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 \tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1}
... is translated to the CAS output ...
Semantic latex: \tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1
Confidence: 0
Mathematica
Translation: Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)] == 1
Information
Sub Equations
- Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)] = 1
Free variables
- a
- b
- x
- y
Tests
Symbolic
Test expression: (Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)])-(1)
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: ((x)**(2))/((a)**(2))+((y)**(2))/((b)**(2)) == 1
Information
Sub Equations
- ((x)**(2))/((a)**(2))+((y)**(2))/((b)**(2)) = 1
Free variables
- a
- b
- x
- y
Tests
Symbolic
Numeric
Maple
Translation: ((x)^(2))/((a)^(2))+((y)^(2))/((b)^(2)) = 1
Information
Sub Equations
- ((x)^(2))/((a)^(2))+((y)^(2))/((b)^(2)) = 1
Free variables
- a
- b
- x
- y
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
- Failed to parse (syntax error): {\displaystyle \frac{\left(x_1 + su\right)^2}{a^2} + \frac{\left(y_1 + sv\right)^2}{b^2} = 1\ \quad\Longrightarrow\quad 2s\left(\frac{x_1u}{a^2} + \frac{y_1v}{b^2}\right) + s^2\left(\frac{u^2}{a^2} + \frac{v^2}{b^2}\right) = 0\}
- Failed to parse (syntax error): {\displaystyle \frac{\left(x - x_\circ\right)^2}{a^2} + \frac{\left(y - y_\circ\right)^2}{b^2} = 1 \}
- Failed to parse (syntax error): {\displaystyle \frac{(x - a)^2}{a^2} + \frac{y^2}{b^2} = 1\}
Description
- ellipse
- intersection point of orthogonal tangent
- circle
- equation
- center
- canonical ellipse equation
- ellipse with equation
- equation of a standard ellipse
- equation of an ellipse
- left vertex
- parametric representation of the standard ellipse
- point of the ellipse
- standard equation of the ellipse
- yield
- affine transformation of the coordinate
- angle from the positive horizontal axis
- axis as major axis
- canonical equation
- canonical form parameter
- eccentricity
- ellipse 's major axis
- expression
- formula
- general equation 's coefficient
- general form coefficient by the equation
- generation of point
- major/minor semi axis
- principle
- rotation angle
- semi-major axis
- semi-minor axis
- standard ellipse
- suitable coordinate system by an equation
- tangent at a point
- family of ellipsis
- metric property
- new parameter
- coordinate equation
- origin with width
- pencil at the vertex
- rational parametric equation of an ellipse
- trigonometric function
- line 's equation into the ellipse equation
- radical by suitable squaring
- section
- substitution
- height
- trigonometric formula
Complete translation information:
{
"id" : "FORMULA_7d0056d71dcc5ec47120f24edf027406",
"formula" : "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2}=1",
"semanticFormula" : "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2}=1",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)] == 1",
"translationInformation" : {
"subEquations" : [ "Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)] = 1" ],
"freeVariables" : [ "a", "b", "x", "y" ]
},
"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" : "Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)]",
"rhs" : "1",
"testExpression" : "(Divide[(x)^(2),(a)^(2)]+Divide[(y)^(2),(b)^(2)])-(1)",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "((x)**(2))/((a)**(2))+((y)**(2))/((b)**(2)) == 1",
"translationInformation" : {
"subEquations" : [ "((x)**(2))/((a)**(2))+((y)**(2))/((b)**(2)) = 1" ],
"freeVariables" : [ "a", "b", "x", "y" ]
}
},
"Maple" : {
"translation" : "((x)^(2))/((a)^(2))+((y)^(2))/((b)^(2)) = 1",
"translationInformation" : {
"subEquations" : [ "((x)^(2))/((a)^(2))+((y)^(2))/((b)^(2)) = 1" ],
"freeVariables" : [ "a", "b", "x", "y" ]
}
}
},
"positions" : [ {
"section" : 20,
"sentence" : 0,
"word" : 3
} ],
"includes" : [ "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2} = 1", "= 1", "b", "\\frac{x^2}{a^2}+\\frac{y^2}{b^2} = 1", "\\tfrac{x^2}{a^2} + \\tfrac{y^2}{b^2} = 1", "a", "y", "x", "\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1", "\\frac{x^2}{a^2}+\\frac{y^2}{b^2}= 1" ],
