)], {t, 1, z}] |
Error | Failure | - | Error |
| 4.37.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@@{z} = \int_{0}^{z}\frac{\diff{t}}{1-t^{2}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, z}]= Integrate[Divide[1,1 - (t)^(2)], {t, 0, z}] |
Error | Failure | - | Successful |
| 4.37.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acsch@@{z} = \Asinh@{1/z}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, Divide[1,z]}]= Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, 1/ z}] |
Error | Failure | - | Successful |
| 4.37.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asech@@{z} = \Acosh@{1/z}} | Error |
Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, Divide[1,z]}]= Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, 1/ z}] |
Error | Failure | - | Error |
| 4.37.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acoth@@{z} = \Atanh@{1/z}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, Divide[1,z]}]= Integrate[Divide[1, 1-t^2], {t, 0, 1/ z}] |
Error | Failure | - | Successful |
| 4.37.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsch@@{z} = \asinh@{1/z}} | arccsch(z)= arcsinh(1/ z) |
ArcCsch[z]= ArcSinh[1/ z] |
Failure | Successful | Successful | - |
| 4.37.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asech@@{z} = \acosh@{1/z}} | arcsech(z)= arccosh(1/ z) |
ArcSech[z]= ArcCosh[1/ z] |
Failure | Successful | Successful | - |
| 4.37.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acoth@@{z} = \atanh@{1/z}} | arccoth(z)= arctanh(1/ z) |
ArcCoth[z]= ArcTanh[1/ z] |
Failure | Successful | Successful | - |
| 4.37.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{-z} = -\asinh@@{z}} | arcsinh(- z)= - arcsinh(z) |
ArcSinh[- z]= - ArcSinh[z] |
Successful | Successful | - | - |
| 4.37.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{-z} = +\pi i+\acosh@@{z}} | arccosh(- z)= + Pi*I + arccosh(z) |
ArcCosh[- z]= + Pi*I + ArcCosh[z] |
Failure | Failure | Error | Error |
| 4.37.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{-z} = -\pi i+\acosh@@{z}} | arccosh(- z)= - Pi*I + arccosh(z) |
ArcCosh[- z]= - Pi*I + ArcCosh[z] |
Failure | Failure | Error | Error |
| 4.37.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@{-z} = -\atanh@@{z}} | arctanh(- z)= - arctanh(z) |
ArcTanh[- z]= - ArcTanh[z] |
Successful | Successful | - | - |
| 4.37.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsch@{-z} = -\acsch@@{z}} | arccsch(- z)= - arccsch(z) |
ArcCsch[- z]= - ArcCsch[z] |
Successful | Successful | - | - |
| 4.37.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asech@{-z} = -\pi i+\asech@@{z}} | arcsech(- z)= - Pi*I + arcsech(z) |
ArcSech[- z]= - Pi*I + ArcSech[z] |
Failure | Failure | Error | Error |
| 4.37.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asech@{-z} = +\pi i+\asech@@{z}} | arcsech(- z)= + Pi*I + arcsech(z) |
ArcSech[- z]= + Pi*I + ArcSech[z] |
Failure | Failure | Error | Error |
| 4.37.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acoth@{-z} = -\acoth@@{z}} | arccoth(- z)= - arccoth(z) |
ArcCoth[- z]= - ArcCoth[z] |
Failure | Successful | Fail 0.-3.141592654*I <- {z = 1/2} |
- |
| 4.37.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@@{z} = \ln@{(z^{2}+1)^{1/2}+z}} | arcsinh(z)= ln(((z)^(2)+ 1)^(1/ 2)+ z) |
ArcSinh[z]= Log[((z)^(2)+ 1)^(1/ 2)+ z] |
Failure | Successful | Error | - |
| 4.37.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{iy} = \tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}+y}} | arcsinh(I*y)=(1)/(2)*Pi*I + ln(((y)^(2)- 1)^(1/ 2)+ y) |
ArcSinh[I*y]=Divide[1,2]*Pi*I + Log[((y)^(2)- 1)^(1/ 2)+ y] |
Failure | Failure | Error | Error |
| 4.37.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{iy} = \tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}+y}} | arcsinh(I*y)=(1)/(2)*Pi*I - ln(((y)^(2)- 1)^(1/ 2)+ y) |
ArcSinh[I*y]=Divide[1,2]*Pi*I - Log[((y)^(2)- 1)^(1/ 2)+ y] |
Failure | Failure | Error | Error |
| 4.37.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{iy} = -\tfrac{1}{2}\pi i+\ln@{(y^{2}-1)^{1/2}-y}} | arcsinh(I*y)= -(1)/(2)*Pi*I + ln(((y)^(2)- 1)^(1/ 2)- y) |
ArcSinh[I*y]= -Divide[1,2]*Pi*I + Log[((y)^(2)- 1)^(1/ 2)- y] |
Failure | Failure | Error | Error |
| 4.37.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{iy} = -\tfrac{1}{2}\pi i-\ln@{(y^{2}-1)^{1/2}-y}} | arcsinh(I*y)= -(1)/(2)*Pi*I - ln(((y)^(2)- 1)^(1/ 2)- y) |
ArcSinh[I*y]= -Divide[1,2]*Pi*I - Log[((y)^(2)- 1)^(1/ 2)- y] |
Failure | Failure | Error | Error |
| 4.37.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{z} = \ln@{+(z^{2}-1)^{1/2}+z}} | arccosh(z)= ln(+((z)^(2)- 1)^(1/ 2)+ z) |
ArcCosh[z]= Log[+((z)^(2)- 1)^(1/ 2)+ z] |
Failure | Failure | Error | Error |
| 4.37.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{z} = \ln@{-(z^{2}-1)^{1/2}+z}} | arccosh(z)= ln(-((z)^(2)- 1)^(1/ 2)+ z) |
ArcCosh[z]= Log[-((z)^(2)- 1)^(1/ 2)+ z] |
Failure | Failure | Error | Error |
| 4.37.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{\iunit y} = +\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}+ y}} | arccosh(I*y)= +(1)/(2)*Pi*I + ln(((y)^(2)+ 1)^(1/ 2)+ y) |
ArcCosh[I*y]= +Divide[1,2]*Pi*I + Log[((y)^(2)+ 1)^(1/ 2)+ y] |
Failure | Failure | Successful | Successful |
| 4.37.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{\iunit y} = -\tfrac{1}{2}\pi\iunit+\ln@{(y^{2}+1)^{1/2}- y}} | arccosh(I*y)= -(1)/(2)*Pi*I + ln(((y)^(2)+ 1)^(1/ 2)- y) |
ArcCosh[I*y]= -Divide[1,2]*Pi*I + Log[((y)^(2)+ 1)^(1/ 2)- y] |
Failure | Failure | Fail .9624236498+3.141592654*I <- {y = 1/2} |
