Results of Weierstrass Elliptic and Modular Functions
DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|
23.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega_{1}+\omega_{2}+\omega_{3} = 0} | omega[1]+ omega[2]+ omega[3] = 0 |
Subscript[\[Omega], 1]+ Subscript[\[Omega], 2]+ Subscript[\[Omega], 3] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \chi_{1} = a\omega_{1}+b\omega_{3}} | chi[1] = a*omega[1]+ b*omega[3] |
Subscript[\[Chi], 1] == a*Subscript[\[Omega], 1]+ b*Subscript[\[Omega], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \chi_{3} = c\omega_{1}+d\omega_{3}} | chi[3] = c*omega[1]+ d*omega[3] |
Subscript[\[Chi], 3] == c*Subscript[\[Omega], 1]+ d*Subscript[\[Omega], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ad-bc = 1} | a*d - b*c = 1 |
a*d - b*c == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1}+\eta_{2}+\eta_{3} = 0} | eta[1]+ eta[2]+ eta[3] = 0 |
Subscript[\[Eta], 1]+ Subscript[\[Eta], 2]+ Subscript[\[Eta], 3] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{3}\omega_{2}-\eta_{2}\omega_{3} = \eta_{2}\omega_{1}-\eta_{1}\omega_{2}} | eta[3]*omega[2]- eta[2]*omega[3] = eta[2]*omega[1]- eta[1]*omega[2] |
Subscript[\[Eta], 3]*Subscript[\[Omega], 2]- Subscript[\[Eta], 2]*Subscript[\[Omega], 3] == Subscript[\[Eta], 2]*Subscript[\[Omega], 1]- Subscript[\[Eta], 1]*Subscript[\[Omega], 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = i\eta_{3}} | eta[1] = I*eta[3] |
Subscript[\[Eta], 1] == I*Subscript[\[Eta], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = \tfrac{1}{2}} | (k)^(2) = (1)/(2) |
(k)^(2) == Divide[1,2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \compellintKk'@{k}} | EllipticK(k) = diff( EllipticK(k), k$(1) ) |
EllipticK[(k)^2] == D[EllipticK[(k)^2], {k, 1}] |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]} Complex[1.3320292471861073, -1.3934110303935494] <- {Rule[k, 2]} |
23.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk'@{k} = \ifrac{\left(\EulerGamma@{\tfrac{1}{4}}\right)^{2}}{\left(4\sqrt{\pi}\right)}} | diff( EllipticK(k), k$(1) ) = ((GAMMA((1)/(4)))^(2))/(4*sqrt(Pi)) |
D[EllipticK[(k)^2], {k, 1}] == Divide[(Gamma[Divide[1,4]])^(2),4*Sqrt[Pi]] |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]} Complex[-2.343228747081181, 0.3151532066437278] <- {Rule[k, 2]} |
23.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = e^{\pi i/3}\eta_{3}} | eta[1] = exp(Pi*I/ 3)*eta[3] |
Subscript[\[Eta], 1] == Exp[Pi*I/ 3]*Subscript[\[Eta], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.5#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = e^{\iunit\pi/3}} | (k)^(2) = exp(I*Pi/ 3) |
(k)^(2) == Exp[I*Pi/ 3] |
Failure | Failure | Failed [3 / 3] 3/3]: [[.5000000000-.8660254040*I <- {k = 1} 3.500000000-.8660254040*I <- {k = 2} |
Failed [3 / 3]
{Complex[0.4999999999999999, -0.8660254037844386] <- {Rule[k, 1]} Complex[3.5, -0.8660254037844386] <- {Rule[k, 2]} |
23.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = e^{\iunit\pi/6}\compellintKk'@{k}} | EllipticK(k) = exp(I*Pi/ 6)*diff( EllipticK(k), k$(1) ) |
EllipticK[(k)^2] == Exp[I*Pi/ 6]*D[EllipticK[(k)^2], {k, 1}] |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]} Complex[1.4240716315220228, -1.1066114718975122] <- {Rule[k, 2]} |
23.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\iunit\pi/6}\compellintKk'@{k} = e^{\iunit\pi/12}\frac{3^{1/4}\left(\EulerGamma@{\frac{1}{3}}\right)^{3}}{2^{7/3}\pi}} | exp(I*Pi/ 6)*diff( EllipticK(k), k$(1) ) = exp(I*Pi/ 12)*((3)^(1/ 4)*(GAMMA((1)/(3)))^(3))/((2)^(7/ 3)* Pi) |
