20.2: Difference between revisions

Latest revision as of 11:55, 28 June 2021

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
20.2.E1	${\displaystyle{\displaystyle\theta_{1}\left(z\middle\|\tau\right)=\theta_{1}% \left(z,q\right)}}$ `\Jacobithetatau{1}@{z}{\tau} = \Jacobithetaq{1}@{z}{q}`	JacobiTheta1(z,exp(IPitau)) = JacobiTheta1(z, q)	EllipticTheta[1, z, Exp[IPi(\[Tau])]] == EllipticTheta[1, z, q]	Failure	Failure	Error	Successful [Tested: 300]
20.2.E2	${\displaystyle{\displaystyle\theta_{2}\left(z\middle\|\tau\right)=\theta_{2}% \left(z,q\right)}}$ `\Jacobithetatau{2}@{z}{\tau} = \Jacobithetaq{2}@{z}{q}`	JacobiTheta2(z,exp(IPitau)) = JacobiTheta2(z, q)	EllipticTheta[2, z, Exp[IPi(\[Tau])]] == EllipticTheta[2, z, q]	Failure	Failure	Error	Successful [Tested: 300]
20.2.E3	${\displaystyle{\displaystyle\theta_{3}\left(z\middle\|\tau\right)=\theta_{3}% \left(z,q\right)}}$ `\Jacobithetatau{3}@{z}{\tau} = \Jacobithetaq{3}@{z}{q}`	JacobiTheta3(z,exp(IPitau)) = JacobiTheta3(z, q)	EllipticTheta[3, z, Exp[IPi(\[Tau])]] == EllipticTheta[3, z, q]	Failure	Failure	Error	Successful [Tested: 300]
20.2.E4	${\displaystyle{\displaystyle\theta_{4}\left(z\middle\|\tau\right)=\theta_{4}% \left(z,q\right)}}$ `\Jacobithetatau{4}@{z}{\tau} = \Jacobithetaq{4}@{z}{q}`	JacobiTheta4(z,exp(IPitau)) = JacobiTheta4(z, q)	EllipticTheta[4, z, Exp[IPi(\[Tau])]] == EllipticTheta[4, z, q]	Failure	Failure	Error	Successful [Tested: 300]
20.2.E5	${\displaystyle{\displaystyle z_{m,n}=(m+n\tau)\pi}}$ `z_{m,n} = (m+n\tau)\pi`	z[m , n] = (m + ntau)Pi	Subscript[z, m , n] == (m + n\[Tau])Pi	Skipped - no semantic math	Skipped - no semantic math	-	-
20.2.E6	${\displaystyle{\displaystyle\theta_{1}\left(z+(m+n\tau)\pi\middle\|\tau\right)=% (-1)^{m+n}q^{-n^{2}}e^{-2inz}\theta_{1}\left(z\middle\|\tau\right)}}$ `\Jacobithetatau{1}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m+n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{1}@{z}{\tau}`	JacobiTheta1(z +(m + ntau)Pi,exp(IPitau)) = (- 1)^(m + n)* (q)^(- (n)^(2))* exp(- 2Inz)JacobiTheta1(z,exp(IPitau))	EllipticTheta[1, z +(m + n\[Tau])Pi, Exp[IPi(\[Tau])]] == (- 1)^(m + n)* (q)^(- (n)^(2))* Exp[- 2Inz]EllipticTheta[1, z, Exp[IPi(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: -18.62843952+6.320473139I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 1} Result: -4187.991134+3174.249087I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 2} ... skip entries to safe data	Failed [72 / 300] Result: Complex[-18.628439525286133, 6.320473094431787] Test Values: {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-4187.991166649552, 3174.249038247393] Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
20.2.E7	${\displaystyle{\displaystyle\theta_{2}\left(z+(m+n\tau)\pi\middle\|\tau\right)=% (-1)^{m}q^{-n^{2}}e^{-2inz}\theta_{2}\left(z\middle\|\tau\right)}}$ `\Jacobithetatau{2}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m}q^{-n^{2}}e^{-2inz}\Jacobithetatau{2}@{z}{\tau}`	JacobiTheta2(z +(m + ntau)Pi,exp(IPitau)) = (- 1)^(m)* (q)^(- (n)^(2))* exp(- 2Inz)JacobiTheta2(z,exp(IPitau))	EllipticTheta[2, z +(m + n\[Tau])Pi, Exp[IPi(\[Tau])]] == (- 1)^(m)* (q)^(- (n)^(2))* Exp[- 2Inz]EllipticTheta[2, z, Exp[IPi(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: 3.950576529-14.16574159I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 1} Result: 194.3416227+3923.809342I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 2} ... skip entries to safe data	Failed [72 / 300] Result: Complex[3.9505765593957305, -14.165741580817551] Test Values: {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[194.34158297403354, 3923.809350793304] Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
20.2.E8	${\displaystyle{\displaystyle\theta_{3}\left(z+(m+n\tau)\pi\middle\|\tau\right)=% q^{-n^{2}}e^{-2inz}\theta_{3}\left(z\middle\|\tau\right)}}$ `\Jacobithetatau{3}@{z+(m+n\tau)\pi}{\tau} = q^{-n^{2}}e^{-2inz}\Jacobithetatau{3}@{z}{\tau}`	JacobiTheta3(z +(m + ntau)Pi,exp(IPitau)) = (q)^(- (n)^(2))* exp(- 2Inz)JacobiTheta3(z,exp(IPitau))	EllipticTheta[3, z +(m + n\[Tau])Pi, Exp[IPi(\[Tau])]] == (q)^(- (n)^(2))* Exp[- 2Inz]EllipticTheta[3, z, Exp[IPi(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: -8.181021151+18.44680448I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 1} Result: 516.5479372-5365.925849I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 2} ... skip entries to safe data	Failed [72 / 300] Result: Complex[-8.181021187984683, 18.446804447343553] Test Values: {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[516.547995329447, -5365.925840115722] Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