Fail
Complex[0.9624236501192068, 3.141592653589793] <- {Rule[y, Rational[1, 2]]} |
| 4.37.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{z} = 2\ln@{\left(\frac{z+1}{2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}}} | arccosh(z)= 2*ln(((z + 1)/(2))^(1/ 2)+((z - 1)/(2))^(1/ 2)) |
ArcCosh[z]= 2*Log[(Divide[z + 1,2])^(1/ 2)+(Divide[z - 1,2])^(1/ 2)] |
Failure | Failure | Error | Error |
| 4.37.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{x} = +\ln@{i(1-x^{2})^{1/2}+x}} | arccosh(x)= + ln(I*(1 - (x)^(2))^(1/ 2)+ x) |
ArcCosh[x]= + Log[I*(1 - (x)^(2))^(1/ 2)+ x] |
Failure | Failure | Error | Error |
| 4.37.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{x} = -\ln@{i(1-x^{2})^{1/2}+x}} | arccosh(x)= - ln(I*(1 - (x)^(2))^(1/ 2)+ x) |
ArcCosh[x]= - Log[I*(1 - (x)^(2))^(1/ 2)+ x] |
Failure | Failure | Error | Error |
| 4.37.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{x} = +\pi i+\ln@{(x^{2}-1)^{1/2}-x}} | arccosh(x)= + Pi*I + ln(((x)^(2)- 1)^(1/ 2)- x) |
ArcCosh[x]= + Pi*I + Log[((x)^(2)- 1)^(1/ 2)- x] |
Failure | Failure | Error | Error |
| 4.37.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{x} = -\pi i+\ln@{(x^{2}-1)^{1/2}-x}} | arccosh(x)= - Pi*I + ln(((x)^(2)- 1)^(1/ 2)- x) |
ArcCosh[x]= - Pi*I + Log[((x)^(2)- 1)^(1/ 2)- x] |
Failure | Failure | Error | Error |
| 4.37.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@@{z} = \tfrac{1}{2}\ln@{\frac{1+z}{1-z}}} | arctanh(z)=(1)/(2)*ln((1 + z)/(1 - z)) |
ArcTanh[z]=Divide[1,2]*Log[Divide[1 + z,1 - z]] |
Failure | Failure | Error | Error |
| 4.37.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@@{x} = +\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}} | arctanh(x)= +(1)/(2)*Pi*I +(1)/(2)*ln((x + 1)/(x - 1)) |
ArcTanh[x]= +Divide[1,2]*Pi*I +Divide[1,2]*Log[Divide[x + 1,x - 1]] |
Failure | Failure | Error | Error |
| 4.37.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@@{x} = -\tfrac{1}{2}\pi i+\tfrac{1}{2}\ln@{\frac{x+1}{x-1}}} | arctanh(x)= -(1)/(2)*Pi*I +(1)/(2)*ln((x + 1)/(x - 1)) |
ArcTanh[x]= -Divide[1,2]*Pi*I +Divide[1,2]*Log[Divide[x + 1,x - 1]] |
Failure | Failure | Error | Error |
| 4.37.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \sinh@@{w}} | z = sinh(w) |
z = Sinh[w] |
Failure | Failure | Fail 1.112452092-.737321978*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.112452092-3.565749102*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.715975032-3.565749102*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.715975032-.737321978*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.1124520925053343, -0.7373219789661911] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1124520925053343, -3.565749103712381] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.715975032240856, -3.565749103712381] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.715975032240856, -0.7373219789661911] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.37.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \cosh@@{w}} | z = cosh(w) |
z = Cosh[w] |
Failure | Failure | Fail 1.074539570-.497179547*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.074539570-3.325606671*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.753887554-3.325606671*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.753887554-.497179547*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.0745395706783705, -0.4971795477911152] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0745395706783705, -3.3256066725373055] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.7538875540678198, -3.3256066725373055] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.7538875540678198, -0.4971795477911152] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.37.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \tanh@@{w}} | z = tanh(w) |
z = Tanh[w] |
Failure | Failure | Fail .295839425+1.373342253*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.295839425-1.455084871*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-2.532587699-1.455084871*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-2.532587699+1.373342253*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.2958394249722609, 1.3733422538097753] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.2958394249722609, -1.455084870936415] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5325876997739294, -1.455084870936415] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5325876997739294, 1.3733422538097753] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.37.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Asinh@@{z}} | Error |
w = Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, z}] |
Error | Failure | - | Fail
Complex[0.022188930362652126, 0.6905247538249891] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.022188930362652126, 2.1379023709212013] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.806238194383538, 2.1379023709212013] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.806238194383538, 0.6905247538249891] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.37.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@@{z} = (-1)^{k}\asinh@@{z}+k\pi i} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, z}]=(- 1)^(k)* ArcSinh[z]+ k*Pi*I |
Error | Failure | - | Fail