Exp[I*Pi/ 6]*D[EllipticK[(k)^2], {k, 1}] == Exp[I*Pi/ 12]*Divide[(3)^(1/ 4)*(Gamma[Divide[1,3]])^(3),(2)^(7/ 3)* Pi] |
Failure | Failure | Error | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]} Complex[-2.1248830880335463, -0.38527593877730804] <- {Rule[k, 2]} |
23.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = e^{i\pi\tau}} | q = exp(I*Pi*tau) |
q == Exp[I*Pi*\[Tau]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.6#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = \omega_{3}/\omega_{1}} | tau = omega[3]/ omega[1] |
\[Tau] == Subscript[\[Omega], 3]/ Subscript[\[Omega], 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = -\frac{\pi^{2}}{12\omega_{1}}\frac{\Jacobithetaq{1}'''@{0}{q}}{\Jacobithetaq{1}'@{0}{q}}} | eta[1] = -((Pi)^(2))/(12*omega[1])*(diff( JacobiTheta1(0, q), 0$(3) ))/(diff( JacobiTheta1(0, q), 0$(1) )) |
Subscript[\[Eta], 1] == -Divide[(Pi)^(2),12*Subscript[\[Omega], 1]]*Divide[D[EllipticTheta[1, 0, q], {0, 3}],D[EllipticTheta[1, 0, q], {0, 1}]] |
Error | Failure | - | Failed [300 / 300]
{Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[0.712277344720507, -0.4112335167120565], Power[D[0.0 <- {0.0, 1.0}], -1], D[0.0, {0.0, 3.0}]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-0.4112335167120564, -0.712277344720507], Power[D[0.0 <- {0.0, 1.0}], -1], D[0.0, {0.0, 3.0}]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} <b |
23.6#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk^{2}@@{k} = (\compellintKk@{k})^{2}} | (EllipticK(k))^(2) = (EllipticK(k))^(2) |
(EllipticK[(k)^2])^(2) == (EllipticK[(k)^2])^(2) |
Successful | Successful | - | Successful [Tested: 3] |
23.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = \frac{\pi^{2}}{2\omega_{1}}\left(\frac{1}{6}+\sum_{n=1}^{\infty}\csc^{2}@{\frac{n\pi\omega_{3}}{\omega_{1}}}\right)} | eta[1] = ((Pi)^(2))/(2*omega[1])*((1)/(6)+ sum((csc((n*Pi*omega[3])/(omega[1])))^(2), n = 1..infinity)) |
Subscript[\[Eta], 1] == Divide[(Pi)^(2),2*Subscript[\[Omega], 1]]*(Divide[1,6]+ Sum[(Csc[Divide[n*Pi*Subscript[\[Omega], 3],Subscript[\[Omega], 1]]])^(2), {n, 1, Infinity}, GenerateConditions->None]) |
Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
23.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}} | c[n] = (3)/((2*n + 1)*(n - 3))*sum(c[m]*c[n - m], m = 2..n - 2) |
Subscript[c, n] == Divide[3,(2*n + 1)*(n - 3)]*Sum[Subscript[c, m]*Subscript[c, n - m], {m, 2, n - 2}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}} | a[m , n] = 3*(m + 1)* a[m + 1 , n - 1]+(16)/(3)*(n + 1)* a[m - 2 , n + 1]-(1)/(3)*(2*m + 3*n - 1)*(4*m + 6*n - 1)* a[m - 1 , n] |
Subscript[a, m , n] == 3*(m + 1)* Subscript[a, m + 1 , n - 1]+Divide[16,3]*(n + 1)* Subscript[a, m - 2 , n + 1]-Divide[1,3]*(2*m + 3*n - 1)*(4*m + 6*n - 1)* Subscript[a, m - 1 , n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.10.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}} | A[n] = exp(-((n - 1)* eta[1])/(3*omega[1])*((2*n - 1)*(omega(omega[1])^(2)+ omega(omega[3])^(2))+ 3*(n - 1)*omega[1]*omega[3])) |
Subscript[A, n] == Exp[-Divide[(n - 1)* Subscript[\[Eta], 1],3*Subscript[\[Omega], 1]]*((2*n - 1)*(\[Omega](Subscript[\[Omega], 1])^(2)+ \[Omega](Subscript[\[Omega], 3])^(2))+ 3*(n - 1)*Subscript[\[Omega], 1]*Subscript[\[Omega], 3])] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.1339745960+.5000000000*I <- {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 1} 1.057001493+.6153915143*I <- {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 2} |