20.2.E9	${\displaystyle{\displaystyle\theta_{4}\left(z+(m+n\tau)\pi\middle\|\tau\right)=% (-1)^{n}q^{-n^{2}}e^{-2inz}\theta_{4}\left(z\middle\|\tau\right)}}$ `\Jacobithetatau{4}@{z+(m+n\tau)\pi}{\tau} = (-1)^{n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{4}@{z}{\tau}`	JacobiTheta4(z +(m + ntau)Pi,exp(IPitau)) = (- 1)^(n)* (q)^(- (n)^(2))* exp(- 2Inz)JacobiTheta4(z,exp(IPitau))	EllipticTheta[4, z +(m + n\[Tau])Pi, Exp[IPi(\[Tau])]] == (- 1)^(n)* (q)^(- (n)^(2))* Exp[- 2Inz]EllipticTheta[4, z, Exp[IPi(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: -4.510694228-11.16801166I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 1} Result: -2085.869632-2449.864344I Test Values: {q = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1, n = 2} ... skip entries to safe data	Failed [72 / 300] Result: Complex[-4.5106942149502025, -11.168011665083736] Test Values: {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2085.8696157878926, -2449.864367431773] Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
20.2.E11	${\displaystyle{\displaystyle\theta_{1}\left(z\middle\|\tau\right)=-\theta_{2}% \left(z+\tfrac{1}{2}\pi\middle\|\tau\right)}}$ `\Jacobithetatau{1}@{z}{\tau} = -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau}`	JacobiTheta1(z,exp(IPitau)) = - JacobiTheta2(z +(1)/(2)Pi,exp(IPi*tau))	EllipticTheta[1, z, Exp[IPi(\[Tau])]] == - EllipticTheta[2, z +Divide[1,2]Pi, Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 70]
20.2.E11	${\displaystyle{\displaystyle-\theta_{2}\left(z+\tfrac{1}{2}\pi\middle\|\tau% \right)=-iM\theta_{4}\left(z+\tfrac{1}{2}\pi\tau\middle\|\tau\right)}}$ `-\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau}`	- JacobiTheta2(z +(1)/(2)Pi,exp(IPitau)) = - IMJacobiTheta4(z +(1)/(2)Pitau,exp(IPi*tau))	- EllipticTheta[2, z +Divide[1,2]Pi, Exp[IPi(\[Tau])]] == - IMEllipticTheta[4, z +Divide[1,2]Pi\[Tau], Exp[IPi*(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: -2.656130280+.8441101403I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: 2.726401771+.6812031274I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [60 / 300] Result: Complex[-2.65613027348202, 0.8441101301235214] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.1127027753782777, -0.09362434622808774] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
20.2.E11	${\displaystyle{\displaystyle-iM\theta_{4}\left(z+\tfrac{1}{2}\pi\tau\middle\|% \tau\right)=-iM\theta_{3}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau\middle\|% \tau\right)}}$ `-iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau} = -iM\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}`	- IMJacobiTheta4(z +(1)/(2)Pitau,exp(IPitau)) = - IMJacobiTheta3(z +(1)/(2)Pi +(1)/(2)Pitau,exp(IPi*tau))	- IMEllipticTheta[4, z +Divide[1,2]Pi\[Tau], Exp[IPi(\[Tau])]] == - IMEllipticTheta[3, z +Divide[1,2]Pi +Divide[1,2]Pi\[Tau], Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 300]
20.2.E12	${\displaystyle{\displaystyle\theta_{2}\left(z\middle\|\tau\right)=\theta_{1}% \left(z+\tfrac{1}{2}\pi\middle\|\tau\right)}}$ `\Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau}`	JacobiTheta2(z,exp(IPitau)) = JacobiTheta1(z +(1)/(2)Pi,exp(IPi*tau))	EllipticTheta[2, z, Exp[IPi(\[Tau])]] == EllipticTheta[1, z +Divide[1,2]Pi, Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 70]
20.2.E12	${\displaystyle{\displaystyle\theta_{1}\left(z+\tfrac{1}{2}\pi\middle\|\tau% \right)=M\theta_{3}\left(z+\tfrac{1}{2}\pi\tau\middle\|\tau\right)}}$ `\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau}`	JacobiTheta1(z +(1)/(2)Pi,exp(IPitau)) = MJacobiTheta3(z +(1)/(2)Pitau,exp(IPitau))	EllipticTheta[1, z +Divide[1,2]Pi, Exp[IPi(\[Tau])]] == MEllipticTheta[3, z +Divide[1,2]Pi\[Tau], Exp[IPi(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: -.5985410657+1.995750316I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -.54909285e-2-5.605651596I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [60 / 300] Result: Complex[-0.5985410729973577, 1.9957503125524838] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.3220776692839347, 1.382964384147599] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
20.2.E12	${\displaystyle{\displaystyle M\theta_{3}\left(z+\tfrac{1}{2}\pi\tau\middle\|% \tau\right)=M\theta_{4}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau\middle\|\tau% \right)}}$ `M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}`	MJacobiTheta3(z +(1)/(2)Pitau,exp(IPitau)) = MJacobiTheta4(z +(1)/(2)Pi +(1)/(2)Pitau,exp(IPi*tau))	MEllipticTheta[3, z +Divide[1,2]Pi\[Tau], Exp[IPi(\[Tau])]] == MEllipticTheta[4, z +Divide[1,2]Pi +Divide[1,2]Pi\[Tau], Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 300]
