LaTeX to CAS translator
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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 A}
... is translated to the CAS output ...
Semantic latex: A
Confidence: 0
Mathematica
Translation: A
Information
Sub Equations
- A
Free variables
- A
Tests
Symbolic
Numeric
SymPy
Translation: A
Information
Sub Equations
- A
Free variables
- A
Tests
Symbolic
Numeric
Maple
Translation: A
Information
Sub Equations
- A
Free variables
- A
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- circle at point
- column vector of the matrix
- regular matrix
- ellipse
- form
- affine transformation of the Euclidean plane
- parametric representation
- arbitrary vector
- unit circle
- semi-minor axis
- conjugate diameter
- diagram
- line
- determinant
- area
- affine transformation of the coordinate
- angle from the positive horizontal axis
- canonical equation
- canonical form parameter
- center
- ellipse 's major axis
- expression
- formula
- general equation 's coefficient
- general form coefficient by the equation
- rotation angle
- semi-major axis
- area of the triangle
- center of the rectangle
- length
- area of the parallelogram
- constant area
- ellipse with semi-axis
- half
- minor axis
- parallelogram of tangent
- related line
- time
- triangle
- upper co-vertex of the ellipse
- degenerate case from the non-degenerate case
- intersection point
- line through the center
- major axis
- point
Complete translation information:
{
"id" : "FORMULA_7fc56270e7a70fa81a5935b72eacbe29",
"formula" : "A",
"semanticFormula" : "A",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "A",
"translationInformation" : {
"subEquations" : [ "A" ],
"freeVariables" : [ "A" ]
},
"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" : "A",
"translationInformation" : {
"subEquations" : [ "A" ],
"freeVariables" : [ "A" ]
},
"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" : "A",
"translationInformation" : {
"subEquations" : [ "A" ],
"freeVariables" : [ "A" ]
},
"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" : 13,
"sentence" : 1,
"word" : 15
}, {
"section" : 13,
"sentence" : 2,
"word" : 9
}, {
"section" : 22,
"sentence" : 2,
"word" : 16
}, {
"section" : 22,
"sentence" : 3,
"word" : 6
} ],
"includes" : [ "A_\\text{ellipse}", "A_\\text{ellipse} = \\pi ab", "A_\\text{ellipse} = \\frac{b}{a}\\pi a^2 = \\pi ab" ],
"isPartOf" : [ "\\vec x \\mapsto \\vec f\\!_0 + A\\vec x", "\\Delta = \\begin{vmatrix} A & \\frac{1}{2}B & \\frac{1}{2}D \\\\ \\frac{1}{2}B & C & \\frac{1}{2}E \\\\ \\frac{1}{2}D & \\frac{1}{2}E & F \\end{vmatrix} = \\left(AC - \\frac{B^2}{4}\\right) F + \\frac{BED}{4} - \\frac{CD^2}{4} - \\frac{AE^2}{4}", "\\begin{align} A &= a^2 \\sin^2\\theta + b^2 \\cos^2\\theta \\\\ B &= 2\\left(b^2 - a^2\\right) \\sin\\theta \\cos\\theta \\\\ C &= a^2 \\cos^2\\theta + b^2 \\sin^2\\theta \\\\ D &= -2A x_\\circ - B y_\\circ \\\\ E &= - B x_\\circ - 2C y_\\circ \\\\ F &= A x_\\circ^2 + B x_\\circ y_\\circ + C y_\\circ^2 - a^2 b^2.\\end{align}", "\\begin{align} a, b &= \\frac{-\\sqrt{2 \\Big(A E^2 + C D^2 - B D E + (B^2 - 4 A C) F\\Big)\\left((A + C) \\pm \\sqrt{(A - C)^2 + B^2}\\right)}}{B^2 - 4 A C} \\\\ x_\\circ &= \\frac{2CD - BE}{B^2 - 4AC} \\\\[3pt] y_\\circ &= \\frac{2AE - BD}{B^2 - 4AC} \\\\[3pt] \\theta &= \\begin{cases} \\arctan\\left(\\frac{1}{B}\\left(C - A - \\sqrt{(A - C)^2 + B^2}\\right)\\right) & \\text{for } B \\ne 0 \\\\ 0 & \\text{for } B = 0,\\ A < C \\\\ 90^\\circ & \\text{for } B = 0,\\ A > C \\\\ \\end{cases}\\end{align}", "A_\\Delta = \\frac{1}{2}ab", "A_\\Delta = \\frac{1}{2}\\det\\left(\\vec c_1,\\, \\vec c_2\\right) = \\cdots = \\frac{1}{2}ab", "A_\\Delta", "A = (-a,\\, 2b),\\, B = (a,\\,2b)", "V_1,\\, V_2,\\, B,\\, A", "V_2 A_i", "A_\\text{ellipse}", "A_\\text{ellipse} = \\pi ab", "A_\\text{ellipse} = \\frac{b}{a}\\pi a^2 = \\pi ab" ],
