Results of Multidimensional Theta Functions: Difference between revisions

Revision as of 19:12, 17 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(2PiI((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(Piz,exp(IPi*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]+ Omegam[2], Omega) = exp(- 2PiI((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(2PiI(2alpha * Omega * alpha + alpha (x + y + u + v))) RiemannTheta(x + Omegaalpha + beta, Omega)RiemannTheta(y + Omegaalpha + beta, Omega)RiemannTheta(u + Omegaalpha + 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 }	4u[t] = 6u*u[x]+ u[x, x, x]	4Subscript[u, t] == 6u*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 }	Iu[t] = -(1)/(2)u[x, x]+(abs(u))^(2)* u	ISubscript[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 }	- 4u[t]+ 6uu[x]+ u[x, x, x][x]+ 3u[y, y] = 0	Subscript[- 4Subscript[u, t]+ 6uSubscript[u, x]+ Subscript[u, x, x, x], x]+ 3Subscript[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 + 2diff(ln(RiemannTheta(kx + ly + omegat + phi, Omega)), [x$(2)])	Error	Missing Macro Error	Missing Macro Error	-	-

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 {| class="wikitable sortable"
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-! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
+! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/21.7.E1 21.7.E1] || [[Item:Q6897|<math>P(\lambda,\mu) = 0</math>]] || <code>P*(lambda , mu) = 0</code> || <code>P*(\[Lambda], \[Mu]) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [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 || - || -
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-| [https://dlmf.nist.gov/21.7.E11 21.7.E11] || [[Item:Q6909|<math>\mu^{2} = Q(\lambda)</math>]] || <code>(mu)^(2) = Q*(lambda)</code> || <code>\[Mu]^(2) == Q*(\[Lambda])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/21.2.E8 21.2.E8] || [[Item:Q6864|<math>\Riemanntheta@{z}{\Omega} = \Jacobithetatau{3}@{\pi z}{\Omega}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{z}{\Omega} = \Jacobithetatau{3}@{\pi z}{\Omega}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(z, Omega) = JacobiTheta3(Pi*z,exp(I*Pi*Omega))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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-| [https://dlmf.nist.gov/21.7.E13 21.7.E13] || [[Item:Q6911|<math>\boldsymbol{{\eta}}(T) = \boldsymbol{{\eta}}(T^{c})</math>]] || <code>eta*(T) = eta*((T)^(c))</code> || <code>\[Eta]*(T) == \[Eta]*((T)^(c))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/21.3.E1 21.3.E1] || [[Item:Q6869|<math>\Riemanntheta@{-\mathbf{z}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{-\mathbf{z}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(- z, Omega) = RiemannTheta(z, Omega)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
 |-
-| [https://dlmf.nist.gov/21.9.E1 21.9.E1] || [[Item:Q6917|<math>4u_{t} = 6uu_{x}+u_{xxx}</math>]] || <code>4*u[t] = 6*u*u[x]+ u[x*x*x]</code> || <code>4*Subscript[u, t] == 6*u*Subscript[u, x]+ Subscript[u, x*x*x]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/21.3.E2 21.3.E2] || [[Item:Q6870|<math>\Riemanntheta@{\mathbf{z}+\mathbf{m}_{1}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Riemanntheta@{\mathbf{z}+\mathbf{m}_{1}}{\boldsymbol{{\Omega}}} = \Riemanntheta@{\mathbf{z}}{\boldsymbol{{\Omega}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>RiemannTheta(z + m[1], Omega) = RiemannTheta(z, Omega)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
 |-