20.2.E13	${\displaystyle{\displaystyle\theta_{3}\left(z\middle\|\tau\right)=\theta_{4}% \left(z+\tfrac{1}{2}\pi\middle\|\tau\right)}}$ `\Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau}`	JacobiTheta3(z,exp(IPitau)) = JacobiTheta4(z +(1)/(2)Pi,exp(IPi*tau))	EllipticTheta[3, z, Exp[IPi(\[Tau])]] == EllipticTheta[4, z +Divide[1,2]Pi, Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 70]
20.2.E13	${\displaystyle{\displaystyle\theta_{4}\left(z+\tfrac{1}{2}\pi\middle\|\tau% \right)=M\theta_{2}\left(z+\tfrac{1}{2}\pi\tau\middle\|\tau\right)}}$ `\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau}`	JacobiTheta4(z +(1)/(2)Pi,exp(IPitau)) = MJacobiTheta2(z +(1)/(2)Pitau,exp(IPitau))	EllipticTheta[4, z +Divide[1,2]Pi, Exp[IPi(\[Tau])]] == MEllipticTheta[2, z +Divide[1,2]Pi\[Tau], Exp[IPi(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: -1.209558888+2.590545189I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -.8537358258+1.281173247I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [60 / 300] Result: Complex[-1.2095588901959111, 2.5905451776573183] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.901447370098885, -0.21207958455265288] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
20.2.E13	${\displaystyle{\displaystyle M\theta_{2}\left(z+\tfrac{1}{2}\pi\tau\middle\|% \tau\right)=M\theta_{1}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau\middle\|\tau% \right)}}$ `M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}`	MJacobiTheta2(z +(1)/(2)Pitau,exp(IPitau)) = MJacobiTheta1(z +(1)/(2)Pi +(1)/(2)Pitau,exp(IPi*tau))	MEllipticTheta[2, z +Divide[1,2]Pi\[Tau], Exp[IPi(\[Tau])]] == MEllipticTheta[1, z +Divide[1,2]Pi +Divide[1,2]Pi\[Tau], Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 300]
20.2.E14	${\displaystyle{\displaystyle\theta_{4}\left(z\middle\|\tau\right)=\theta_{3}% \left(z+\tfrac{1}{2}\pi\middle\|\tau\right)}}$ `\Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau}`	JacobiTheta4(z,exp(IPitau)) = JacobiTheta3(z +(1)/(2)Pi,exp(IPi*tau))	EllipticTheta[4, z, Exp[IPi(\[Tau])]] == EllipticTheta[3, z +Divide[1,2]Pi, Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 70]
20.2.E14	${\displaystyle{\displaystyle\theta_{3}\left(z+\tfrac{1}{2}\pi\middle\|\tau% \right)=-iM\theta_{1}\left(z+\tfrac{1}{2}\pi\tau\middle\|\tau\right)}}$ `\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau}`	JacobiTheta3(z +(1)/(2)Pi,exp(IPitau)) = - IMJacobiTheta1(z +(1)/(2)Pitau,exp(IPi*tau))	EllipticTheta[3, z +Divide[1,2]Pi, Exp[IPi(\[Tau])]] == - IMEllipticTheta[1, z +Divide[1,2]Pi\[Tau], Exp[IPi*(\[Tau])]]	Failure	Failure	Failed [300 / 300] Result: .6082553523+1.594370406I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -3.995156823-3.872683361I Test Values: {M = 1/23^(1/2)+1/2I, tau = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [60 / 300] Result: Complex[0.6082553477594059, 1.594370409676146] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.5995966648178563, -0.1152010311326023] Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
20.2.E14	${\displaystyle{\displaystyle-iM\theta_{1}\left(z+\tfrac{1}{2}\pi\tau\middle\|% \tau\right)=iM\theta_{2}\left(z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau\middle\|% \tau\right)}}$ `-iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau} = iM\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}`	- IMJacobiTheta1(z +(1)/(2)Pitau,exp(IPitau)) = IMJacobiTheta2(z +(1)/(2)Pi +(1)/(2)Pitau,exp(IPi*tau))	- IMEllipticTheta[1, z +Divide[1,2]Pi\[Tau], Exp[IPi(\[Tau])]] == IMEllipticTheta[2, z +Divide[1,2]Pi +Divide[1,2]Pi\[Tau], Exp[IPi*(\[Tau])]]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 300]

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/20.2.E1 20.2.E1] || [[Item:Q6741|<math>\Jacobithetatau{1}@{z}{\tau} = \Jacobithetaq{1}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z}{\tau} = \Jacobithetaq{1}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z,exp(I*Pi*tau)) = JacobiTheta1(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[1, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E1 20.2.E1] || <math qid="Q6741">\Jacobithetatau{1}@{z}{\tau} = \Jacobithetaq{1}@{z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z}{\tau} = \Jacobithetaq{1}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z,exp(I*Pi*tau)) = JacobiTheta1(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[1, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/20.2.E2 20.2.E2] || [[Item:Q6742|<math>\Jacobithetatau{2}@{z}{\tau} = \Jacobithetaq{2}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{2}@{z}{\tau} = \Jacobithetaq{2}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta2(z,exp(I*Pi*tau)) = JacobiTheta2(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[2, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[2, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E2 