Complex[2.784049264020886, -1.694215036493581] <- {Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -6.283185307179586] <- {Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.784049264020886, -7.9774003436731675] <- {Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.784049264020886, -4.588970270686005] <- {Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.37.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Acosh@@{z}} | Error |
w = Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, z}] |
Error | Failure | - | Error |
| 4.37.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acosh@@{z} = +\acosh@@{z}+2k\pi i} | Error |
Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, z}]= + ArcCosh[z]+ 2*k*Pi*I |
Error | Failure | - | Error |
| 4.37.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acosh@@{z} = -\acosh@@{z}+2k\pi i} | Error |
Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, z}]= - ArcCosh[z]+ 2*k*Pi*I |
Error | Failure | - | Error |
| 4.37.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \Atanh@@{z}} | Error |
w = Integrate[Divide[1, 1-t^2], {t, 0, z}] |
Error | Failure | - | Fail
Complex[0.8649074180390404, 1.4142135623730951] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]}Complex[0.8649074180390404, -1.4142135623730951] <- {Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]}Complex[-1.96351970670715, -1.4142135623730951] <- {Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]}Complex[-1.96351970670715, 1.4142135623730951] <- {Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Rational[1, 2]]} |
| 4.37.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@@{z} = \atanh@@{z}+k\pi i} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, z}]= ArcTanh[z]+ k*Pi*I |
Error | Failure | - | Fail
Complex[0.0, -3.141592653589793] <- {Rule[k, 1], Rule[z, Rational[1, 2]]}Complex[0.0, -6.283185307179586] <- {Rule[k, 2], Rule[z, Rational[1, 2]]}Complex[0.0, -9.42477796076938] <- {Rule[k, 3], Rule[z, Rational[1, 2]]} |
| 4.38.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\asinh@@{z} = (1+z^{2})^{-1/2}} | diff(arcsinh(z), z)=(1 + (z)^(2))^(- 1/ 2) |
D[ArcSinh[z], z]=(1 + (z)^(2))^(- 1/ 2) |
Successful | Successful | - | - |
| 4.38.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acosh@@{z} = +(z^{2}-1)^{-1/2}} | diff(arccosh(z), z)= +((z)^(2)- 1)^(- 1/ 2) |
D[ArcCosh[z], z]= +((z)^(2)- 1)^(- 1/ 2) |
Failure | Failure | Successful | Successful |
| 4.38.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acosh@@{z} = -(z^{2}-1)^{-1/2}} | diff(arccosh(z), z)= -((z)^(2)- 1)^(- 1/ 2) |
D[ArcCosh[z], z]= -((z)^(2)- 1)^(- 1/ 2) |
Failure | Failure | Fail -2.309401076*I <- {z = 1/2} |
Fail
Complex[0.0, -2.3094010767585034] <- {Rule[z, Rational[1, 2]]} |
| 4.38.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\atanh@@{z} = \frac{1}{1-z^{2}}} | diff(arctanh(z), z)=(1)/(1 - (z)^(2)) |
D[ArcTanh[z], z]=Divide[1,1 - (z)^(2)] |
Successful | Successful | - | - |
| 4.38.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acsch@@{z} = -\frac{1}{z(1+z^{2})^{1/2}}} | diff(arccsch(z), z)= -(1)/(z*(1 + (z)^(2))^(1/ 2)) |
D[ArcCsch[z], z]= -Divide[1,z*(1 + (z)^(2))^(1/ 2)] |
Failure | Failure | Successful | Successful |
| 4.38.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acsch@@{z} = +\frac{1}{z(1+z^{2})^{1/2}}} | diff(arccsch(z), z)= +(1)/(z*(1 + (z)^(2))^(1/ 2)) |
D[ArcCsch[z], z]= +Divide[1,z*(1 + (z)^(2))^(1/ 2)] |
Failure | Failure | Fail -3.577708764 <- {z = 1/2} |
Fail
-3.5777087639996634 <- {Rule[z, Rational[1, 2]]} |
| 4.38.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\asech@@{z} = -\frac{1}{z(1-z^{2})^{1/2}}} | diff(arcsech(z), z)= -(1)/(z*(1 - (z)^(2))^(1/ 2)) |
D[ArcSech[z], z]= -Divide[1,z*(1 - (z)^(2))^(1/ 2)] |
Failure | Failure | Successful | Successful |
| 4.38.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\acoth@@{z} = \frac{1}{1-z^{2}}} | diff(arccoth(z), z)=(1)/(1 - (z)^(2)) |
D[ArcCoth[z], z]=Divide[1,1 - (z)^(2)] |
Successful | Successful | - | - |
| 4.38.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@@{u}+\Asinh@@{v} = \Asinh@{u(1+v^{2})^{1/2}+ v(1+u^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u}]+ Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, v}]= Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u*(1 + (v)^(2))^(1/ 2)+ v*(1 + (u)^(2))^(1/ 2)}] |
Error | Failure | - | Successful |
| 4.38.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@@{u}-\Asinh@@{v} = \Asinh@{u(1+v^{2})^{1/2}- v(1+u^{2})^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u}]- Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, v}]= Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u*(1 + (v)^(2))^(1/ 2)- v*(1 + (u)^(2))^(1/ 2)}] |
Error | Failure | - | Skip |
| 4.38.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acosh@@{u}+\Acosh@@{v} = \Acosh@{uv+((u^{2}-1)(v^{2}-1))^{1/2}}} | Error |
Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, u}]+ Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, v}]= Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, u*v +(((u)^(2)- 1)*((v)^(2)- 1))^(1/ 2)}] |
Error | Failure | - | Error |
| 4.38.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Acosh@@{u}-\Acosh@@{v} = \Acosh@{uv-((u^{2}-1)(v^{2}-1))^{1/2}}} | Error |
Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, u}]- Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, v}]= Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, u*v -(((u)^(2)- 1)*((v)^(2)- 1))^(1/ 2)}] |
Error | Failure | - | Error |
| 4.38.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@@{u}+\Atanh@@{v} = \Atanh@{\frac{u+ v}{1+ uv}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, u}]+ Integrate[Divide[1, 1-t^2], {t, 0, v}]= Integrate[Divide[1, 1-t^2], {t, 0, Divide[u + v,1 + u*v]}] |
