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 Y_{\ell, m}(\theta, \phi)}
... is translated to the CAS output ...
Semantic latex: \sphharmonicY{\ell}{m}@{\theta}{\phi}
Confidence: 0.92732082802543
Mathematica
Translation: SphericalHarmonicY[\[ScriptL], m, \[Theta], \[Phi]]
Information
Sub Equations
- SphericalHarmonicY[\[ScriptL], m, \[Theta], \[Phi]]
Free variables
- \[Phi]
- \[ScriptL]
- \[Theta]
- m
Symbol info
- Spherical harmonics; Example: \sphharmonicY{l}{m}@{\theta}{\phi}
Will be translated to: SphericalHarmonicY[$0, $1, $2, $3] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.30#E1 Mathematica: https://reference.wolfram.com/language/ref/SphericalHarmonicY.html
- was translated to: \[ScriptL]
- Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \sphharmonicY [\sphharmonicY]
Tests
Symbolic
Numeric
Maple
Translation: SphericalY(ell, m, theta, phi)
Information
Sub Equations
- SphericalY(ell, m, theta, phi)
Free variables
- ell
- m
- phi
- theta
Symbol info
- Spherical harmonics; Example: \sphharmonicY{l}{m}@{\theta}{\phi}
Will be translated to: SphericalY($0, $1, $2, $3) Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.30#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=SphericalY
- was translated to: ell
- Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- spherical harmonic
- function
- identity
- normalizing factor
- quantity in the square root
- solution
- term
- relation
- Legendre function
Complete translation information:
{
"id" : "FORMULA_93157dd7c297fd36ded248449857eac3",
"formula" : "Y_{\\ell, m}(\\theta, \\phi)",
"semanticFormula" : "\\sphharmonicY{\\ell}{m}@{\\theta}{\\phi}",
"confidence" : 0.9273208280254316,
"translations" : {
"Mathematica" : {
"translation" : "SphericalHarmonicY[\\[ScriptL], m, \\[Theta], \\[Phi]]",
"translationInformation" : {
"subEquations" : [ "SphericalHarmonicY[\\[ScriptL], m, \\[Theta], \\[Phi]]" ],
"freeVariables" : [ "\\[Phi]", "\\[ScriptL]", "\\[Theta]", "m" ],
"tokenTranslations" : {
"\\sphharmonicY" : "Spherical harmonics; Example: \\sphharmonicY{l}{m}@{\\theta}{\\phi}\nWill be translated to: SphericalHarmonicY[$0, $1, $2, $3]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.30#E1\nMathematica: https://reference.wolfram.com/language/ref/SphericalHarmonicY.html",
"\\ell" : "was translated to: \\[ScriptL]",
"\\phi" : "Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\sphharmonicY [\\sphharmonicY]"
}
},
"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" : "SphericalY(ell, m, theta, phi)",
"translationInformation" : {
"subEquations" : [ "SphericalY(ell, m, theta, phi)" ],
"freeVariables" : [ "ell", "m", "phi", "theta" ],
"tokenTranslations" : {
"\\sphharmonicY" : "Spherical harmonics; Example: \\sphharmonicY{l}{m}@{\\theta}{\\phi}\nWill be translated to: SphericalY($0, $1, $2, $3)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.30#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=SphericalY",
"\\ell" : "was translated to: ell",
"\\phi" : "Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : 12,
"sentence" : 12,
"word" : 2
} ],
"includes" : [ "m", "\\phi", "\\theta" ],
"isPartOf" : [ "Y_{\\ell, m}(\\theta, \\phi) = \\sqrt{\\frac{(2\\ell+1)(\\ell-m)!}{4\\pi(\\ell+m)!}}\\ P_\\ell^{m}(\\cos \\theta)\\ e^{im\\phi}\\qquad -\\ell \\le m \\le \\ell", "Y_{\\ell, m}^*(\\theta, \\phi) = (-1)^m Y_{\\ell, -m}(\\theta, \\phi)" ],
"definiens" : [ {
"definition" : "spherical harmonic",
"score" : 0.8728715749853855
}, {
"definition" : "function",
"score" : 0.722
}, {
"definition" : "identity",
"score" : 0.6793245439387732
}, {
"definition" : "normalizing factor",
"score" : 0.6687181434333315
}, {
"definition" : "quantity in the square root",
"score" : 0.6288842031023242
}, {
"definition" : "solution",
"score" : 0.6033992232315736
}, {
"definition" : "term",
"score" : 0.6033992232315736
}, {
"definition" : "relation",
"score" : 0.5561420434722057
}, {
"definition" : "Legendre function",
"score" : 0.5074197820340112
} ]
}