20.2.E2] || <math qid="Q6742">\Jacobithetatau{2}@{z}{\tau} = \Jacobithetaq{2}@{z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{2}@{z}{\tau} = \Jacobithetaq{2}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta2(z,exp(I*Pi*tau)) = JacobiTheta2(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[2, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[2, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/20.2.E3 20.2.E3] || [[Item:Q6743|<math>\Jacobithetatau{3}@{z}{\tau} = \Jacobithetaq{3}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z}{\tau} = \Jacobithetaq{3}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z,exp(I*Pi*tau)) = JacobiTheta3(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[3, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E3 20.2.E3] || <math qid="Q6743">\Jacobithetatau{3}@{z}{\tau} = \Jacobithetaq{3}@{z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z}{\tau} = \Jacobithetaq{3}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z,exp(I*Pi*tau)) = JacobiTheta3(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[3, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/20.2.E4 20.2.E4] || [[Item:Q6744|<math>\Jacobithetatau{4}@{z}{\tau} = \Jacobithetaq{4}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z}{\tau} = \Jacobithetaq{4}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z,exp(I*Pi*tau)) = JacobiTheta4(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[4, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E4 20.2.E4] || <math qid="Q6744">\Jacobithetatau{4}@{z}{\tau} = \Jacobithetaq{4}@{z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z}{\tau} = \Jacobithetaq{4}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z,exp(I*Pi*tau)) = JacobiTheta4(z, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[4, z, q]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/20.2.E5 20.2.E5] || [[Item:Q6745|<math>z_{m,n} = (m+n\tau)\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{m,n} = (m+n\tau)\pi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[m , n] = (m + n*tau)*Pi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, m , n] == (m + n*\[Tau])*Pi</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/20.2.E5 20.2.E5] || <math qid="Q6745">z_{m,n} = (m+n\tau)\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{m,n} = (m+n\tau)\pi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[m , n] = (m + n*tau)*Pi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, m , n] == (m + n*\[Tau])*Pi</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/20.2.E6 20.2.E6] || [[Item:Q6746|<math>\Jacobithetatau{1}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m+n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{1}@{z}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m+n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{1}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (- 1)^(m + n)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta1(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (- 1)^(m + n)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[1, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -18.62843952+6.320473139*I
+| [https://dlmf.nist.gov/20.2.E6 20.2.E6] || <math qid="Q6746">\Jacobithetatau{1}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m+n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{1}@{z}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m+n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{1}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (- 1)^(m + n)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta1(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (- 1)^(m + n)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[1, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -18.62843952+6.320473139*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -4187.991134+3174.249087*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-18.628439525286133, 6.320473094431787]
@@ Line 30: / Line 30: @@
 Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E7 20.2.E7] || [[Item:Q6747|<math>\Jacobithetatau{2}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m}q^{-n^{2}}e^{-2inz}\Jacobithetatau{2}@{z}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{2}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m}q^{-n^{2}}e^{-2inz}\Jacobithetatau{2}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta2(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (- 1)^(m)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta2(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[2, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (- 1)^(m)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[2, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.950576529-14.16574159*I