"isPartOf" : [ "\\frac{\\left(x_1 + su\\right)^2}{a^2} + \\frac{\\left(y_1 + sv\\right)^2}{b^2} = 1\\ \\quad\\Longrightarrow\\quad 2s\\left(\\frac{x_1u}{a^2} + \\frac{y_1v}{b^2}\\right) + s^2\\left(\\frac{u^2}{a^2} + \\frac{v^2}{b^2}\\right) = 0\\", "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2} = 1", "\\frac{x^2}{a^2}+\\frac{y^2}{b^2} = 1", "\\tfrac{x^2}{a^2} + \\tfrac{y^2}{b^2} = 1", "\\frac{\\left(x - x_\\circ\\right)^2}{a^2} + \\frac{\\left(y - y_\\circ\\right)^2}{b^2} = 1 \\", "\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1", "\\frac{(x - a)^2}{a^2} + \\frac{y^2}{b^2} = 1\\", "\\tfrac{\\left(x - x_\\circ\\right)^2}{a^2} + \\tfrac{\\left(y - y_\\circ\\right)^2}{b^2} = 1", "\\frac{x^2}{a^2}+\\frac{y^2}{b^2}= 1" ],
"definiens" : [ {
"definition" : "ellipse",
"score" : 0.8609998166517733
}, {
"definition" : "intersection point of orthogonal tangent",
"score" : 0.722
}, {
"definition" : "circle",
"score" : 0.6584038577190456
}, {
"definition" : "equation",
"score" : 0.47231271046425893
}, {
"definition" : "center",
"score" : 0.42102418301027866
}, {
"definition" : "canonical ellipse equation",
"score" : 0.35068571428571427
}, {
"definition" : "ellipse with equation",
"score" : 0.3412842247769857
}, {
"definition" : "equation of a standard ellipse",
"score" : 0.3412842247769857
}, {
"definition" : "equation of an ellipse",
"score" : 0.3412842247769857
}, {
"definition" : "left vertex",
"score" : 0.3412842247769857
}, {
"definition" : "parametric representation of the standard ellipse",
"score" : 0.3412842247769857
}, {
"definition" : "point of the ellipse",
"score" : 0.3412842247769857
}, {
"definition" : "standard equation of the ellipse",
"score" : 0.3412842247769857
}, {
"definition" : "yield",
"score" : 0.3412842247769857
}, {
"definition" : "affine transformation of the coordinate",
"score" : 0.31459433390952196
}, {
"definition" : "angle from the positive horizontal axis",
"score" : 0.31459433390952196
}, {
"definition" : "axis as major axis",
"score" : 0.31459433390952196
}, {
"definition" : "canonical equation",
"score" : 0.31459433390952196
}, {
"definition" : "canonical form parameter",
"score" : 0.31459433390952196
}, {
"definition" : "eccentricity",
"score" : 0.31459433390952196
}, {
"definition" : "ellipse 's major axis",
"score" : 0.31459433390952196
}, {
"definition" : "expression",
"score" : 0.31459433390952196
}, {
"definition" : "formula",
"score" : 0.31459433390952196
}, {
"definition" : "general equation 's coefficient",
"score" : 0.31459433390952196
}, {
"definition" : "general form coefficient by the equation",
"score" : 0.31459433390952196
}, {
"definition" : "generation of point",
"score" : 0.31459433390952196
}, {
"definition" : "major/minor semi axis",
"score" : 0.31459433390952196
}, {
"definition" : "principle",
"score" : 0.31459433390952196
}, {
"definition" : "rotation angle",
"score" : 0.31459433390952196
}, {
"definition" : "semi-major axis",
"score" : 0.31459433390952196
}, {
"definition" : "semi-minor axis",
"score" : 0.31459433390952196
}, {
"definition" : "standard ellipse",
"score" : 0.31459433390952196
}, {
"definition" : "suitable coordinate system by an equation",
"score" : 0.31459433390952196
}, {
"definition" : "tangent at a point",
"score" : 0.31459433390952196
}, {
"definition" : "family of ellipsis",
"score" : 0.27476039357851473
}, {
"definition" : "metric property",
"score" : 0.27476039357851473
}, {
"definition" : "new parameter",
"score" : 0.27476039357851473
}, {
"definition" : "coordinate equation",
"score" : 0.22750321381914684
}, {
"definition" : "origin with width",
"score" : 0.22750321381914684
}, {
"definition" : "pencil at the vertex",
"score" : 0.22750321381914684
}, {
"definition" : "rational parametric equation of an ellipse",
"score" : 0.22750321381914684
}, {
"definition" : "trigonometric function",
"score" : 0.22750321381914684
}, {
"definition" : "line 's equation into the ellipse equation",
"score" : 0.17878095238095237
}, {
"definition" : "radical by suitable squaring",
"score" : 0.17878095238095237
}, {
"definition" : "section",
"score" : 0.17878095238095237
}, {
"definition" : "substitution",
"score" : 0.17878095238095237
}, {
"definition" : "height",
"score" : 0.13359313986716373
}, {
"definition" : "trigonometric formula",
"score" : 0.13359313986716373
} ]
}