Error | Failure | - | Skip |
| 4.38.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@@{u}-\Atanh@@{v} = \Atanh@{\frac{u- v}{1- uv}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, u}]- Integrate[Divide[1, 1-t^2], {t, 0, v}]= Integrate[Divide[1, 1-t^2], {t, 0, Divide[u - v,1 - u*v]}] |
Error | Failure | - | Fail
Complex[0.0, 1.6296538327419778] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1102230246251565*^-16, 3.141592653589793] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -3.141592653589793] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1102230246251565*^-16, -3.141592653589793] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.38.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@@{u}+\Acosh@@{v} = \Asinh@{uv+((1+u^{2})(v^{2}-1))^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u}]+ Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, v}]= Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u*v +((1 + (u)^(2))*((v)^(2)- 1))^(1/ 2)}] |
Error | Failure | - | Error |
| 4.38.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@@{u}-\Acosh@@{v} = \Asinh@{uv-((1+u^{2})(v^{2}-1))^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u}]- Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, v}]= Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u*v -((1 + (u)^(2))*((v)^(2)- 1))^(1/ 2)}] |
Error | Failure | - | Error |
| 4.38.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@{uv+((1+u^{2})(v^{2}-1))^{1/2}} = \Acosh@{v(1+u^{2})^{1/2}+ u(v^{2}-1)^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u*v +((1 + (u)^(2))*((v)^(2)- 1))^(1/ 2)}]= Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, v*(1 + (u)^(2))^(1/ 2)+ u*((v)^(2)- 1)^(1/ 2)}] |
Error | Failure | - | Error |
| 4.38.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asinh@{uv-((1+u^{2})(v^{2}-1))^{1/2}} = \Acosh@{v(1+u^{2})^{1/2}- u(v^{2}-1)^{1/2}}} | Error |
Integrate[Divide[1, (1+t^2)^(1/2)], {t, 0, u*v -((1 + (u)^(2))*((v)^(2)- 1))^(1/ 2)}]= Integrate[Divide[1, (t^2-1)^(1/2)], {t, 1, v*(1 + (u)^(2))^(1/ 2)- u*((v)^(2)- 1)^(1/ 2)}] |
Error | Failure | - | Error |
| 4.38.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@@{u}+\Acoth@@{v} = \Atanh@{\frac{uv+ 1}{v+ u}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, u}]+ Integrate[Divide[1, 1-t^2], {t, 0, Divide[1,v]}]= Integrate[Divide[1, 1-t^2], {t, 0, Divide[u*v + 1,v + u]}] |
Error | Failure | - | Skip |
| 4.38.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@@{u}-\Acoth@@{v} = \Atanh@{\frac{uv- 1}{v- u}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, u}]- Integrate[Divide[1, 1-t^2], {t, 0, Divide[1,v]}]= Integrate[Divide[1, 1-t^2], {t, 0, Divide[u*v - 1,v - u]}] |
Error | Failure | - | Fail
Complex[5.551115123125783*^-17, -1.6296538327419778] <- {Rule[u, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.282309879460564, -1.6296538327419778] <- {Rule[u, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.551115123125783*^-17, -1.6296538327419778] <- {Rule[u, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.282309879460564, 1.6296538327419778] <- {Rule[u, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[v, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} |
| 4.38.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@{\frac{uv+ 1}{v+ u}} = \Acoth@{\frac{v+ u}{uv+ 1}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, Divide[u*v + 1,v + u]}]= Integrate[Divide[1, 1-t^2], {t, 0, Divide[1,Divide[v + u,u*v + 1]]}] |
Error | Failure | - | Successful |
| 4.38.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Atanh@{\frac{uv- 1}{v- u}} = \Acoth@{\frac{v- u}{uv- 1}}} | Error |
Integrate[Divide[1, 1-t^2], {t, 0, Divide[u*v - 1,v - u]}]= Integrate[Divide[1, 1-t^2], {t, 0, Divide[1,Divide[v - u,u*v - 1]]}] |
Error | Failure | - | Error |
| 4.40.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\sinh@@{x}\diff{x} = \cosh@@{x}} | int(sinh(x), x)= cosh(x) |
Integrate[Sinh[x], x]= Cosh[x] |
Successful | Successful | - | - |
| 4.40.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\cosh@@{x}\diff{x} = \sinh@@{x}} | int(cosh(x), x)= sinh(x) |
Integrate[Cosh[x], x]= Sinh[x] |
Successful | Successful | - | - |
| 4.40.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\tanh@@{x}\diff{x} = \ln@{\cosh@@{x}}} | int(tanh(x), x)= ln(cosh(x)) |
Integrate[Tanh[x], x]= Log[Cosh[x]] |
Successful | Successful | - | - |
| 4.40.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\csch@@{x}\diff{x} = \ln@{\tanh@{\tfrac{1}{2}x}}} | int(csch(x), x)= ln(tanh((1)/(2)*x)) |
Integrate[Csch[x], x]= Log[Tanh[Divide[1,2]*x]] |
Successful | Successful | - | - |
| 4.40.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\sech@@{x}\diff{x} = \Gudermannian@{x}} | int(sech(x), x)= arctan(sinh(x)) |
Integrate[Sech[x], x]= Gudermannian[x] |
Successful | Failure | - | Successful |
| 4.40.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\coth@@{x}\diff{x} = \ln@{\sinh@@{x}}} | int(coth(x), x)= ln(sinh(x)) |
Integrate[Coth[x], x]= Log[Sinh[x]] |
Successful | Successful | - | - |
| 4.40.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-x}\frac{\sin@{ax}}{\sinh@@{x}}\diff{x} = \tfrac{1}{2}\pi\coth@{\tfrac{1}{2}\pi a}-\frac{1}{a}} | int(exp(- x)*(sin(a*x))/(sinh(x)), x = 0..infinity)=(1)/(2)*Pi*coth((1)/(2)*Pi*a)-(1)/(a) |
Integrate[Exp[- x]*Divide[Sin[a*x],Sinh[x]], {x, 0, Infinity}]=Divide[1,2]*Pi*Coth[Divide[1,2]*Pi*a]-Divide[1,a] |
