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 r}
... is translated to the CAS output ...
Semantic latex: r
Confidence: 0
Mathematica
Translation: r
Information
Sub Equations
- r
Free variables
- r
Tests
Symbolic
Numeric
SymPy
Translation: r
Information
Sub Equations
- r
Free variables
- r
Tests
Symbolic
Numeric
Maple
Translation: r
Information
Sub Equations
- r
Free variables
- r
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- circle with radius
- ellipse
- special case of the hypotrochoid
- special case
- adjacent image
- point
- Tusi couple
- circle with equation
- line
- angle
- circle
- diagram
- inscribed angle theorem for circle
- parameter
- simple way
- statement
- angular coordinate
- ellipse 's equation
- major axis
- center
- general case of an ellipse
- harmonic mean
- origin at the center
- other word
- polar coordinate
- polar form
- arithmetic mean
- closest distance
- direction
- eccentricity
- elliptical orbit
- farthest distance
- focus
- geometric mean
- length of the semi-major axis
- other focus at angular coordinate
- point towards the center
- polar coordinate with the origin
- radius at apoapsis
- radius at periapsis
- reference direction
- semi-latus rectum
- semi-major axis
- semi-minor axis
- sign in the denominator
- term
- useful relation
- focus at the origin
Complete translation information:
{
"id" : "FORMULA_4b43b0aee35624cd95b910189b3dc231",
"formula" : "r",
"semanticFormula" : "r",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "r",
"translationInformation" : {
"subEquations" : [ "r" ],
"freeVariables" : [ "r" ]
},
"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" : "r",
"translationInformation" : {
"subEquations" : [ "r" ],
"freeVariables" : [ "r" ]
},
"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" : "r",
"translationInformation" : {
"subEquations" : [ "r" ],
"freeVariables" : [ "r" ]
},
"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" : 27,
"sentence" : 0,
"word" : 12
}, {
"section" : 27,
"sentence" : 1,
"word" : 9
} ],
"includes" : [ ],
"isPartOf" : [ "r=\\frac{a (1-e^2)}{1 - e\\cos(\\theta - \\phi)}", "r(\\theta) = \\frac{ab}{\\sqrt{(b \\cos \\theta)^2 + (a\\sin \\theta)^2}}=\\frac{b}{\\sqrt{1 - (e\\cos\\theta)^2}}", "r(\\theta)=\\frac{a (1-e^2)}{1 \\pm e\\cos\\theta}", "R = 2r", "\\left(x - x_\\circ\\right)^2 + \\left(y - y_\\circ\\right)^2 = r^2", "x_\\circ,y_\\circ,r", "r = \\sqrt{\\left(x_1 - x_\\circ\\right)^2 + \\left(y_1 - y_\\circ\\right)^2} = \\sqrt{\\left(x_2 - x_\\circ\\right)^2 + \\left(y_2 - y_\\circ\\right)^2} = \\sqrt{\\left(x_3 - x_\\circ\\right)^2 + \\left(y_3 - y_\\circ\\right)^2}", "\\begin{align} e &= \\frac{r_a - r_p}{r_a + r_p} = \\frac{r_a - r_p}{2a} \\\\ r_a &= (1 + e)a \\\\ r_p &= (1 - e)a\\end{align}", "r_a", "r_p", "\\begin{align} a &= \\frac{r_a + r_p}{2} \\\\[2pt] b &= \\sqrt{r_a r_p} \\\\[2pt] \\ell &= \\frac{2}{\\frac{1}{r_a} + \\frac{1}{r_p}} = \\frac{2r_ar_p}{r_a + r_p}\\end{align}" ],
"definiens" : [ {
"definition" : "circle with radius",
"score" : 0.8869384888466118
}, {
"definition" : "ellipse",
"score" : 0.7408816962532279
}, {
"definition" : "special case of the hypotrochoid",
"score" : 0.6896778755706364
}, {
"definition" : "special case",
"score" : 0.6375030048324222
}, {
"definition" : "adjacent image",
"score" : 0.6231540443721655
}, {
"definition" : "point",
"score" : 0.6162685553493461
}, {
"definition" : "Tusi couple",
"score" : 0.5504118847420469
}, {
"definition" : "circle with equation",
"score" : 0.5177731136658746
}, {
"definition" : "line",
"score" : 0.45124928246740353
}, {
"definition" : "angle",
"score" : 0.41944440929531046
}, {
"definition" : "circle",
"score" : 0.41944440929531046
}, {
"definition" : "diagram",
"score" : 0.41944440929531046
}, {
"definition" : "inscribed angle theorem for circle",
"score" : 0.41944440929531046
}, {
"definition" : "parameter",
"score" : 0.41944440929531046
}, {
"definition" : "simple way",
"score" : 0.41944440929531046
}, {
"definition" : "statement",
"score" : 0.41944440929531046
}, {
"definition" : "angular coordinate",
"score" : 0.40617210308498164
}, {
"definition" : "ellipse 's equation",
"score" : 0.40617210308498164
}, {
"definition" : "major axis",
"score" : 0.3862764275452791
}, {
"definition" : "center",
"score" : 0.34586835176111275
}, {
"definition" : "general case of an ellipse",
"score" : 0.34586835176111275
}, {
"definition" : "harmonic mean",
"score" : 0.34586835176111275
}, {
"definition" : "origin at the center",
"score" : 0.34586835176111275
}, {
"definition" : "other word",
"score" : 0.34586835176111275
}, {
"definition" : "polar coordinate",
"score" : 0.34586835176111275
}, {
"definition" : "polar form",
"score" : 0.34586835176111275
}, {
"definition" : "arithmetic mean",
"score" : 0.31917846089364893
}, {
"definition" : "closest distance",
"score" : 0.31917846089364893
}, {
"definition" : "direction",
"score" : 0.31917846089364893
}, {
"definition" : "eccentricity",
"score" : 0.31917846089364893
}, {
"definition" : "elliptical orbit",
"score" : 0.31917846089364893
}, {
"definition" : "farthest distance",
"score" : 0.31917846089364893
}, {
"definition" : "focus",
"score" : 0.31917846089364893
}, {
"definition" : "geometric mean",
"score" : 0.31917846089364893
}, {
"definition" : "length of the semi-major axis",
"score" : 0.31917846089364893
}, {
"definition" : "other focus at angular coordinate",
"score" : 0.31917846089364893
}, {
"definition" : "point towards the center",
"score" : 0.31917846089364893
}, {
"definition" : "polar coordinate with the origin",
"score" : 0.31917846089364893
}, {
"definition" : "radius at apoapsis",
"score" : 0.31917846089364893
}, {
"definition" : "radius at periapsis",
"score" : 0.31917846089364893
}, {
"definition" : "reference direction",
"score" : 0.31917846089364893
}, {
"definition" : "semi-latus rectum",
"score" : 0.31917846089364893
}, {
"definition" : "semi-major axis",
"score" : 0.31917846089364893
}, {
"definition" : "semi-minor axis",
"score" : 0.31917846089364893
}, {
"definition" : "sign in the denominator",
"score" : 0.31917846089364893
}, {
"definition" : "term",
"score" : 0.31917846089364893
}, {
"definition" : "useful relation",
"score" : 0.31917846089364893
}, {
"definition" : "focus at the origin",
"score" : 0.2793445205626417
} ]
}