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^{[\alpha]}(x)}
... is translated to the CAS output ...
Semantic latex: \mathit{He}_n^{[\alpha]}(x)
Confidence: 0
Mathematica
Translation: (Subscript[He, n])^(\[Alpha])[x]
Information
Sub Equations
- (Subscript[He, n])^(\[Alpha])[x]
Free variables
- \[Alpha]
- n
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
SymPy
Translation: (Symbol('{He}_{n}'))**(Symbol('alpha'))(x)
Information
Sub Equations
- (Symbol('{He}_{n}'))**(Symbol('alpha'))(x)
Free variables
- Symbol('alpha')
- n
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Maple
Translation: (He[n])^(alpha)(x)
Information
Sub Equations
- (He[n])^(alpha)(x)
Free variables
- alpha
- n
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- variance
- generalized Hermite polynomial
- positive number
- scaling
- polynomial sequence
- umbral composition
- identity
- coefficient
- term
- moment of the normal distribution
- sequence
- absolute value
- moment of normal probability distribution
- normal distribution
- special case of the cross-sequence identity
- group under the operation
- Hermite polynomial of negative variance
- value
- minus sign
Complete translation information:
{
"id" : "FORMULA_916cc84e1ef0503a8203854322a0adaa",
"formula" : "\\mathit{He}_n^{[\\alpha]}(x)",
"semanticFormula" : "\\mathit{He}_n^{[\\alpha]}(x)",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "(Subscript[He, n])^(\\[Alpha])[x]",
"translationInformation" : {
"subEquations" : [ "(Subscript[He, n])^(\\[Alpha])[x]" ],
"freeVariables" : [ "\\[Alpha]", "n", "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",
"He" : "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" : "(Symbol('{He}_{n}'))**(Symbol('alpha'))(x)",
"translationInformation" : {
"subEquations" : [ "(Symbol('{He}_{n}'))**(Symbol('alpha'))(x)" ],
"freeVariables" : [ "Symbol('alpha')", "n", "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",
"He" : "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" : "(He[n])^(alpha)(x)",
"translationInformation" : {
"subEquations" : [ "(He[n])^(alpha)(x)" ],
"freeVariables" : [ "alpha", "n", "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",
"He" : "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" : [ {
"section" : 17,
"sentence" : 1,
"word" : 12
}, {
"section" : 18,
"sentence" : 1,
"word" : 17
} ],
"includes" : [ "He", "n", "x", "\\alpha" ],
"isPartOf" : [ "\\mathit{He}_n^{[\\alpha]}(x) = \\alpha^{\\frac{n}{2}}\\mathit{He}_n\\left(\\frac{x}{\\sqrt{\\alpha}}\\right) = \\left(\\frac{\\alpha}{2}\\right)^{\\frac{n}{2}} H_n\\left( \\frac{x}{\\sqrt{2 \\alpha}}\\right) = e^{-\\frac{\\alpha D^2}{2}} \\left(x^n\\right)", "\\mathit{He}_n^{[\\alpha]}(x) = \\sum_{k=0}^n h^{[\\alpha]}_{n,k} x^k", "\\left(\\mathit{He}_n^{[\\alpha]} \\circ \\mathit{He}^{[\\beta]}\\right)(x) = \\mathit{He}_n^{[\\alpha+\\beta]}(x)", "\\mathit{He}_n^{[\\alpha+\\beta]}(x + y) = \\sum_{k=0}^n \\binom{n}{k} \\mathit{He}_k^{[\\alpha]}(x) \\mathit{He}_{n-k}^{[\\beta]}(y)", "\\mathit{He}_n^{[-\\alpha]}(x)", "E[X^n] = \\mathit{He}_n^{[-\\sigma^2]}(\\mu)", "\\sum_{k=0}^n \\binom{n}{k} \\mathit{He}_k^{[\\alpha]}(x) \\mathit{He}_{n-k}^{[-\\alpha]}(y) = \\mathit{He}_n^{[0]}(x + y) = (x + y)^n" ],
"definiens" : [ {
"definition" : "variance",
"score" : 0.7567828878819742
}, {
"definition" : "generalized Hermite polynomial",
"score" : 0.722
}, {
"definition" : "positive number",
"score" : 0.6629879847031728
}, {
"definition" : "scaling",
"score" : 0.6629879847031728
}, {
"definition" : "polynomial sequence",
"score" : 0.5954181816892302
}, {
"definition" : "umbral composition",
"score" : 0.5583345920624354
}, {
"definition" : "identity",
"score" : 0.4555357896715027
}, {
"definition" : "coefficient",
"score" : 0.4391501501950797
}, {
"definition" : "term",
"score" : 0.40399210270803576
}, {
"definition" : "moment of the normal distribution",
"score" : 0.34589919335754316
}, {
"definition" : "sequence",
"score" : 0.3198499638698394
}, {
"definition" : "absolute value",
"score" : 0.319333892799869
}, {
"definition" : "moment of normal probability distribution",
"score" : 0.31920930249007934
}, {
"definition" : "normal distribution",
"score" : 0.31920930249007934
}, {
"definition" : "special case of the cross-sequence identity",
"score" : 0.3191837070106504
}, {
"definition" : "group under the operation",
"score" : 0.2800160235388322
}, {
"definition" : "Hermite polynomial of negative variance",
"score" : 0.2800160235388322
}, {
"definition" : "value",
"score" : 0.2793753621590721
}, {
"definition" : "minus sign",
"score" : 0.18403658234126982
} ]
}