Failure | Failure | Skip | Successful |
| 4.40.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\sinh@{ax}}{\sinh@{\pi x}}\diff{x} = \tfrac{1}{2}\tan@{\tfrac{1}{2}a}} | int((sinh(a*x))/(sinh(Pi*x)), x = 0..infinity)=(1)/(2)*tan((1)/(2)*a) |
Integrate[Divide[Sinh[a*x],Sinh[Pi*x]], {x, 0, Infinity}]=Divide[1,2]*Tan[Divide[1,2]*a] |
Failure | Failure | Skip | Successful |
| 4.40.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\frac{e^{ax}}{\left(\cosh@{\tfrac{1}{2}x}\right)^{2}}\diff{x} = \frac{4\pi a}{\sin@{\pi a}}} | int((exp(a*x))/((cosh((1)/(2)*x))^(2)), x = - infinity..infinity)=(4*Pi*a)/(sin(Pi*a)) |
Integrate[Divide[Exp[a*x],(Cosh[Divide[1,2]*x])^(2)], {x, - Infinity, Infinity}]=Divide[4*Pi*a,Sin[Pi*a]] |
Failure | Failure | Skip | Skip |
| 4.40.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\asinh@@{x}\diff{x} = x\asinh@@{x}-(1+x^{2})^{1/2}} | int(arcsinh(x), x)= x*arcsinh(x)-(1 + (x)^(2))^(1/ 2) |
Integrate[ArcSinh[x], x]= x*ArcSinh[x]-(1 + (x)^(2))^(1/ 2) |
Successful | Successful | - | - |
| 4.40.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\acosh@@{x}\diff{x} = x\acosh@@{x}-(x^{2}-1)^{1/2}} | int(arccosh(x), x)= x*arccosh(x)-((x)^(2)- 1)^(1/ 2) |
Integrate[ArcCosh[x], x]= x*ArcCosh[x]-((x)^(2)- 1)^(1/ 2) |
Failure | Successful | Skip | - |
| 4.40.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\atanh@@{x}\diff{x} = x\atanh@@{x}+\tfrac{1}{2}\ln@{1-x^{2}}} | int(arctanh(x), x)= x*arctanh(x)+(1)/(2)*ln(1 - (x)^(2)) |
Integrate[ArcTanh[x], x]= x*ArcTanh[x]+Divide[1,2]*Log[1 - (x)^(2)] |
Successful | Successful | - | - |
| 4.40.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\acsch@@{x}\diff{x} = x\acsch@@{x}+\asinh@@{x}} | int(arccsch(x), x)= x*arccsch(x)+ arcsinh(x) |
Integrate[ArcCsch[x], x]= x*ArcCsch[x]+ ArcSinh[x] |
Failure | Successful | Skip | - |
| 4.40.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\asech@@{x}\diff{x} = x\asech@@{x}+\asin@@{x}} | int(arcsech(x), x)= x*arcsech(x)+ arcsin(x) |
Integrate[ArcSech[x], x]= x*ArcSech[x]+ ArcSin[x] |
Failure | Successful | Skip | - |
| 4.40.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\acoth@@{x}\diff{x} = x\acoth@@{x}+\tfrac{1}{2}\ln@{x^{2}-1}} | int(arccoth(x), x)= x*arccoth(x)+(1)/(2)*ln((x)^(2)- 1) |
Integrate[ArcCoth[x], x]= x*ArcCoth[x]+Divide[1,2]*Log[(x)^(2)- 1] |
Successful | Failure | - | Fail
Complex[0.0, 1.5707963267948966] <- {Rule[x, 2]}Complex[0.0, 1.5707963267948966] <- {Rule[x, 3]} |
| 4.42.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{A} = \frac{a}{c}} | sin(A)=(a)/(c) |
Sin[A]=Divide[a,c] |
Failure | Failure | Fail 1.151535540+.3017614705*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}2.151535540-.6982385295*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}3.151535540+.3017614705*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}2.151535540+1.301761470*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.1515355413392863, 0.30176146986776087] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.1515355413392863, -0.6982385301322391] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.1515355413392863, 0.30176146986776087] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.1515355413392863, 1.3017614698677609] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{a}{c} = \frac{1}{\csc@@{A}}} | (a)/(c)=(1)/(csc(A)) |
Divide[a,c]=Divide[1,Csc[A]] |
Failure | Failure | Fail -1.151535541-.3017614705*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}-2.151535541+.6982385295*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}-3.151535541-.3017614705*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}-2.151535541-1.301761470*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-1.1515355413392863, -0.30176146986776087] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.1515355413392863, 0.6982385301322391] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.1515355413392863, -0.30176146986776087] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.1515355413392863, -1.3017614698677609] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{A} = \frac{b}{c}} | cos(A)=(b)/(c) |
Cos[A]=Divide[b,c] |
Failure | Failure | Fail -.6603260076-1.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}.3396739924-2.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}1.339673992-1.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}.3396739924-.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.6603260083052754, -1.9113931101642103] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.33967399169472456, -2.9113931101642105] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.3396739916947245, -1.9113931101642103] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.33967399169472456, -0.9113931101642103] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{b}{c} = \frac{1}{\sec@@{A}}} | (b)/(c)=(1)/(sec(A)) |
Divide[b,c]=Divide[1,Sec[A]] |
Failure | Failure | Fail .6603260076+1.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}-.3396739924+2.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}-1.339673992+1.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}-.3396739924+.911393109*I <- {A = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.6603260083052754, 1.9113931101642103] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.33967399169472456, 2.9113931101642105] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.3396739916947245, 1.9113931101642103] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.33967399169472456, 0.9113931101642103] <- {Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{A} = \frac{a}{b}} | tan(A)=(a)/(b) |