"definiens" : [ {
"definition" : "circle at point",
"score" : 0.722
}, {
"definition" : "column vector of the matrix",
"score" : 0.722
}, {
"definition" : "regular matrix",
"score" : 0.722
}, {
"definition" : "ellipse",
"score" : 0.7178799072356039
}, {
"definition" : "form",
"score" : 0.699079365079365
}, {
"definition" : "affine transformation of the Euclidean plane",
"score" : 0.6629879847031728
}, {
"definition" : "parametric representation",
"score" : 0.6629879847031728
}, {
"definition" : "arbitrary vector",
"score" : 0.6231540443721655
}, {
"definition" : "unit circle",
"score" : 0.5976690645014149
}, {
"definition" : "semi-minor axis",
"score" : 0.43286199395744857
}, {
"definition" : "conjugate diameter",
"score" : 0.40617210308498164
}, {
"definition" : "diagram",
"score" : 0.40617210308498164
}, {
"definition" : "line",
"score" : 0.3970721724437041
}, {
"definition" : "determinant",
"score" : 0.3552698412698419
}, {
"definition" : "area",
"score" : 0.3552698412698413
}, {
"definition" : "affine transformation of the coordinate",
"score" : 0.3458683517661158
}, {
"definition" : "angle from the positive horizontal axis",
"score" : 0.3458683517661158
}, {
"definition" : "canonical equation",
"score" : 0.3458683517661158
}, {
"definition" : "canonical form parameter",
"score" : 0.3458683517661158
}, {
"definition" : "center",
"score" : 0.3458683517661158
}, {
"definition" : "ellipse 's major axis",
"score" : 0.3458683517661158
}, {
"definition" : "expression",
"score" : 0.3458683517661158
}, {
"definition" : "formula",
"score" : 0.3458683517661158
}, {
"definition" : "general equation 's coefficient",
"score" : 0.3458683517661158
}, {
"definition" : "general form coefficient by the equation",
"score" : 0.3458683517661158
}, {
"definition" : "rotation angle",
"score" : 0.3458683517661158
}, {
"definition" : "semi-major axis",
"score" : 0.3458683517661158
}, {
"definition" : "area of the triangle",
"score" : 0.34586835176111275
}, {
"definition" : "center of the rectangle",
"score" : 0.34586835176111275
}, {
"definition" : "length",
"score" : 0.34586835176111275
}, {
"definition" : "area of the parallelogram",
"score" : 0.31917846089364893
}, {
"definition" : "constant area",
"score" : 0.31917846089364893
}, {
"definition" : "ellipse with semi-axis",
"score" : 0.31917846089364893
}, {
"definition" : "half",
"score" : 0.31917846089364893
}, {
"definition" : "minor axis",
"score" : 0.31917846089364893
}, {
"definition" : "parallelogram of tangent",
"score" : 0.31917846089364893
}, {
"definition" : "related line",
"score" : 0.31917846089364893
}, {
"definition" : "time",
"score" : 0.31917846089364893
}, {
"definition" : "triangle",
"score" : 0.31917846089364893
}, {
"definition" : "upper co-vertex of the ellipse",
"score" : 0.31917846089364893
}, {
"definition" : "degenerate case from the non-degenerate case",
"score" : 0.2793445205626423
}, {
"definition" : "intersection point",
"score" : 0.2793445205626417
}, {
"definition" : "line through the center",
"score" : 0.2793445205626417
}, {
"definition" : "major axis",
"score" : 0.23208734080327384
}, {
"definition" : "point",
"score" : 0.23208734080327384
} ]
}