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 \frac{1}{(1-2xt+t^2)^\alpha}=\sum_{n=0}^\infty C_n^{(\alpha)}(x) t^n.}
... is translated to the CAS output ...
Semantic latex: \frac{1}{(1-2xt+t^2)^\alpha} = \sum_{n=0}^\infty \ultrasphpoly{\alpha}{n}@{x} t^n
Confidence: 0.6805
Mathematica
Translation: Divide[1,(1 - 2*x*t + (t)^(2))^\[Alpha]] == Sum[GegenbauerC[n, \[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- Divide[1,(1 - 2*x*t + (t)^(2))^\[Alpha]] = Sum[GegenbauerC[n, \[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None]
Free variables
- \[Alpha]
- t
- x
Symbol info
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Ultraspherical Gegenbauer polynomial; Example: \ultrasphpoly{\lambda}{n}@{x}
Will be translated to: GegenbauerC[$1, $0, $2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3 Mathematica: https://reference.wolfram.com/language/ref/GegenbauerC.html
Tests
Symbolic
Test expression: (Divide[1,(1 - 2*x*t + (t)^(2))^\[Alpha]])-(Sum[GegenbauerC[n, \[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \ultrasphpoly [\ultrasphpoly]
Tests
Symbolic
Numeric
Maple
Translation: (1)/((1 - 2*x*t + (t)^(2))^(alpha)) = sum(GegenbauerC(n, alpha, x)*(t)^(n), n = 0..infinity)
Information
Sub Equations
- (1)/((1 - 2*x*t + (t)^(2))^(alpha)) = sum(GegenbauerC(n, alpha, x)*(t)^(n), n = 0..infinity)
Free variables
- alpha
- t
- x
Symbol info
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Ultraspherical Gegenbauer polynomial; Example: \ultrasphpoly{\lambda}{n}@{x}
Will be translated to: GegenbauerC($1, $0, $2) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GegenbauerC
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- term
- function
- polynomial
Complete translation information:
{
"id" : "FORMULA_d5c06dec4eda047cbeb93360a4340771",
"formula" : "\\frac{1}{(1-2xt+t^2)^\\alpha}=\\sum_{n=0}^\\infty C_n^{(\\alpha)}(x) t^n",
"semanticFormula" : "\\frac{1}{(1-2xt+t^2)^\\alpha} = \\sum_{n=0}^\\infty \\ultrasphpoly{\\alpha}{n}@{x} t^n",
"confidence" : 0.6805,
"translations" : {
"Mathematica" : {
"translation" : "Divide[1,(1 - 2*x*t + (t)^(2))^\\[Alpha]] == Sum[GegenbauerC[n, \\[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "Divide[1,(1 - 2*x*t + (t)^(2))^\\[Alpha]] = Sum[GegenbauerC[n, \\[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "t", "x" ],
"tokenTranslations" : {
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\ultrasphpoly" : "Ultraspherical Gegenbauer polynomial; Example: \\ultrasphpoly{\\lambda}{n}@{x}\nWill be translated to: GegenbauerC[$1, $0, $2]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r3\nMathematica: https://reference.wolfram.com/language/ref/GegenbauerC.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "Divide[1,(1 - 2*x*t + (t)^(2))^\\[Alpha]]",
"rhs" : "Sum[GegenbauerC[n, \\[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(Divide[1,(1 - 2*x*t + (t)^(2))^\\[Alpha]])-(Sum[GegenbauerC[n, \\[Alpha], x]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\ultrasphpoly [\\ultrasphpoly]"
}
}
},
"Maple" : {
"translation" : "(1)/((1 - 2*x*t + (t)^(2))^(alpha)) = sum(GegenbauerC(n, alpha, x)*(t)^(n), n = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "(1)/((1 - 2*x*t + (t)^(2))^(alpha)) = sum(GegenbauerC(n, alpha, x)*(t)^(n), n = 0..infinity)" ],
"freeVariables" : [ "alpha", "t", "x" ],
"tokenTranslations" : {
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\ultrasphpoly" : "Ultraspherical Gegenbauer polynomial; Example: \\ultrasphpoly{\\lambda}{n}@{x}\nWill be translated to: GegenbauerC($1, $0, $2)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r3\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GegenbauerC"
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 2,
"word" : 12
} ],
"includes" : [ "\\alpha", "C_{n}^{(\\alpha)}(x)", "n", "\\mathbf{R}^{n}" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "term",
"score" : 0.7125985104912714
}, {
"definition" : "function",
"score" : 0.6859086196238077
}, {
"definition" : "polynomial",
"score" : 0.6460746792928004
} ]
}