LaTeX to CAS translator

This mockup demonstrates the concept of TeX to Computer Algebra System (CAS) conversion.

The demo-application converts LaTeX functions which directly translate to CAS counterparts.

Functions without explicit CAS support are available for translation via a DRMF package (under development).

The following LaTeX input ...

{\displaystyle \Theta_\Lambda(\tau) = \sum_{x\in\Lambda}e^{i\pi\tau\|x\|^2}\qquad\mathrm{Im}\,\tau > 0.}

${\displaystyle \Theta _{\Lambda }(\tau )=\sum _{x\in \Lambda }e^{i\pi \tau \|x\|^{2}}\qquad \mathrm {Im} \,\tau >0.}$

... is translated to the CAS output ...

Semantic latex: \Theta_\Lambda(\tau) = \sum_{x\in\Lambda} \expe^{\iunit \cpi \tau \|x \|^2} \qquad \mathrm{Im} \tau > 0

Confidence: 0

Mathematica

Translation: Subscript[\[CapitalTheta], \[CapitalLambda]][\[Tau]] == Sum[Exp[I*Pi*\[Tau]*(Norm[x])^(2)], {x, \[CapitalLambda]}, GenerateConditions->None] > 0

Information

Sub Equations

Subscript[\[CapitalTheta], \[CapitalLambda]][\[Tau]] = Sum[Exp[I*Pi*\[Tau]*(Norm[x])^(2)], {x, \[CapitalLambda]}, GenerateConditions->None]

Sum[Exp[I*Pi*\[Tau]*(Norm[x])^(2)], {x, \[CapitalLambda]}, GenerateConditions->None] > 0

Free variables

I

Subscript[\[CapitalTheta], \[CapitalLambda]]

\[CapitalLambda]

\[Tau]

m

Constraints

I*m*\[Tau]

Symbol info

Pi was translated to: Pi

Unable to translate operator (imaginary part of complex number $arg1). Interpret it as a sequence of multiplications instead.

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Recognizes e with power as the exponential function. It was translated as a function.

Imaginary unit was translated to: I

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) No translation possible for given token: norm [\|x\|]

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

(LaTeX -> Maple) No translation possible for given token: norm [\|x\|]

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$\Theta _{\Lambda }(\tau )=\sum _{x\in \Lambda }e^{i\pi \tau \|x\|^{2}}\qquad \mathrm {Im} \,\tau >0$

$\Lambda$

Is part of

$\Theta _{\Lambda }(\tau )=\sum _{x\in \Lambda }e^{i\pi \tau \|x\|^{2}}\qquad \mathrm {Im} \,\tau >0$

Complete translation information:

{
  "id" : "FORMULA_e0eeb35abfd1bb59f64ea48c5ae017ae",
  "formula" : "\\Theta_\\Lambda(\\tau) = \\sum_{x\\in\\Lambda}e^{i\\pi\\tau\\|x\\|^2}\\qquad\\mathrm{Im}\\tau > 0",
  "semanticFormula" : "\\Theta_\\Lambda(\\tau) = \\sum_{x\\in\\Lambda} \\expe^{\\iunit \\cpi \\tau \\|x \\|^2} \\qquad \\mathrm{Im} \\tau > 0",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "Subscript[\\[CapitalTheta], \\[CapitalLambda]][\\[Tau]] == Sum[Exp[I*Pi*\\[Tau]*(Norm[x])^(2)], {x, \\[CapitalLambda]}, GenerateConditions->None] > 0",
      "translationInformation" : {
        "subEquations" : [ "Subscript[\\[CapitalTheta], \\[CapitalLambda]][\\[Tau]] = Sum[Exp[I*Pi*\\[Tau]*(Norm[x])^(2)], {x, \\[CapitalLambda]}, GenerateConditions->None]", "Sum[Exp[I*Pi*\\[Tau]*(Norm[x])^(2)], {x, \\[CapitalLambda]}, GenerateConditions->None] > 0" ],
        "freeVariables" : [ "I", "Subscript[\\[CapitalTheta], \\[CapitalLambda]]", "\\[CapitalLambda]", "\\[Tau]", "m" ],
        "constraints" : [ "I*m*\\[Tau]" ],
        "tokenTranslations" : {
          "\\cpi" : "Pi was translated to: Pi",
          "Im" : "Unable to translate operator (imaginary part of complex number $arg1). Interpret it as a sequence of multiplications instead.",
          "\\Theta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\iunit" : "Imaginary unit was translated to: I"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "SymPy" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> SymPy) No translation possible for given token: norm [\\|x\\|]"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "Maple" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Maple) No translation possible for given token: norm [\\|x\\|]"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    }
  },
  "positions" : [ ],
  "includes" : [ "\\Theta_\\Lambda(\\tau) = \\sum_{x\\in\\Lambda}e^{i\\pi\\tau\\|x\\|^2}\\qquad\\mathrm{Im}\\,\\tau > 0", "\\Lambda" ],
  "isPartOf" : [ "\\Theta_\\Lambda(\\tau) = \\sum_{x\\in\\Lambda}e^{i\\pi\\tau\\|x\\|^2}\\qquad\\mathrm{Im}\\,\\tau > 0" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	In [[mathematics]], the '''theta function of a lattice''' is a function whose coefficients give the number of vectors of a given norm. ==Definition== One can associate to any (positive-definite) [[Lattice (discrete subgroup)\|lattice]] Λ a [[theta function]] given by :<math>\Theta_\Lambda(\tau) = \sum_{x\in\Lambda}e^{i\pi\tau\\|x\\|^2}\qquad\mathrm{Im}\,\tau > 0.</math> The theta function of a [[Lattice (discrete subgroup)\|lattice]] is then a [[holomorphic function]] on the [[upper half-plane]]. Furthermore, the theta function of an even [[unimodular lattice]] of rank ''n'' is actually a [[modular form]] of weight ''n''/2. The theta function of an integral lattice is often written as a power series in <math>q = e^{2i\pi\tau}</math> so that the coefficient of ''q''<sup>''n''</sup> gives the number of lattice vectors of norm 2''n''. ==References== *{{dlmf\|id=21\|title=Multidimensional Theta Functions\|first=Bernard \|last=Deconinck}} [[Category:Theta functions]] {{numtheory-stub}}
	Purge cached results.

LaTeX to CAS translator

Mathematica

Information

Tests

Symbolic

Numeric

SymPy

Information

Tests

Symbolic

Numeric

Maple

Information

Tests

Symbolic

Numeric

Dependency Graph Information

Specify your own input

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