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 I=\int^{x_2}_{x_{1}}f(x)e^{i\phi(x)}dx}

${\displaystyle I=\int _{x_{1}}^{x_{2}}f(x)e^{i\phi (x)}dx}$

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

Semantic latex: I = \int_{x_{1}}^{x_2} f(x) \expe^{\iunit \phi(x)} \diff{x}

Confidence: 0

Mathematica

Translation: I == Integrate[f[x]* Exp[I*\[Phi][x]], {x, Subscript[x, 1], Subscript[x, 2]}, GenerateConditions->None]

Information

Sub Equations

I = Integrate[f[x]* Exp[I*\[Phi][x]], {x, Subscript[x, 1], Subscript[x, 2]}, GenerateConditions->None]

Free variables

I

Subscript[x, 1]

Subscript[x, 2]

\[Phi]

Symbol info

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

Imaginary unit was translated to: I

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

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

Tests

Symbolic

Numeric

SymPy

Translation: I == integrate(f(x)* exp(I*Symbol('phi')(x)), (x, Symbol('{x}_{1}'), Symbol('{x}_{2}')))

Information

Sub Equations

I = integrate(f(x)* exp(I*Symbol('phi')(x)), (x, Symbol('{x}_{1}'), Symbol('{x}_{2}')))

Free variables

I

Symbol('phi')

Symbol('{x}_{1}')

Symbol('{x}_{2}')

Symbol info

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

Imaginary unit was translated to: I

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

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

Tests

Symbolic

Numeric

Maple

Translation: I = int(f(x)* exp(I*phi(x)), x = x[1]..x[2])

Information

Sub Equations

I = int(f(x)* exp(I*phi(x)), x = x[1]..x[2])

Free variables

I

phi

x[1]

x[2]

Symbol info

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

Imaginary unit was translated to: I

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

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$x$

$x)$

Complete translation information:

{
  "id" : "FORMULA_ca28fb6b98d6784ad4be031aad681678",
  "formula" : "I=\\int^{x_2}_{x_{1}}f(x)e^{i\\phi(x)}dx",
  "semanticFormula" : "I = \\int_{x_{1}}^{x_2} f(x) \\expe^{\\iunit \\phi(x)} \\diff{x}",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "I == Integrate[f[x]* Exp[I*\\[Phi][x]], {x, Subscript[x, 1], Subscript[x, 2]}, GenerateConditions->None]",
      "translationInformation" : {
        "subEquations" : [ "I = Integrate[f[x]* Exp[I*\\[Phi][x]], {x, Subscript[x, 1], Subscript[x, 2]}, GenerateConditions->None]" ],
        "freeVariables" : [ "I", "Subscript[x, 1]", "Subscript[x, 2]", "\\[Phi]" ],
        "tokenTranslations" : {
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\iunit" : "Imaginary unit was translated to: I",
          "f" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
        }
      },
      "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" : "I == integrate(f(x)* exp(I*Symbol('phi')(x)), (x, Symbol('{x}_{1}'), Symbol('{x}_{2}')))",
      "translationInformation" : {
        "subEquations" : [ "I = integrate(f(x)* exp(I*Symbol('phi')(x)), (x, Symbol('{x}_{1}'), Symbol('{x}_{2}')))" ],
        "freeVariables" : [ "I", "Symbol('phi')", "Symbol('{x}_{1}')", "Symbol('{x}_{2}')" ],
        "tokenTranslations" : {
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\iunit" : "Imaginary unit was translated to: I",
          "f" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
        }
      },
      "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" : "I = int(f(x)* exp(I*phi(x)), x = x[1]..x[2])",
      "translationInformation" : {
        "subEquations" : [ "I = int(f(x)* exp(I*phi(x)), x = x[1]..x[2])" ],
        "freeVariables" : [ "I", "phi", "x[1]", "x[2]" ],
        "tokenTranslations" : {
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\iunit" : "Imaginary unit was translated to: I",
          "f" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
        }
      },
      "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" : [ "x", "x)" ],
  "isPartOf" : [ ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	[[File:Mplwp Scorers Gi Hi.svg\|300px\|thumb\|[[Graph of a function\|Graph]] of <math>\mathrm{Gi}(x)</math> and <math>\mathrm{Hi}(x)</math>]] In [[mathematics]], the '''Scorer's functions''' are [[special function]]s studied by {{harvtxt\|Scorer\|1950}} and denoted Gi(''x'') and Hi(''x''). Hi(''x'') and Gi(''x'') solve the equation :<math>y''(x) - x\ y(x) = \frac{1}{\pi}</math> and are given by :<math>\mathrm{Gi}(x) = \frac{1}{\pi} \int_0^\infty \sin\left(\frac{t^3}{3} + xt\right)\, dt,</math> :<math>\mathrm{Hi}(x) = \frac{1}{\pi} \int_0^\infty \exp\left(-\frac{t^3}{3} + xt\right)\, dt.</math> The Scorer's functions can also be defined in terms of [[Airy function]]s: :<math>\begin{align} \mathrm{Gi}(x) &{}= \mathrm{Bi}(x) \int_x^\infty \mathrm{Ai}(t) \, dt + \mathrm{Ai}(x) \int_0^x \mathrm{Bi}(t) \, dt, \\ \mathrm{Hi}(x) &{}= \mathrm{Bi}(x) \int_{-\infty}^x \mathrm{Ai}(t) \, dt - \mathrm{Ai}(x) \int_{-\infty}^x \mathrm{Bi}(t) \, dt. \end{align} </math> ==References== * {{dlmf\|title= Scorer functions \|id=9.12\|first=F. W. J.\|last= Olver}} *{{Citation \| last1=Scorer \| first1=R. S. \| title=Numerical evaluation of integrals of the form <math>I=\int^{x_2}_{x_{1}}f(x)e^{i\phi(x)}dx</math> and the tabulation of the function <math>{\rm Gi} (z)=\frac{1}{\pi}\int^\infty_0{\rm sin}\left(uz+\frac 13 u^3\right)du</math> \| doi=10.1093/qjmam/3.1.107 \| mr=0037604 \|id=\| year=1950 \| journal=The Quarterly Journal of Mechanics and Applied Mathematics \| issn=0033-5614 \| volume=3 \| pages=107–112}} [[Category:Special functions]] {{mathanalysis-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

Navigation menu

Search