+| [https://dlmf.nist.gov/20.2.E7 20.2.E7] || <math qid="Q6747">\Jacobithetatau{2}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m}q^{-n^{2}}e^{-2inz}\Jacobithetatau{2}@{z}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{2}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m}q^{-n^{2}}e^{-2inz}\Jacobithetatau{2}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta2(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (- 1)^(m)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta2(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[2, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (- 1)^(m)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[2, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.950576529-14.16574159*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 194.3416227+3923.809342*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.9505765593957305, -14.165741580817551]
@@ Line 36: / Line 36: @@
 Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E8 20.2.E8] || [[Item:Q6748|<math>\Jacobithetatau{3}@{z+(m+n\tau)\pi}{\tau} = q^{-n^{2}}e^{-2inz}\Jacobithetatau{3}@{z}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z+(m+n\tau)\pi}{\tau} = q^{-n^{2}}e^{-2inz}\Jacobithetatau{3}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta3(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[3, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -8.181021151+18.44680448*I
+| [https://dlmf.nist.gov/20.2.E8 20.2.E8] || <math qid="Q6748">\Jacobithetatau{3}@{z+(m+n\tau)\pi}{\tau} = q^{-n^{2}}e^{-2inz}\Jacobithetatau{3}@{z}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z+(m+n\tau)\pi}{\tau} = q^{-n^{2}}e^{-2inz}\Jacobithetatau{3}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta3(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[3, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -8.181021151+18.44680448*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 516.5479372-5365.925849*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-8.181021187984683, 18.446804447343553]
@@ Line 42: / Line 42: @@
 Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E9 20.2.E9] || [[Item:Q6749|<math>\Jacobithetatau{4}@{z+(m+n\tau)\pi}{\tau} = (-1)^{n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{4}@{z}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z+(m+n\tau)\pi}{\tau} = (-1)^{n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{4}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (- 1)^(n)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta4(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (- 1)^(n)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[4, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.510694228-11.16801166*I
+| [https://dlmf.nist.gov/20.2.E9 20.2.E9] || <math qid="Q6749">\Jacobithetatau{4}@{z+(m+n\tau)\pi}{\tau} = (-1)^{n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{4}@{z}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z+(m+n\tau)\pi}{\tau} = (-1)^{n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{4}@{z}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z +(m + n*tau)*Pi,exp(I*Pi*tau)) = (- 1)^(n)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta4(z,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z +(m + n*\[Tau])*Pi, Exp[I*Pi*(\[Tau])]] == (- 1)^(n)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[4, z, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.510694228-11.16801166*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2085.869632-2449.864344*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-4.5106942149502025, -11.168011665083736]
@@ Line 48: / Line 48: @@
 Test Values: {Rule[m, 1], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E11 20.2.E11] || [[Item:Q6751|<math>\Jacobithetatau{1}@{z}{\tau} = -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z}{\tau} = -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z,exp(I*Pi*tau)) = - JacobiTheta2(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z, Exp[I*Pi*(\[Tau])]] == - EllipticTheta[2, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