-| [https://dlmf.nist.gov/21.9.E2 21.9.E2] || [[Item:Q6918|<math>iu_{t} = -\tfrac{1}{2}u_{xx}+|u|^{2}u</math>]] || <code>I*u[t] = -(1)/(2)*u[x*x]+(abs(u))^(2)* u</code> || <code>I*Subscript[u, t] == -Divide[1,2]*Subscript[u, x*x]+(Abs[u])^(2)* u</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/21.3.E3 21.3.E3] || [[Item:Q6871|<math>\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}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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-| [https://dlmf.nist.gov/21.9.E3 21.9.E3] || [[Item:Q6919|<math>(-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy} = 0</math>]] || <code>- 4*u[t]+ 6*u*u[x]+ u[x*x*x][x]+ 3*u[y*y] = 0</code> || <code>Subscript[- 4*Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x*x*x], x]+ 3*Subscript[u, y*y] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/21.6.E6 21.6.E6] || [[Item:Q6894|<math>\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}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
+|-
+| [https://dlmf.nist.gov/21.7.E1 21.7.E1] || [[Item:Q6897|<math>P(\lambda,\mu) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>P(\lambda,\mu) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>P(lambda , mu) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>P[\[Lambda], \[Mu]] == 0</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
+|-
+| [https://dlmf.nist.gov/21.7.E11 21.7.E11] || [[Item:Q6909|<math>\mu^{2} = Q(\lambda)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mu^{2} = Q(\lambda)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(mu)^(2) = Q(lambda)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Mu]^(2) == Q[\[Lambda]]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
+|-
+| [https://dlmf.nist.gov/21.7.E13 21.7.E13] || [[Item:Q6911|<math>\boldsymbol{{\eta}}(T) = \boldsymbol{{\eta}}(T^{c})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\boldsymbol{{\eta}}(T) = \boldsymbol{{\eta}}(T^{c})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>eta(T) = eta((T)^(c))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Eta][T] == \[Eta][(T)^(c)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
+|-
+| [https://dlmf.nist.gov/21.9.E1 21.9.E1] || [[Item:Q6917|<math>4u_{t} = 6uu_{x}+u_{xxx}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>4u_{t} = 6uu_{x}+u_{xxx}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>4*u[t] = 6*u*u[x]+ u[x, x, x]</syntaxhighlight> || <syntaxhighlight lang=mathematica>4*Subscript[u, t] == 6*u*Subscript[u, x]+ Subscript[u, x, x, x]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
+|-
+| [https://dlmf.nist.gov/21.9.E2 21.9.E2] || [[Item:Q6918|<math>iu_{t} = -\tfrac{1}{2}u_{xx}+|u|^{2}u</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>iu_{t} = -\tfrac{1}{2}u_{xx}+|u|^{2}u</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>I*u[t] = -(1)/(2)*u[x, x]+(abs(u))^(2)* u</syntaxhighlight> || <syntaxhighlight lang=mathematica>I*Subscript[u, t] == -Divide[1,2]*Subscript[u, x, x]+(Abs[u])^(2)* u</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
+|-
+| [https://dlmf.nist.gov/21.9.E3 21.9.E3] || [[Item:Q6919|<math>(-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- 4*u[t]+ 6*u*u[x]+ u[x, x, x][x]+ 3*u[y, y] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[- 4*Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x, x, x], x]+ 3*Subscript[u, y, y] == 0</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
+|-
+| [https://dlmf.nist.gov/21.9.E4 21.9.E4] || [[Item:Q6920|<math>u(x,y,t) = c+2\pderiv[2]{}{x}\ln@{\Riemanntheta@{\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+\boldsymbol{{\phi}}}{\boldsymbol{{\Omega}}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>u(x,y,t) = c+2\pderiv[2]{}{x}\ln@{\Riemanntheta@{\mathbf{k}x+\mathbf{l}y+\boldsymbol{{\omega}}t+\boldsymbol{{\phi}}}{\boldsymbol{{\Omega}}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>u(x , y , t) = c + 2*diff(ln(RiemannTheta(k*x + l*y + omega*t + phi, Omega)), [x$(2)])</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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Results of Multidimensional Theta Functions: Difference between revisions

Revision as of 19:12, 17 May 2021

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