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}{dx^2} + (\Lambda - \kappa^2 \operatorname{sn}^2x - \Omega^2k^4 \operatorname{sn}^4x)y = 0, }
... is translated to the CAS output ...
Semantic latex: \deriv [2]{y}{x} +(\Lambda - \kappa^2 \Jacobiellsnk@@{x}{k}^2 - \Omega^2 k^4 \Jacobiellsnk@@{x}{k}^4) y = 0
Confidence: 0.51053965490595
Mathematica
Translation: D[y, {x, 2}]+(\[CapitalLambda]- \[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y == 0
Information
Sub Equations
- D[y, {x, 2}]+(\[CapitalLambda]- \[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y = 0
Free variables
- \[CapitalLambda]
- \[CapitalOmega]
- \[Kappa]
- k
- x
- y
Symbol info
- 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
- Could be The omega constant == the Adamchik constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Jacobian elliptic function; Example: \Jacobiellsnk@@{z}{k}
Will be translated to: JacobiSN[$0, ($1)^2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/22.2#E4 Mathematica: https://reference.wolfram.com/language/ref/JacobiSN.html
Tests
Symbolic
Test expression: (D[y, {x, 2}]+(\[CapitalLambda]- \[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y)-(0)
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: \Jacobiellsnk [\Jacobiellsnk]
Tests
Symbolic
Numeric
Maple
Translation: diff(y, [x$(2)])+(Lambda - (kappa)^(2)* (JacobiSN(x, k))^(2)- (Omega)^(2)* (k)^(4)* (JacobiSN(x, k))^(4))*y = 0
Information
Sub Equations
- diff(y, [x$(2)])+(Lambda - (kappa)^(2)* (JacobiSN(x, k))^(2)- (Omega)^(2)* (k)^(4)* (JacobiSN(x, k))^(4))*y = 0
Free variables
- Lambda
- Omega
- k
- kappa
- x
- y
Symbol info
- 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
- Could be The omega constant == the Adamchik constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Jacobian elliptic function; Example: \Jacobiellsnk@@{z}{k}
Will be translated to: JacobiSN($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/22.2#E4 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=JacobiSN
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- constant
- ellipsoidal equation
- ellipsoidal wave equation
- elliptic modulus of the Jacobian elliptic function
- general form of Lamé 's equation
Complete translation information:
{
"id" : "FORMULA_8e35cbe109edd547afb6535cbb735a32",
"formula" : "\\frac{d^2y}{dx^2} + (\\Lambda - \\kappa^2 \\operatorname{sn}^2x - \\Omega^2k^4 \\operatorname{sn}^4x)y = 0",
"semanticFormula" : "\\deriv [2]{y}{x} +(\\Lambda - \\kappa^2 \\Jacobiellsnk@@{x}{k}^2 - \\Omega^2 k^4 \\Jacobiellsnk@@{x}{k}^4) y = 0",
"confidence" : 0.510539654905952,
"translations" : {
"Mathematica" : {
"translation" : "D[y, {x, 2}]+(\\[CapitalLambda]- \\[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \\[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y == 0",
"translationInformation" : {
"subEquations" : [ "D[y, {x, 2}]+(\\[CapitalLambda]- \\[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \\[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y = 0" ],
"freeVariables" : [ "\\[CapitalLambda]", "\\[CapitalOmega]", "\\[Kappa]", "k", "x", "y" ],
"tokenTranslations" : {
"\\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",
"\\Omega" : "Could be The omega constant == the Adamchik constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\Jacobiellsnk" : "Jacobian elliptic function; Example: \\Jacobiellsnk@@{z}{k}\nWill be translated to: JacobiSN[$0, ($1)^2]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/22.2#E4\nMathematica: https://reference.wolfram.com/language/ref/JacobiSN.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "D[y, {x, 2}]+(\\[CapitalLambda]- \\[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \\[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y",
"rhs" : "0",
"testExpression" : "(D[y, {x, 2}]+(\\[CapitalLambda]- \\[Kappa]^(2)* (JacobiSN[x, (k)^2])^(2)- \\[CapitalOmega]^(2)* (k)^(4)* (JacobiSN[x, (k)^2])^(4))*y)-(0)",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\Jacobiellsnk [\\Jacobiellsnk]"
}
}
},
"Maple" : {
"translation" : "diff(y, [x$(2)])+(Lambda - (kappa)^(2)* (JacobiSN(x, k))^(2)- (Omega)^(2)* (k)^(4)* (JacobiSN(x, k))^(4))*y = 0",
"translationInformation" : {
"subEquations" : [ "diff(y, [x$(2)])+(Lambda - (kappa)^(2)* (JacobiSN(x, k))^(2)- (Omega)^(2)* (k)^(4)* (JacobiSN(x, k))^(4))*y = 0" ],
"freeVariables" : [ "Lambda", "Omega", "k", "kappa", "x", "y" ],
"tokenTranslations" : {
"\\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",
"\\Omega" : "Could be The omega constant == the Adamchik constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\Jacobiellsnk" : "Jacobian elliptic function; Example: \\Jacobiellsnk@@{z}{k}\nWill be translated to: JacobiSN($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/22.2#E4\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=JacobiSN"
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 4,
"word" : 32
} ],
"includes" : [ "\\operatorname{sn}", "k", "\\Lambda", "\\kappa", "\\Omega" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "constant",
"score" : 0.7125985104912714
}, {
"definition" : "ellipsoidal equation",
"score" : 0.6859086196238077
}, {
"definition" : "ellipsoidal wave equation",
"score" : 0.6859086196238077
}, {
"definition" : "elliptic modulus of the Jacobian elliptic function",
"score" : 0.6859086196238077
}, {
"definition" : "general form of Lamé 's equation",
"score" : 0.6859086196238077
} ]
}