+| [https://dlmf.nist.gov/20.2.E11 20.2.E11] || <math qid="Q6751">\Jacobithetatau{1}@{z}{\tau} = -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z}{\tau} = -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z,exp(I*Pi*tau)) = - JacobiTheta2(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z, Exp[I*Pi*(\[Tau])]] == - EllipticTheta[2, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/20.2.E11 20.2.E11] || [[Item:Q6751|<math>-\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- JacobiTheta2(z +(1)/(2)*Pi,exp(I*Pi*tau)) = - I*M*JacobiTheta4(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- EllipticTheta[2, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == - I*M*EllipticTheta[4, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.656130280+.8441101403*I
+| [https://dlmf.nist.gov/20.2.E11 20.2.E11] || <math qid="Q6751">-\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- JacobiTheta2(z +(1)/(2)*Pi,exp(I*Pi*tau)) = - I*M*JacobiTheta4(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- EllipticTheta[2, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == - I*M*EllipticTheta[4, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.656130280+.8441101403*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.726401771+.6812031274*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.65613027348202, 0.8441101301235214]
@@ Line 56: / Line 56: @@
 Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E11 20.2.E11] || [[Item:Q6751|<math>-iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau} = -iM\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau} = -iM\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- I*M*JacobiTheta4(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = - I*M*JacobiTheta3(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*M*EllipticTheta[4, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == - I*M*EllipticTheta[3, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E11 20.2.E11] || <math qid="Q6751">-iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau} = -iM\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau} = -iM\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- I*M*JacobiTheta4(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = - I*M*JacobiTheta3(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*M*EllipticTheta[4, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == - I*M*EllipticTheta[3, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/20.2.E12 20.2.E12] || [[Item:Q6752|<math>\Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta2(z,exp(I*Pi*tau)) = JacobiTheta1(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[2, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[1, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
+| [https://dlmf.nist.gov/20.2.E12 20.2.E12] || <math qid="Q6752">\Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta2(z,exp(I*Pi*tau)) = JacobiTheta1(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[2, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[1, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/20.2.E12 20.2.E12] || [[Item:Q6752|<math>\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z +(1)/(2)*Pi,exp(I*Pi*tau)) = M*JacobiTheta3(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[3, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5985410657+1.995750316*I
+| [https://dlmf.nist.gov/20.2.E12 20.2.E12] || <math qid="Q6752">\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta1(z +(1)/(2)*Pi,exp(I*Pi*tau)) = M*JacobiTheta3(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[1, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[3, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5985410657+1.995750316*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.54909285e-2-5.605651596*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5985410729973577, 1.9957503125524838]
@@ Line 66: / Line 66: @@
 Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E12 20.2.E12] || [[Item:Q6752|<math>M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>M*JacobiTheta3(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = M*JacobiTheta4(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>M*EllipticTheta[3, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[4, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E12 20.2.E12] || <math qid="Q6752">M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>M*JacobiTheta3(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = M*JacobiTheta4(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>M*EllipticTheta[3, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[4, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/20.2.E13 20.2.E13] || [[Item:Q6753|<math>\Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z,exp(I*Pi*tau)) = JacobiTheta4(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[4, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
