Weierstrass Elliptic and Modular Functions - 23.19 Interrelations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
23.19.E1	${\displaystyle{\displaystyle\lambda\left(\tau\right)=16\left(\frac{{\eta^{2}}\left(2\tau\right)\eta\left(\tfrac{1}{2}\tau\right)}{{\eta^{3}}\left(\tau\right)}\right)^{8}}}$ \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	${\displaystyle{\displaystyle J\left(\tau\right)=\frac{4}{27}\frac{\left(1-\lambda\left(\tau\right)+{\lambda^{2}}\left(\tau\right)\right)^{3}}{\left(\lambda\left(\tau\right)\left(1-\lambda\left(\tau\right)\right)\right)^{2}}}}$ \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	${\displaystyle{\displaystyle\Delta=(2\pi)^{12}{\eta^{24}}\left(\tau\right)}}$ \Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}		Error	\[CapitalDelta] == (2*Pi)^(12)* (DedekindEta[\[Tau]])^(24)	Missing Macro Error	Failure	-	Failed [20 / 100] Result: Complex[-8.27953934969212*^7, 0.49999990438754693] Test Values: {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.8191325291713696*^7, 0.49999997450648886] Test Values: {Rule[Δ, 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