Skipped - Because timed out |
23.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = e^{\pi i\omega_{3}/\omega_{1}}} | q = exp(Pi*I*omega[3]/ omega[1]) |
q == Exp[Pi*I*Subscript[\[Omega], 3]/ Subscript[\[Omega], 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle G = \prod_{n=1}^{\infty}(1-q^{2n})} | G = product(1 - (q)^(2*n), n = 1..infinity) |
G == Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.11#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(s,\tau) = \frac{\cosh^{2}@{\tfrac{1}{2}\tau s}}{1-2e^{-s}\cosh@{\tau s}+e^{-2s}}} | f[1]*(s , tau) = ((cosh((1)/(2)*tau*s))^(2))/(1 - 2*exp(- s)*cosh(tau*s)+ exp(- 2*s)) |
Subscript[f, 1]*(s , \[Tau]) == Divide[(Cosh[Divide[1,2]*\[Tau]*s])^(2),1 - 2*Exp[- s]*Cosh[\[Tau]*s]+ Exp[- 2*s]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[(.8660254040+.5000000000*I)*(-1.500000000, .8660254040+.5000000000*I)-.2283852288e-1-.9974318068e-1*I <- {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I} (-.5000000000+.8660254040*I)*(-1.500000000, .8660254040+.5000000000*I)-.2283852288e-1-.9974318068e-1*I <- {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[1] = -1/2+1/2*I*3^(1/2)} |
Error |
23.11#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(s,\tau) = \frac{\cos^{2}@{\tfrac{1}{2}s}}{1-2e^{i\tau s}\cos@@{s}+e^{2i\tau s}}} | f[2]*(s , tau) = ((cos((1)/(2)*s))^(2))/(1 - 2*exp(I*tau*s)*cos(s)+ exp(2*I*tau*s)) |
Subscript[f, 2]*(s , \[Tau]) == Divide[(Cos[Divide[1,2]*s])^(2),1 - 2*Exp[I*\[Tau]*s]*Cos[s]+ Exp[2*I*\[Tau]*s]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[(.8660254040+.5000000000*I)*(-1.500000000, .8660254040+.5000000000*I)+.1236929557-.8606824183e-1*I <- {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I} (-.5000000000+.8660254040*I)*(-1.500000000, .8660254040+.5000000000*I)+.1236929557-.8606824183e-1*I <- {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[2] = -1/2+1/2*I*3^(1/2)} |
Error |
23.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = \exp@{-\pi\frac{\ccompellintKk@{k}}{\compellintKk@{k}}}} | q = exp(- Pi*(EllipticCK(k))/(EllipticK(k))) |
q == Exp[- Pi*Divide[EllipticK[1-(k)^2],EllipticK[(k)^2]]] |
Failure | Failure | Error | Failed [30 / 30]
{Complex[-0.1339745962155613, 0.49999999999999994] <- {Rule[k, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[0.9466424242240871, 0.7022944994770247] <- {Rule[k, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
23.15#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = \frac{\Jacobithetaq{2}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}} | k = ((JacobiTheta2(0, q))^(2))/((JacobiTheta3(0, q))^(2)) |
k == Divide[(EllipticTheta[2, 0, q])^(2),(EllipticTheta[3, 0, q])^(2)] |
Failure | Failure | Error | Failed [5 / 30]
{Complex[1.0, -308.9309168668012] <- {Rule[k, 1], Rule[q, -0.5]} Complex[2.0, -308.9309168668012] <- {Rule[k, 2], Rule[q, -0.5]} |
23.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{A}\tau = \frac{a\tau+b}{c\tau+d}} | A*tau = (a*tau + b)/(c*tau + d) |
A*\[Tau] == Divide[a*\[Tau]+ b,c*\[Tau]+ d] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.15.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ad-bc = 1} | a*d - b*c = 1 |