Tan[A]=Divide[a,b] |
Failure | Failure | Fail -.9591286913+1.118374137*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2)}.4087130869e-1+.118374137*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2)}1.040871309+1.118374137*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2)}.4087130869e-1+2.118374137*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.9591286914366802, 1.1183741374008342] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.04087130856331978, 0.11837413740083425] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0408713085633199, 1.1183741374008342] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.04087130856331978, 2.118374137400834] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{a}{b} = \frac{1}{\cot@@{A}}} | (a)/(b)=(1)/(cot(A)) |
Divide[a,b]=Divide[1,Cot[A]] |
Failure | Failure | Fail .9591286913-1.118374138*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2)}-.4087130870e-1-.118374138*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2)}-1.040871309-1.118374138*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2)}-.4087130870e-1-2.118374138*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.9591286914366802, -1.1183741374008342] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.04087130856331978, -0.11837413740083425] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0408713085633199, -1.1183741374008342] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.04087130856331978, -2.118374137400834] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{a}{\sin@@{A}} = \frac{b}{\sin@@{B}}} | (a)/(sin(A))=(b)/(sin(B)) |
Divide[a,Sin[A]]=Divide[b,Sin[B]] |
Failure | Failure | Fail .1808221319+1.289247572*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2)}1.470069704+1.108425440*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2)}1.289247572-.1808221319*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2)}-.1808221319-1.289247572*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.18082213138216385, -0.18082213138216385] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4700697033135184, 1.1084254405491907] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.2892475719313545, 1.2892475719313545] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.18082213138216377, 1.2892475719313545] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{b}{\sin@@{B}} = \frac{c}{\sin@@{C}}} | (b)/(sin(B))=(c)/(sin(C)) |
Divide[b,Sin[B]]=Divide[c,Sin[C]] |
Failure | Failure | Fail .1808221319+1.289247572*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}1.470069704+1.108425440*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}1.289247572-.1808221319*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}-.1808221319-1.289247572*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.18082213138216385, -0.18082213138216385] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4700697033135184, 1.1084254405491907] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.2892475719313545, 1.2892475719313545] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.18082213138216377, 1.2892475719313545] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c^{2} = a^{2}+b^{2}-2ab\cos@@{C}} | (c)^(2)= (a)^(2)+ (b)^(2)- 2*a*b*cos(C) |
(c)^(2)= (a)^(2)+ (b)^(2)- 2*a*b*Cos[C] |
Failure | Failure | Fail 15.29114486-1.282608060*I <- {C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}15.29114486-9.282608052*I <- {C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}15.29114486-1.282608060*I <- {C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}15.29114486-9.282608052*I <- {C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[15.291144881313683, -1.2826080664422035] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-15.291144881313683, -1.2826080664422035] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[15.291144881313683, -1.2826080664422035] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-15.291144881313683, -1.2826080664422035] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = b\cos@@{C}+c\cos@@{B}} | a = b*cos(C)+ c*cos(B) |
a = b*Cos[C]+ c*Cos[B] |
Failure | Failure | Skip | Skip |
| 4.42.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hbox{area} = \tfrac{1}{2}bc\sin@@{A}} | a*r*exp(1)*a*=(1)/(2)*b*c*sin(A) |
a*r*E*a*=Divide[1,2]*b*c*Sin[A] |
Failure | Failure | Skip | Skip |
| 4.42.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}bc\sin@@{A} = \left(s(s-a)(s-b)(s-c)\right)^{1/2}} | (1)/(2)*b*c*sin(A)=(s*(s - a)*(s - b)*(s - c))^(1/ 2) |
Divide[1,2]*b*c*Sin[A]=(s*(s - a)*(s - b)*(s - c))^(1/ 2) |
Failure | Failure | Skip | Skip |
| 4.42.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{a} = \cos@@{b}\cos@@{c}+\sin@@{b}\sin@@{c}\cos@@{A}} | cos(a)= cos(b)*cos(c)+ sin(b)*sin(c)*cos(A) |
Cos[a]= Cos[b]*Cos[c]+ Sin[b]*Sin[c]*Cos[A] |
Failure | Failure | Fail -.145682713+7.620029224*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}-5.032445392+7.110698060*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}7.901121089-8.845813328*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}-1.825810700-10.93348428*I <- {A = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.14568270504338976, 7.6200292388764925] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.032445395391095, 7.11069807526626] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.901121090331609, -8.845813349495826] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8258107056535384, -10.933484295594681] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{A}}{\sin@@{a}} = \frac{\sin@@{B}}{\sin@@{b}}} | (sin(A))/(sin(a))=(sin(B))/(sin(b)) |
