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 \mathit{He}_n(x) = (-1)^n e^{\frac{x^2}{2}}\frac{d^n}{dx^n}e^{-\frac{x^2}{2}},}
... is translated to the CAS output ...
Semantic latex: H \expe_n(x) =(- 1)^n \expe^{\frac{x^2}{2}} \deriv [n]{ }{x} \expe^{-\frac{x^2}{2}}
Confidence: 0
Mathematica
Translation: H*Subscript[E, n]*(x) == (- 1)^(n)* Exp[Divide[(x)^(2),2]]*D[Exp[-Divide[(x)^(2),2]], {x, n}]
Information
Sub Equations
- H*Subscript[E, n]*(x) = (- 1)^(n)* Exp[Divide[(x)^(2),2]]*D[Exp[-Divide[(x)^(2),2]], {x, n}]
Free variables
- H
- n
- x
Symbol info
- Recognizes e with power as the exponential function. It was translated as a function.
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: D[$1, {$2, $0}] Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 Mathematica: https://reference.wolfram.com/language/ref/D.html
Tests
Symbolic
Numeric
SymPy
Translation: H*Symbol('{E}_{n}')*(x) == (- 1)**(n)* exp(((x)**(2))/(2))*diff(exp(-((x)**(2))/(2)), x, n)
Information
Sub Equations
- H*Symbol('{E}_{n}')*(x) = (- 1)**(n)* exp(((x)**(2))/(2))*diff(exp(-((x)**(2))/(2)), x, n)
Free variables
- H
- n
- x
Symbol info
- Recognizes e with power as the exponential function. It was translated as a function.
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: diff($1, $2, $0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 SymPy: https://docs.sympy.org/latest/tutorial/calculus.html#derivatives
Tests
Symbolic
Numeric
Maple
Translation: H*exp(1)[n]*(x) = (- 1)^(n)* exp(((x)^(2))/(2))*diff(exp(-((x)^(2))/(2)), [x$(n)])
Information
Sub Equations
- H*exp(1)[n]*(x) = (- 1)^(n)* exp(((x)^(2))/(2))*diff(exp(-((x)^(2))/(2)), [x$(n)])
Free variables
- H
- n
- x
Symbol info
- Recognizes e with power as the exponential function. It was translated as a function.
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: diff($1, [$2$($0)]) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 Maple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=diff
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- probabilists ' Hermite polynomial
- convenient method
- physicists ' Hermite polynomial
- outset
- different standardization in common use
Complete translation information:
{
"id" : "FORMULA_4ec340c8eb40d66aef54e2742a4a7e53",
"formula" : "\\mathit{He}_n(x) = (-1)^n e^{\\frac{x^2}{2}}\\frac{d^n}{dx^n}e^{-\\frac{x^2}{2}}",
"semanticFormula" : "H \\expe_n(x) =(- 1)^n \\expe^{\\frac{x^2}{2}} \\deriv [n]{ }{x} \\expe^{-\\frac{x^2}{2}}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "H*Subscript[E, n]*(x) == (- 1)^(n)* Exp[Divide[(x)^(2),2]]*D[Exp[-Divide[(x)^(2),2]], {x, n}]",
"translationInformation" : {
"subEquations" : [ "H*Subscript[E, n]*(x) = (- 1)^(n)* Exp[Divide[(x)^(2),2]]*D[Exp[-Divide[(x)^(2),2]], {x, n}]" ],
"freeVariables" : [ "H", "n", "x" ],
"tokenTranslations" : {
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: D[$1, {$2, $0}]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nMathematica: https://reference.wolfram.com/language/ref/D.html"
}
},
"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" : "H*Symbol('{E}_{n}')*(x) == (- 1)**(n)* exp(((x)**(2))/(2))*diff(exp(-((x)**(2))/(2)), x, n)",
"translationInformation" : {
"subEquations" : [ "H*Symbol('{E}_{n}')*(x) = (- 1)**(n)* exp(((x)**(2))/(2))*diff(exp(-((x)**(2))/(2)), x, n)" ],
"freeVariables" : [ "H", "n", "x" ],
"tokenTranslations" : {
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: diff($1, $2, $0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nSymPy: https://docs.sympy.org/latest/tutorial/calculus.html#derivatives"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "H*exp(1)[n]*(x) = (- 1)^(n)* exp(((x)^(2))/(2))*diff(exp(-((x)^(2))/(2)), [x$(n)])",
"translationInformation" : {
"subEquations" : [ "H*exp(1)[n]*(x) = (- 1)^(n)* exp(((x)^(2))/(2))*diff(exp(-((x)^(2))/(2)), [x$(n)])" ],
"freeVariables" : [ "H", "n", "x" ],
"tokenTranslations" : {
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: diff($1, [$2$($0)])\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nMaple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=diff"
}
},
"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" : [ {
"section" : 1,
"sentence" : 1,
"word" : 33
} ],
"includes" : [ "He", "He_{n}", "H_{n}", "n", "H_{n}(x)", "He_{n}(x)", "x", "x^{n}", "D_{n}(z)", "\\psi_{n}", "\\psi_{n}(x)", "x^{k}", "H_{n}(y)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "probabilists ' Hermite polynomial",
"score" : 0.6460746792928004
}, {
"definition" : "convenient method",
"score" : 0.5988174995334326
}, {
"definition" : "physicists ' Hermite polynomial",
"score" : 0.5988174995334326
}, {
"definition" : "outset",
"score" : 0.5500952380952381
}, {
"definition" : "different standardization in common use",
"score" : 0.5049074255814494
} ]
}