Multidimensional Theta Functions - 21.3 Symmetry and Quasi-Periodicity

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
21.3.E1	${\displaystyle{\displaystyle\theta\left(-\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)=\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)}}$ \Riemanntheta@{-\mathbf{z}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}		RiemannTheta(- z, Omega) = RiemannTheta(z, Omega)	Error	Missing Macro Error	Missing Macro Error	-	-
21.3.E2	${\displaystyle{\displaystyle\theta\left(\mathbf{z}+\mathbf{m}_{1}\middle|\boldsymbol{{\Omega}}\right)=\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)}}$ \Riemanntheta@{\mathbf{z}+\mathbf{m}_{1}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}		RiemannTheta(z + m[1], Omega) = RiemannTheta(z, Omega)	Error	Missing Macro Error	Missing Macro Error	-	-
21.3.E3	${\displaystyle{\displaystyle\theta\left(\mathbf{z}+\mathbf{m}_{1}+\boldsymbol{{\Omega}}\mathbf{m}_{2}\middle|\boldsymbol{{\Omega}}\right)=e^{-2\pi i\left(\frac{1}{2}\mathbf{m}_{2}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{m}_{2}+\mathbf{m}_{2}\cdot\mathbf{z}\right)}\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)}}$ \Riemanntheta@{\mathbf{z}+\mathbf{m}_{1}+\boldsymbol{{\Omega}}\mathbf{m}_{2}}{\boldsymbol{{\Omega}}} = e^{-2\pi i\left(\frac{1}{2}\mathbf{m}_{2}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{m}_{2}+\mathbf{m}_{2}\cdot\mathbf{z}\right)}\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}		RiemannTheta(z + m[1]+ Omega*m[2], Omega) = exp(- 2*Pi*I*((1)/(2)*m[2] * Omega * m[2]+ m[2] * z))*RiemannTheta(z, Omega)	Error	Missing Macro Error	Missing Macro Error	-	-