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 B}
... is translated to the CAS output ...
Semantic latex: B
Confidence: 0
Mathematica
Translation: B
Information
Sub Equations
- B
Free variables
- B
Tests
Symbolic
Numeric
SymPy
Translation: B
Information
Sub Equations
- B
Free variables
- B
Tests
Symbolic
Numeric
Maple
Translation: B
Information
Sub Equations
- B
Free variables
- B
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- line
- circle at point
- major axis
- minor axis
- line through the center
- ellipse
- intersection point
- division
- point
- area
- determinant
- implicit equation
- affine transformation of the coordinate
- angle from the positive horizontal axis
- canonical equation
- canonical form parameter
- center
- center of the rectangle
- ellipse 's major axis
- expression
- formula
- general equation 's coefficient
- general form coefficient by the equation
- non-degenerate projective conic section
- related line
- rotation angle
- semi-major axis
- semi-minor axis
- following method
- pencil
- perspective mapping
- set of point
- single point of an ellipse
- Steiner generation of a conic section
- upper co-vertex of the ellipse
- degenerate case from the non-degenerate case
- equal spaced line segment
- n
- non-degenerate case
- side
- analytic geometry
- Cartesian plane
- diagram
- direction onto the line segment
- quadric
- rectangle
Complete translation information:
{
"id" : "FORMULA_9d5ed678fe57bcca610140957afab571",
"formula" : "B",
"semanticFormula" : "B",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "B",
"translationInformation" : {
"subEquations" : [ "B" ],
"freeVariables" : [ "B" ]
},
"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" : "B",
"translationInformation" : {
"subEquations" : [ "B" ],
"freeVariables" : [ "B" ]
},
"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" : "B",
"translationInformation" : {
"subEquations" : [ "B" ],
"freeVariables" : [ "B" ]
},
"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" : 22,
"sentence" : 2,
"word" : 18
}, {
"section" : 22,
"sentence" : 3,
"word" : 20
} ],
"includes" : [ ],
"isPartOf" : [ "\\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}", "B^2 - 4AC < 0", "\\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}", "AX^2 + B X Y + C Y^2 + D X + E Y + F = 0", "B(U),\\, B(V)", "B(U)", "B(V)", "A = (-a,\\, 2b),\\, B = (a,\\,2b)", "V_1,\\, V_2,\\, B,\\, A", "\\overline{V_1B}", "V_1 B_i", "2\\pi / \\sqrt{4AC - B^2}" ],
"definiens" : [ {
"definition" : "line",
"score" : 0.801430138372194
}, {
"definition" : "circle at point",
"score" : 0.6584038577190456
}, {
"definition" : "major axis",
"score" : 0.6329188778482951
}, {
"definition" : "minor axis",
"score" : 0.6329188778482951
}, {
"definition" : "line through the center",
"score" : 0.5713127376286706
}, {
"definition" : "ellipse",
"score" : 0.4058440032797556
}, {
"definition" : "intersection point",
"score" : 0.3949093921155009
}, {
"definition" : "division",
"score" : 0.3858094614742233
}, {
"definition" : "point",
"score" : 0.3858094614742233
}, {
"definition" : "area",
"score" : 0.35068571428571427
}, {
"definition" : "determinant",
"score" : 0.35068571428571427
}, {
"definition" : "implicit equation",
"score" : 0.35068571428571427
}, {
"definition" : "affine transformation of the coordinate",
"score" : 0.3412842247769857
}, {
"definition" : "angle from the positive horizontal axis",
"score" : 0.3412842247769857
}, {
"definition" : "canonical equation",
"score" : 0.3412842247769857
}, {
"definition" : "canonical form parameter",
"score" : 0.3412842247769857
}, {
"definition" : "center",
"score" : 0.3412842247769857
}, {
"definition" : "center of the rectangle",
"score" : 0.3412842247769857
}, {
"definition" : "ellipse 's major axis",
"score" : 0.3412842247769857
}, {
"definition" : "expression",
"score" : 0.3412842247769857
}, {
"definition" : "formula",
"score" : 0.3412842247769857
}, {
"definition" : "general equation 's coefficient",
"score" : 0.3412842247769857
}, {
"definition" : "general form coefficient by the equation",
"score" : 0.3412842247769857
}, {
"definition" : "non-degenerate projective conic section",
"score" : 0.3412842247769857
}, {
"definition" : "related line",
"score" : 0.3412842247769857
}, {
"definition" : "rotation angle",
"score" : 0.3412842247769857
}, {
"definition" : "semi-major axis",
"score" : 0.3412842247769857
}, {
"definition" : "semi-minor axis",
"score" : 0.3412842247769857
}, {
"definition" : "following method",
"score" : 0.31459433390952196
}, {
"definition" : "pencil",
"score" : 0.31459433390952196
}, {
"definition" : "perspective mapping",
"score" : 0.31459433390952196
}, {
"definition" : "set of point",
"score" : 0.31459433390952196
}, {
"definition" : "single point of an ellipse",
"score" : 0.31459433390952196
}, {
"definition" : "Steiner generation of a conic section",
"score" : 0.31459433390952196
}, {
"definition" : "upper co-vertex of the ellipse",
"score" : 0.31459433390952196
}, {
"definition" : "degenerate case from the non-degenerate case",
"score" : 0.27476039357851473
}, {
"definition" : "equal spaced line segment",
"score" : 0.27476039357851473
}, {
"definition" : "n",
"score" : 0.27476039357851473
}, {
"definition" : "non-degenerate case",
"score" : 0.27476039357851473
}, {
"definition" : "side",
"score" : 0.27476039357851473
}, {
"definition" : "analytic geometry",
"score" : 0.22750321381914684
}, {
"definition" : "Cartesian plane",
"score" : 0.22750321381914684
}, {
"definition" : "diagram",
"score" : 0.22750321381914684
}, {
"definition" : "direction onto the line segment",
"score" : 0.22750321381914684
}, {
"definition" : "quadric",
"score" : 0.22750321381914684
}, {
"definition" : "rectangle",
"score" : 0.22750321381914684
} ]
}