+| [https://dlmf.nist.gov/20.2.E13 20.2.E13] || <math qid="Q6753">\Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z,exp(I*Pi*tau)) = JacobiTheta4(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[4, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/20.2.E13 20.2.E13] || [[Item:Q6753|<math>\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z +(1)/(2)*Pi,exp(I*Pi*tau)) = M*JacobiTheta2(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[2, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.209558888+2.590545189*I
+| [https://dlmf.nist.gov/20.2.E13 20.2.E13] || <math qid="Q6753">\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z +(1)/(2)*Pi,exp(I*Pi*tau)) = M*JacobiTheta2(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[2, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.209558888+2.590545189*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8537358258+1.281173247*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2095588901959111, 2.5905451776573183]
@@ Line 76: / Line 76: @@
 Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E13 20.2.E13] || [[Item:Q6753|<math>M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>M*JacobiTheta2(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = M*JacobiTheta1(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>M*EllipticTheta[2, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[1, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E13 20.2.E13] || <math qid="Q6753">M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>M*JacobiTheta2(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = M*JacobiTheta1(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>M*EllipticTheta[2, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == M*EllipticTheta[1, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/20.2.E14 20.2.E14] || [[Item:Q6754|<math>\Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z,exp(I*Pi*tau)) = JacobiTheta3(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[3, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
+| [https://dlmf.nist.gov/20.2.E14 20.2.E14] || <math qid="Q6754">\Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta4(z,exp(I*Pi*tau)) = JacobiTheta3(z +(1)/(2)*Pi,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[4, z, Exp[I*Pi*(\[Tau])]] == EllipticTheta[3, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/20.2.E14 20.2.E14] || [[Item:Q6754|<math>\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z +(1)/(2)*Pi,exp(I*Pi*tau)) = - I*M*JacobiTheta1(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == - I*M*EllipticTheta[1, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6082553523+1.594370406*I
+| [https://dlmf.nist.gov/20.2.E14 20.2.E14] || <math qid="Q6754">\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiTheta3(z +(1)/(2)*Pi,exp(I*Pi*tau)) = - I*M*JacobiTheta1(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticTheta[3, z +Divide[1,2]*Pi, Exp[I*Pi*(\[Tau])]] == - I*M*EllipticTheta[1, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6082553523+1.594370406*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.995156823-3.872683361*I
 Test Values: {M = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6082553477594059, 1.594370409676146]
@@ Line 86: / Line 86: @@
 Test Values: {Rule[M, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/20.2.E14 20.2.E14] || [[Item:Q6754|<math>-iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau} = iM\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau} = iM\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- I*M*JacobiTheta1(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = I*M*JacobiTheta2(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*M*EllipticTheta[1, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == I*M*EllipticTheta[2, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
+| [https://dlmf.nist.gov/20.2.E14 20.2.E14] || <math qid="Q6754">-iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau} = iM\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau} = iM\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- I*M*JacobiTheta1(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) = I*M*JacobiTheta2(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*M*EllipticTheta[1, z +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]] == I*M*EllipticTheta[2, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], Exp[I*Pi*(\[Tau])]]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 300]
 |}
 </div>

20.2: Difference between revisions

Latest revision as of 11:55, 28 June 2021

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