Divide[Sin[A],Sin[a]]=Divide[Sin[B],Sin[b]] |
Failure | Failure | Fail .385833893e-1-.2750965298*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2)}2. <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2)}1.961416611+.2750965298*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2)}-.385833893e-1+.2750965298*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.03858338910209658, 0.2750965290395158] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}2.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.9614166108979034, -0.2750965290395158] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.03858338910209658, -0.2750965290395158] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{B}}{\sin@@{b}} = \frac{\sin@@{C}}{\sin@@{c}}} | (sin(B))/(sin(b))=(sin(C))/(sin(c)) |
Divide[Sin[B],Sin[b]]=Divide[Sin[C],Sin[c]] |
Failure | Failure | Fail .385833893e-1-.2750965298*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2)}2. <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2)}1.961416611+.2750965298*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2)}-.385833893e-1+.2750965298*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), c = 2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.03858338910209658, 0.2750965290395158] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}2.0 <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.9614166108979034, -0.2750965290395158] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.03858338910209658, -0.2750965290395158] <- {Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{a}\cos@@{B} = \cos@@{b}\sin@@{c}-\sin@@{b}\cos@@{c}\cos@@{A}} | sin(a)*cos(B)= cos(b)*sin(c)- sin(b)*cos(c)*cos(A) |
Sin[a]*Cos[B]= Cos[b]*Sin[c]- Sin[b]*Cos[c]*Cos[A] |
Failure | Failure | Skip | Skip |
| 4.42.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{a}\cos@@{C} = \sin@@{a}\cot@@{b}-\sin@@{C}\cot@@{B}} | cos(a)*cos(C)= sin(a)*cot(b)- sin(C)*cot(B) |
Cos[a]*Cos[C]= Sin[a]*Cot[b]- Sin[C]*Cot[B] |
Failure | Failure | Fail -3.538045196-1.298501057*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2)}-2.999121811-5.140982387*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2)}-2.858697211-5.121287275*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2)}-3.397620597-1.278805945*I <- {B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-3.538045200949385, -1.2985010548545435] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.229878658191402, -0.019695112023684347] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.217393184338834, 2.524285165473877] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.628377442853231, 3.842481332352105] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.42.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{A} = -\cos@@{B}\cos@@{C}+\sin@@{B}\sin@@{C}\cos@@{a}} | cos(A)= - cos(B)*cos(C)+ sin(B)*sin(C)*cos(a) |
Cos[A]= - Cos[B]*Cos[C]+ Sin[B]*Sin[C]*Cos[a] |
Failure | Failure | Fail -7.221773105+5.023027110*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)+I*2^(1/2)}-2.257881161-12.32494952*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = 2^(1/2)-I*2^(1/2)}-7.221773105+5.023027110*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = -2^(1/2)-I*2^(1/2)}-2.257881161-12.32494952*I <- {A = 2^(1/2)+I*2^(1/2), B = 2^(1/2)+I*2^(1/2), C = 2^(1/2)+I*2^(1/2), a = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-7.22177310694216, 5.023027129167406] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.5051586890429873, 7.11069807526626] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.8250306884328387, -11.442815459204912] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.711793378780543, -10.933484295594681] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[A, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[B, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[C, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{x} = 2^{m}\ln@{1+y}} | ln(x)= (2)^(m)* ln(1 + y) |
Log[x]= (2)^(m)* Log[1 + y] |
Failure | Failure | Fail -1.386294361 <- {m = 1, x = 1, y = 1}-2.197224578 <- {m = 1, x = 1, y = 2}-2.772588722 <- {m = 1, x = 1, y = 3}-.6931471804 <- {m = 1, x = 2, y = 1}... skip entries to safe data |
Fail
-1.3862943611198906 <- {Rule[m, 1], Rule[x, 1], Rule[y, 1]}-2.1972245773362196 <- {Rule[m, 1], Rule[x, 1], Rule[y, 2]}-2.772588722239781 <- {Rule[m, 1], Rule[x, 1], Rule[y, 3]}-0.6931471805599453 <- {Rule[m, 1], Rule[x, 2], Rule[y, 1]}... skip entries to safe data |
| 4.45.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{x} = \ln@@{\xi}+m\ln@@{10}} | ln(x)= ln(xi)+ m*ln(10) |
Log[x]= Log[\[Xi]]+ m*Log[10] |
Failure | Failure | Fail -2.995732273-.7853981634*I <- {xi = 2^(1/2)+I*2^(1/2), m = 1, x = 1}-2.302585093-.7853981634*I <- {xi = 2^(1/2)+I*2^(1/2), m = 1, x = 2}-1.897119984-.7853981634*I <- {xi = 2^(1/2)+I*2^(1/2), m = 1, x = 3}-5.298317366-.7853981634*I <- {xi = 2^(1/2)+I*2^(1/2), m = 2, x = 1}... skip entries to safe data |
Fail
Complex[-2.9957322735539913, -0.7853981633974483] <- {Rule[m, 1], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.302585092994046, -0.7853981633974483] <- {Rule[m, 1], Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.8971199848858813, -0.7853981633974483] <- {Rule[m, 1], Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.298317366548037, -0.7853981633974483] <- {Rule[m, 2], Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.45#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m = \floor{\frac{x}{\ln@@{10}}+\frac{1}{2}}} | m = floor((x)/(ln(10))+(1)/(2)) |