a*d - b*c == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.15.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{\tau} = \frac{\Jacobithetaq{2}^{4}@{0}{q}}{\Jacobithetaq{3}^{4}@{0}{q}}} | Error |
ModularLambda[\[Tau]] == Divide[(EllipticTheta[2, 0, q])^(4),(EllipticTheta[3, 0, q])^(4)] |
Missing Macro Error | Failure | - | Failed [4 / 100]
{Complex[95438.81139616246, 21.966995277463894] <- {Rule[q, -0.5], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[95438.81139616246, -0.8660254037844387] <- {Rule[q, -0.5], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KleincompinvarJtau@{\tau} = \frac{\left(\Jacobithetaq{2}^{8}@{0}{q}+\Jacobithetaq{3}^{8}@{0}{q}+\Jacobithetaq{4}^{8}@{0}{q}\right)^{3}}{54\left(\Jacobithetaq{1}'@{0}{q}\right)^{8}}} | Error |
KleinInvariantJ[\[Tau]] == Divide[((EllipticTheta[2, 0, q])^(8)+ (EllipticTheta[3, 0, q])^(8)+ (EllipticTheta[4, 0, q])^(8))^(3),54*(D[EllipticTheta[1, 0, q], {0, 1}])^(8)] |
Missing Macro Error | Failure | - | Failed [100 / 100]
{Plus[Complex[-71.08223570333668, -2.1851275073468844*^-14], Times[-0.018518518518518517, Power[D[0.0 <- {0.0, 1.0}], -8], Power[Plus[Power[EllipticTheta[2, 0.0, Complex[0.8660254037844387, 0.49999999999999994]], 8], Power[EllipticTheta[3, 0.0, Complex[0.8660254037844387, 0.49999999999999994]], 8], Power[EllipticTheta[4, 0.0, Complex[0.8660254037844387, 0.49999999999999994]], 8]], 3]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Times[-0.018518518518518517, Power[D[0.0 <- {0.0, 1.0}], -8], Power[Plus[Power[EllipticTheta[2, 0.0, Complex[0.8660254037844387, 0.49999999999999994]], 8], Power[EllipticTheta[3, 0.0, Complex[0.8660254037844387, 0.49999999999999994]], 8], Power[EllipticTheta[4, 0.0, Complex[0.8660254037844387, 0.49999999999999994]], 8]], 3]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\tau} = \left(\tfrac{1}{2}\Jacobithetaq{1}'@{0}{q}\right)^{1/3}} | Error |
DedekindEta[\[Tau]] == (Divide[1,2]*D[EllipticTheta[1, 0, q], {0, 1}])^(1/ 3) |
Missing Macro Error | Failure | - | Failed [10 / 10]
{Plus[0.7682254223260567, Times[-0.7937005259840998, Power[D[0.0 <- {0.0, 1.0}], Rational[1, 3]]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Complex[0, 1]]} Plus[0.7682254223260567, Times[-0.7937005259840998, Power[D[0.0 <- {0.0, 1.0}], Rational[1, 3]]]], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Complex[0, 1]]} |
23.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\tfrac{1}{2}\Jacobithetaq{1}'@{0}{q}\right)^{1/3} = e^{i\pi\tau/12}\Jacobithetatau{3}@{\tfrac{1}{2}\pi(1+\tau)}{3\tau}} | ((1)/(2)*diff( JacobiTheta1(0, q), 0$(1) ))^(1/ 3) = exp(I*Pi*tau/ 12)*JacobiTheta3((1)/(2)*Pi*(1 + tau),exp(I*Pi*3*tau)) |
(Divide[1,2]*D[EllipticTheta[1, 0, q], {0, 1}])^(1/ 3) == Exp[I*Pi*\[Tau]/ 12]*EllipticTheta[3, Divide[1,2]*Pi*(1 + \[Tau]), Exp[I*Pi*(3*\[Tau])]] |
Error | Failure | - | Failed [10 / 10]
{Plus[Complex[-0.7682254223260567, 1.7569052324234997*^-19], Times[0.7937005259840998, Power[D[0.0 <- {0.0, 1.0}], Rational[1, 3]]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Complex[0, 1]]} Plus[Complex[-0.7682254223260567, 1.7569052324234997*^-19], Times[0.7937005259840998, Power[D[0.0 <- {0.0, 1.0}], Rational[1, 3]]]], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Complex[0, 1]]} |
23.17#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{i} = \tfrac{1}{2}} | Error |
ModularLambda[I] == Divide[1,2] |
Missing Macro Error | Successful | - | Successful [Tested: 1] |
