Results of Multidimensional Theta Functions: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/21.2.E1 21.2.E1] || [[Item:Q6857|<math>\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(z, Omega) = sum(exp(2*Pi*I*((1)/(2)*n * Omega * n + n * z)),  = ..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/21.2.E1 21.2.E1] || [[Item:Q6857|<math>\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(z, Omega) = sum(exp(2*Pi*I*((1)/(2)*n * Omega * n + n * z)),  = ..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -

Revision as of 13:27, 22 May 2021

DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
21.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}}
\Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}} = \sum_{\mathbf{n}\in\Integers^{g}}e^{2\pi i\left(\frac{1}{2}\mathbf{n}\cdot\boldsymbol{{\Omega}}\cdot\mathbf{n}+\mathbf{n}\cdot\mathbf{z}\right)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
RiemannTheta(z, Omega) = sum(exp(2*Pi*I*((1)/(2)*n * Omega * n + n * z)),  = ..infinity)

Error
Missing Macro Error Missing Macro Error - -
21.2.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{z}{\Omega} = \Jacobithetatau{3}@{\pi z}{\Omega}}
\Riemanntheta@{z}{\Omega} = \Jacobithetatau{3}@{\pi z}{\Omega}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
RiemannTheta(z, Omega) = JacobiTheta3(Pi*z,exp(I*Pi*Omega))

Error
Missing Macro Error Missing Macro Error - -
21.3.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{-\mathbf{z}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}}
\Riemanntheta@{-\mathbf{z}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
RiemannTheta(- z, Omega) = RiemannTheta(z, Omega)

Error
Missing Macro Error Missing Macro Error - -
21.3.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{\mathbf{z}+\mathbf{m}_{1}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}}
\Riemanntheta@{\mathbf{z}+\mathbf{m}_{1}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
RiemannTheta(z + m[1], Omega) = RiemannTheta(z, Omega)

Error
Missing Macro Error Missing Macro Error - -
21.3.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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@{\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}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 - -
21.6.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}}
\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
RiemannTheta((x + y + u + v)/(2), Omega)*RiemannTheta((x + y - u - v)/(2), Omega)*RiemannTheta((x - y + u - v)/(2), Omega)*RiemannTheta((x - y - u + v)/(2), Omega) = (1)/((2)^(g))*sum(sum(exp(2*Pi*I*(2*alpha * Omega * alpha + alpha *(x + y + u + v)))* RiemannTheta(x + Omega*alpha + beta, Omega)*RiemannTheta(y + Omega*alpha + beta, Omega)*RiemannTheta(u + Omega*alpha + beta, Omega)*RiemannTheta(v + Omega*alpha + beta, Omega),  = ..infinity),  = ..infinity)

Error
Missing Macro Error Missing Macro Error - -
21.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(\lambda,\mu) = 0}
P(\lambda,\mu) = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
P(lambda , mu) = 0
 
P[\[Lambda], \[Mu]] == 0
 Skipped - no semantic math Skipped - no semantic math - -
21.7.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu^{2} = Q(\lambda)}
\mu^{2} = Q(\lambda)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(mu)^(2) = Q(lambda)
 
\[Mu]^(2) == Q[\[Lambda]]
 Skipped - no semantic math Skipped - no semantic math - -
21.7.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \boldsymbol{{\eta}}(T) = \boldsymbol{{\eta}}(T^{c})}
\boldsymbol{{\eta}}(T) = \boldsymbol{{\eta}}(T^{c})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
eta(T) = eta((T)^(c))
 
\[Eta][T] == \[Eta][(T)^(c)]
 Skipped - no semantic math Skipped - no semantic math - -
21.9.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4u_{t} = 6uu_{x}+u_{xxx}}
4u_{t} = 6uu_{x}+u_{xxx}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
4*u[t] = 6*u*u[x]+ u[x, x, x]
 
4*Subscript[u, t] == 6*u*Subscript[u, x]+ Subscript[u, x, x, x]
 Skipped - no semantic math Skipped - no semantic math - -
21.9.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle iu_{t} = -\tfrac{1}{2}u_{xx}+|u|^{2}u}
iu_{t} = -\tfrac{1}{2}u_{xx}+|u|^{2}u		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
I*u[t] = -(1)/(2)*u[x, x]+(abs(u))^(2)* u
 
I*Subscript[u, t] == -Divide[1,2]*Subscript[u, x, x]+(Abs[u])^(2)* u
 Skipped - no semantic math Skipped - no semantic math - -
21.9.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy} = 0}
(-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
- 4*u[t]+ 6*u*u[x]+ u[x, x, x][x]+ 3*u[y, y] = 0
 
Subscript[- 4*Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x, x, x], x]+ 3*Subscript[u, y, y] == 0
 Skipped - no semantic math Skipped - no semantic math - -
21.9.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,y,t) = c+2\pderiv[2]{}{x}\ln@{\Riemanntheta@{\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+\boldsymbol{{\phi}}}{\boldsymbol{{\Omega}}}}}
u(x,y,t) = c+2\pderiv[2]{}{x}\ln@{\Riemanntheta@{\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+\boldsymbol{{\phi}}}{\boldsymbol{{\Omega}}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u(x , y , t) = c + 2*diff(ln(RiemannTheta(k*x + l*y + omega*t + phi, Omega)), [x$(2)])

Error
Missing Macro Error Missing Macro Error - -
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