m = Floor[Divide[x,Log[10]]+Divide[1,2]] |
Failure | Failure | Fail 1. <- {m = 1, x = 1}2. <- {m = 2, x = 1}1. <- {m = 2, x = 2}1. <- {m = 2, x = 3}... skip entries to safe data |
Fail
1.0 <- {Rule[m, 1], Rule[x, 1]}2.0 <- {Rule[m, 2], Rule[x, 1]}1.0 <- {Rule[m, 2], Rule[x, 2]}1.0 <- {Rule[m, 2], Rule[x, 3]}... skip entries to safe data |
| 4.45#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = x-m\ln@@{10}} | y = x - m*ln(10) |
y = x - m*Log[10] |
Failure | Failure | Fail 2.302585093 <- {m = 1, x = 1, y = 1}3.302585093 <- {m = 1, x = 1, y = 2}4.302585093 <- {m = 1, x = 1, y = 3}1.302585093 <- {m = 1, x = 2, y = 1}... skip entries to safe data |
Fail
2.302585092994046 <- {Rule[m, 1], Rule[x, 1], Rule[y, 1]}3.302585092994046 <- {Rule[m, 1], Rule[x, 1], Rule[y, 2]}4.302585092994046 <- {Rule[m, 1], Rule[x, 1], Rule[y, 3]}1.302585092994046 <- {Rule[m, 1], Rule[x, 2], Rule[y, 1]}... skip entries to safe data |
| 4.45#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m = \floor{\xi+\tfrac{1}{2}}} | m = floor(xi +(1)/(2)) |
m = Floor[\[Xi]+Divide[1,2]] |
Failure | Failure | Fail -1.-1.*I <- {xi = 2^(1/2)+I*2^(1/2), m = 1}0.-1.*I <- {xi = 2^(1/2)+I*2^(1/2), m = 2}1.-1.*I <- {xi = 2^(1/2)+I*2^(1/2), m = 3}-1.+2.*I <- {xi = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Fail
Complex[0.0, -1.0] <- {Rule[m, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[m, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.0, -1.0] <- {Rule[m, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.0] <- {Rule[m, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.45#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{x} = (-1)^{m}\sin@@{\theta}} | sin(x)=(- 1)^(m)* sin(theta) |
Sin[x]=(- 1)^(m)* Sin[\[Theta]] |
Failure | Failure | Fail 2.993006525+.3017614705*I <- {theta = 2^(1/2)+I*2^(1/2), m = 1, x = 1}3.060832967+.3017614705*I <- {theta = 2^(1/2)+I*2^(1/2), m = 1, x = 2}2.292655548+.3017614705*I <- {theta = 2^(1/2)+I*2^(1/2), m = 1, x = 3}-1.310064555-.3017614705*I <- {theta = 2^(1/2)+I*2^(1/2), m = 2, x = 1}... skip entries to safe data |
Fail
Complex[2.993006526147183, 0.30176146986776087] <- {Rule[m, 1], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.060832968164968, 0.30176146986776087] <- {Rule[m, 1], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.2926555493991536, 0.30176146986776087] <- {Rule[m, 1], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.3100645565313898, -0.30176146986776087] <- {Rule[m, 2], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.45#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{x} = (-1)^{m}\cos@@{\theta}} | cos(x)=(- 1)^(m)* cos(theta) |
Cos[x]=(- 1)^(m)* Cos[\[Theta]] |
Failure | Failure | Fail .8799762983-1.911393109*I <- {theta = 2^(1/2)+I*2^(1/2), m = 1, x = 1}-.764728441e-1-1.911393109*I <- {theta = 2^(1/2)+I*2^(1/2), m = 1, x = 2}-.6503185042-1.911393109*I <- {theta = 2^(1/2)+I*2^(1/2), m = 1, x = 3}.2006283135+1.911393109*I <- {theta = 2^(1/2)+I*2^(1/2), m = 2, x = 1}... skip entries to safe data |
Fail
Complex[0.8799762975628643, -1.9113931101642103] <- {Rule[m, 1], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.07647284485241784, -1.9113931101642103] <- {Rule[m, 1], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6503185049057209, -1.9113931101642103] <- {Rule[m, 1], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.2006283141734152, 1.9113931101642103] <- {Rule[m, 2], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 4.45.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\atan@@{\frac{x}{1+(1+x^{2})^{1/2}}} = \atan@@{x}} | 2*arctan((x)/(1 +(1 + (x)^(2))^(1/ 2)))= arctan(x) |
2*ArcTan[Divide[x,1 +(1 + (x)^(2))^(1/ 2)]]= ArcTan[x] |
Successful | Failure | - | Successful |
| 4.45.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{x} = 2^{n}\atan@@{x_{n}}} | arctan(x)= (2)^(n)* arctan(x[n]) |
ArcTan[x]= (2)^(n)* ArcTan[Subscript[x, n]] |
Failure | Failure | Fail -1.600225078-.6411549398*I <- {x[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 1}-1.278474524-.6411549398*I <- {x[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 2}-1.136577470-.6411549398*I <- {x[n] = 2^(1/2)+I*2^(1/2), n = 1, x = 3}-3.985848320-1.282309880*I <- {x[n] = 2^(1/2)+I*2^(1/2), n = 2, x = 1}... skip entries to safe data |
Successful |
| 4.45.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{x} = 16\atan@@{x_{4}}} | arctan(x)= 16*arctan(x[4]) |
ArcTan[x]= 16*ArcTan[Subscript[x, 4]] |
Failure | Failure | Fail -18.29958778-5.129239518*I <- {x[4] = 2^(1/2)+I*2^(1/2), x = 1}-17.97783722-5.129239518*I <- {x[4] = 2^(1/2)+I*2^(1/2), x = 2}-17.83594017-5.129239518*I <- {x[4] = 2^(1/2)+I*2^(1/2), x = 3}-18.29958778+5.129239518*I <- {x[4] = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Successful |
| 4.45.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{z} = \ln@@{|z|}+i\phase@@{z}} | ln(z)= ln(abs(z))+ I*argument(z) |
Log[z]= Log[Abs[z]]+ I*Arg[z] |
Failure | Successful | Skip | - |
| 4.45.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z} = e^{\realpart@@{z}}(\cos@{\imagpart@@{z}}+i\sin@{\imagpart@@{z}})} | exp(z)= exp(Re(z))*(cos(Im(z))+ I*sin(Im(z))) |
Exp[z]= Exp[Re[z]]*(Cos[Im[z]]+ I*Sin[Im[z]]) |
Failure | Successful | Successful | - |