23.17#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KleincompinvarJtau@{i} = 1} | Error |
KleinInvariantJ[I] == 1 |
Missing Macro Error | Successful | - | Successful [Tested: 1] |
23.17#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{i} = \frac{\EulerGamma@{\tfrac{1}{4}}}{2\pi^{3/4}}} | Error |
DedekindEta[I] == Divide[Gamma[Divide[1,4]],2*(Pi)^(3/ 4)] |
Missing Macro Error | Successful | - | Successful [Tested: 1] |
23.17.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\tau} = \sum_{n=-\infty}^{\infty}(-1)^{n}q^{(6n+1)^{2}/12}} | Error |
DedekindEta[\[Tau]] == Sum[(- 1)^(n)* (q)^((6*n + 1)^(2)/ 12), {n, - Infinity, Infinity}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Failed [10 / 10]
{Plus[0.7682254223260567, Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[Rational[1, 12], Power[Plus[1, Times[6, n]], 2]]]] <- {n, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Complex[0, 1]]} Plus[0.7682254223260567, Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Times[Rational[1, 12], Power[Plus[1, Times[6, n]], 2]]]] <- {n, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Complex[0, 1]]} |
23.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{\tau} = 16q\prod_{n=1}^{\infty}\left(\frac{1+q^{2n}}{1+q^{2n-1}}\right)^{8}} | Error |
ModularLambda[\[Tau]] == 16*q*Product[(Divide[1 + (q)^(2*n),1 + (q)^(2*n - 1)])^(8), {n, 1, Infinity}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Failed [24 / 100]
{Indeterminate <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Indeterminate <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.17.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\tau} = q^{1/12}\prod_{n=1}^{\infty}(1-q^{2n})} | Error |
DedekindEta[\[Tau]] == (q)^(1/ 12)* Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Failed [4 / 10]
{DirectedInfinity[] <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Complex[0, 1]]} DirectedInfinity[] <- {Rule[q, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[τ, Complex[0, 1]]} |
23.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{\mathcal{A}\tau} = \modularlambdatau@{\tau}} | Error |
ModularLambda[A*\[Tau]] == ModularLambda[\[Tau]] |
Missing Macro Error | Failure | - | Failed [10 / 100]
{Complex[-5.551115123125783*^-17, -21.100969873679457] <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-4.440892098500626*^-16, -21.100969873679432] <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KleincompinvarJtau@{\mathcal{A}\tau} = \KleincompinvarJtau@{\tau}} | Error |
KleinInvariantJ[A*\[Tau]] == KleinInvariantJ[\[Tau]] |
Missing Macro Error | Failure | - | Failed [8 / 100]
{Complex[71.08223570333668, 2.1851275073468844*^-14] <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-71.08223570333656, -1.2998925520285436*^-13] <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\mathcal{A}\tau} = \varepsilon(\mathcal{A})\left(-i(c\tau+d)\right)^{1/2}\Dedekindeta@{\tau}} | Error |
DedekindEta[A*\[Tau]] == \[CurlyEpsilon]*(A)*(- I*(c*\[Tau]+ d))^(1/ 2)* DedekindEta[\[Tau]] |
Missing Macro Error | Failure | - | Failed [180 / 300]
{Complex[0.11245781368984653, 0.4581664384510718] <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 1], Rule[τ, Complex[0, 1]]} Complex[-0.5688147076679476, 1.020829457922046] <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 2], Rule[τ, Complex[0, 1]]} |
