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{d^2y}{dz^2} + (\lambda - 2h^2\cos 2z)y = 0. }
... is translated to the CAS output ...
Semantic latex: \deriv [2]{y}{z} +(\lambda - 2 h^2 \cos 2 z) y = 0
Confidence: 0
Mathematica
Translation: D[y, {z, 2}]+(\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y == 0
Information
Sub Equations
- D[y, {z, 2}]+(\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y = 0
Free variables
- \[Lambda]
- h
- y
- z
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: Cos[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Mathematica: https://reference.wolfram.com/language/ref/Cos.html
- 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
Test expression: (D[y, {z, 2}]+(\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y)-(0)
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: diff(y, z, 2)+(Symbol('lambda')- 2*(h)**(2)* cos(2)*z)*y == 0
Information
Sub Equations
- diff(y, z, 2)+(Symbol('lambda')- 2*(h)**(2)* cos(2)*z)*y = 0
Free variables
- Symbol('lambda')
- h
- y
- z
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cos
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: diff($1, $2, $0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 SymPy: https://docs.sympy.org/latest/tutorial/calculus.html#derivatives
Tests
Symbolic
Numeric
Maple
Translation: diff(y, [z$(2)])+(lambda - 2*(h)^(2)* cos(2)*z)*y = 0
Information
Sub Equations
- diff(y, [z$(2)])+(lambda - 2*(h)^(2)* cos(2)*z)*y = 0
Free variables
- h
- lambda
- y
- z
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos
- 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
Description
- Mathieu equation
- equation
Complete translation information:
{
"id" : "FORMULA_f61c342fb49ca917eb79ec57a8a34d98",
"formula" : "\\frac{d^2y}{dz^2} + (\\lambda - 2h^2\\cos 2z)y = 0",
"semanticFormula" : "\\deriv [2]{y}{z} +(\\lambda - 2 h^2 \\cos 2 z) y = 0",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "D[y, {z, 2}]+(\\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y == 0",
"translationInformation" : {
"subEquations" : [ "D[y, {z, 2}]+(\\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y = 0" ],
"freeVariables" : [ "\\[Lambda]", "h", "y", "z" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: Cos[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMathematica: https://reference.wolfram.com/language/ref/Cos.html",
"\\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" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "D[y, {z, 2}]+(\\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y",
"rhs" : "0",
"testExpression" : "(D[y, {z, 2}]+(\\[Lambda]- 2*(h)^(2)* Cos[2]*z)*y)-(0)",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "diff(y, z, 2)+(Symbol('lambda')- 2*(h)**(2)* cos(2)*z)*y == 0",
"translationInformation" : {
"subEquations" : [ "diff(y, z, 2)+(Symbol('lambda')- 2*(h)**(2)* cos(2)*z)*y = 0" ],
"freeVariables" : [ "Symbol('lambda')", "h", "y", "z" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cos",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: diff($1, $2, $0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nSymPy: https://docs.sympy.org/latest/tutorial/calculus.html#derivatives"
}
}
},
"Maple" : {
"translation" : "diff(y, [z$(2)])+(lambda - 2*(h)^(2)* cos(2)*z)*y = 0",
"translationInformation" : {
"subEquations" : [ "diff(y, [z$(2)])+(lambda - 2*(h)^(2)* cos(2)*z)*y = 0" ],
"freeVariables" : [ "h", "lambda", "y", "z" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos",
"\\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"
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 6,
"word" : 9
} ],
"includes" : [ ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "Mathieu equation",
"score" : 0.722
}, {
"definition" : "equation",
"score" : 0.6859086196238077
} ]
}