23.18.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon(\mathcal{A}) = \exp@{\pi i\left(\frac{a+d}{12c}+s(-d,c)\right)}} | varepsilon*(A) = exp(Pi*I*((a + d)/(12*c)+ s*(- d , c))) |
\[CurlyEpsilon]*(A) == Exp[Pi*I*(Divide[a + d,12*c]+ s*(- d , c))] |
Failure | Failure | Error | Error |
23.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(d,c) = \sum_{r=1}^{c-1}\frac{r}{c}\left(\frac{dr}{c}-\floor{\frac{dr}{c}}-\frac{1}{2}\right),} | s*(d , c) = sum((r)/(c)*((d*r)/(c)- floor((d*r)/(c))-(1)/(2)), r = 1..c - 1), |
s*(d , c) == Sum[Divide[r,c]*(Divide[d*r,c]- Floor[Divide[d*r,c]]-Divide[1,2]), {r, 1, c - 1}, GenerateConditions->None], |
Skipped - Unable to analyze test case: Null | Skipped - Unable to analyze test case: Null | - | - |
23.19.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{\tau} = 16\left(\frac{\Dedekindeta^{2}@{2\tau}\Dedekindeta@{\tfrac{1}{2}\tau}}{\Dedekindeta^{3}@{\tau}}\right)^{8}} | Error |
ModularLambda[\[Tau]] == 16*(Divide[(DedekindEta[2*\[Tau]])^(2)* DedekindEta[Divide[1,2]*\[Tau]],(DedekindEta[\[Tau]])^(3)])^(8) |
Missing Macro Error | Failure | - | Successful [Tested: 10] |
23.19.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KleincompinvarJtau@{\tau} = \frac{4}{27}\frac{\left(1-\modularlambdatau@{\tau}+\modularlambdatau^{2}@{\tau}\right)^{3}}{\left(\modularlambdatau@{\tau}\left(1-\modularlambdatau@{\tau}\right)\right)^{2}}} | Error |
KleinInvariantJ[\[Tau]] == Divide[4,27]*Divide[(1 - ModularLambda[\[Tau]]+ (ModularLambda[\[Tau]])^(2))^(3),(ModularLambda[\[Tau]]*(1 - ModularLambda[\[Tau]]))^(2)] |
Missing Macro Error | Failure | - | Successful [Tested: 10] |
23.19.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}} | Error |
\[CapitalDelta] == (2*Pi)^(12)* (DedekindEta[\[Tau]])^(24) |
Missing Macro Error | Failure | - | Failed [20 / 100]
{Complex[-8.27953934969212*^7, 0.49999990438754693] <- {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[1.8191325291713696*^7, 0.49999997450648886] <- {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.20#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{3} = m^{2}-x_{1}-x_{2}} | x[3] = (m)^(2)- x[1]- x[2] |
Subscript[x, 3] == (m)^(2)- Subscript[x, 1]- Subscript[x, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.20#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y_{3} = -m(x_{3}-x_{1})-y_{1}} | y[3] = - m*(x[3]- x[1])- y[1] |
Subscript[y, 3] == - m*(Subscript[x, 3]- Subscript[x, 1])- Subscript[y, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.20.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v^{8}(1+u^{8}) = 4u^{4}} | (v)^(8)*(1 + (u)^(8)) = 4*(u)^(4) |
(v)^(8)*(1 + (u)^(8)) == 4*(u)^(4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.20.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u^{4}-v^{4}+2uv(1-u^{2}v^{2}) = 0} | (u)^(4)- (v)^(4)+ 2*u*v*(1 - (u)^(2)* (v)^(2)) = 0 |
(u)^(4)- (v)^(4)+ 2*u*v*(1 - (u)^(2)* (v)^(2)) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.20.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u^{6}-v^{6}+5u^{2}v^{2}(u^{2}-v^{2})+4uv(1-u^{4}v^{4}) = 0} | (u)^(6)- (v)^(6)+ 5*(u)^(2)* (v)^(2)*((u)^(2)- (v)^(2))+ 4*u*v*(1 - (u)^(4)* (v)^(4)) = 0 |
(u)^(6)- (v)^(6)+ 5*(u)^(2)* (v)^(2)*((u)^(2)- (v)^(2))+ 4*u*v*(1 - (u)^(4)* (v)^(4)) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.20.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-u^{8})(1-v^{8}) = (1-uv)^{8}} | (1 - (u)^(8))*(1 - (v)^(8)) = (1 - u*v)^(8) |
(1 - (u)^(8))*(1 - (v)^(8)) == (1 - u*v)^(8) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.22.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{1} = -2i\omega_{3}} | 2*omega[1] = - 2*I*omega[3] |
2*Subscript[\[Omega], 1] == - 2*I*Subscript[\[Omega], 3] |
Failure | Failure | Failed [288 / 300] 288/300]: [[.732050808+2.732050808*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} 3.464101616+2.000000000*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2-1/2*I*3^(1/2)} |
Failed [288 / 300]
{Complex[0.7320508075688775, 2.732050807568877] <- {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[3.4641016151377544, 2.0] <- {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
23.22.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -2i\omega_{3} = \frac{\left(\EulerGamma@{\frac{1}{4}}\right)^{2}}{2\sqrt{\pi}c^{1/4}}} | - 2*I*omega[3] = ((GAMMA((1)/(4)))^(2))/(2*sqrt(Pi)*(c)^(1/ 4)) |
- 2*I*Subscript[\[Omega], 3] == Divide[(Gamma[Divide[1,4]])^(2),2*Sqrt[Pi]*(c)^(1/ 4)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.369296462+.637245654*I <- {c = -3/2, omega = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} -.637245654+3.369296462*I <- {c = -3/2, omega = 1/2*3^(1/2)+1/2*I, omega[3] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-1.3692964596386887, 0.6372456520698113] <- {Rule[c, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-0.6372456520698113, 3.3692964596386883] <- {Rule[c, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{1} = 2e^{-\pi i/3}\omega_{3}} | 2*omega[1] = 2*exp(- Pi*I/ 3)*omega[3] |
2*Subscript[\[Omega], 1] == 2*Exp[- Pi*I/ 3]*Subscript[\[Omega], 3] |
Failure | Failure | Failed [300 / 300] 300/300]: [[0.+2.000000001*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} .732050807-.732050808*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.0, 1.9999999999999998] <- {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[0.7320508075688772, -0.7320508075688773] <- {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2e^{-\pi i/3}\omega_{3} = \frac{\left(\EulerGamma@{\frac{1}{3}}\right)^{3}}{2\pi d^{1/6}}} | 2*exp(- Pi*I/ 3)*omega[3] = ((GAMMA((1)/(3)))^(3))/(2*Pi*(d)^(1/ 6)) |
2*Exp[- Pi*I/ 3]*Subscript[\[Omega], 3] == Divide[(Gamma[Divide[1,3]])^(3),2*Pi*(d)^(1/ 6)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.316213396-.7333114397*I <- {d = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} -2.048264203+1.998739369*I <- {d = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, omega[3] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-1.3162133925119985, -0.7333114390610043] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Complex[-2.048264200080876, 1.9987393685078727] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
23.22#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{1} = 0.867568+i1.466607} | 2*omega[1] = 0.867568 + I*1.466607 |
2*Subscript[\[Omega], 1] == 0.867568 + I*1.466607 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.22#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{3} = -1.223741+i1.328694} | 2*omega[3] = - 1.223741 + I*1.328694 |
2*Subscript[\[Omega], 3] == - 1.223741 + I*1.328694 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
23.22#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = 0.305480+i1.015109} | tau = 0.305480 + I*1.015109 |
\[Tau] == 0.305480 + I*1.015109 |
Skipped - no semantic math | Skipped - no semantic math | - | - |