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 \pi b^2}
... is translated to the CAS output ...
Semantic latex: \cpi b^2
Confidence: 0
Mathematica
Translation: Pi*(b)^(2)
Information
Sub Equations
- Pi*(b)^(2)
Free variables
- b
Symbol info
- Pi was translated to: Pi
Tests
Symbolic
Numeric
SymPy
Translation: pi*(b)**(2)
Information
Sub Equations
- pi*(b)**(2)
Free variables
- b
Symbol info
- Pi was translated to: pi
Tests
Symbolic
Numeric
Maple
Translation: Pi*(b)^(2)
Information
Sub Equations
- Pi*(b)^(2)
Free variables
- b
Symbol info
- Pi was translated to: Pi
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- ellipse
- area
- stretch
- circle of radius
- factor
- area formula
- area by the same factor
- expression
- conjugate diameter
- focus
- area of the ellipse
- circumference
- area of a circle
- integral
- circle
- eccentricity
- exact infinite series
- Bessel
- close approximation for the circumference
- James Ivory
- series
- Srinivasa Ramanujan
- term
- minor axis
- coordinate
- distance from the center
- second integral
- length of the semi-major axis
- canonical ellipse
- concentric circle
- endpoint
- endpoint of the ellipse 's major axis
- perimeter
- rhombus with vertex
- upper bound on the circumference
- affine transformation of the coordinate
- angle from the positive horizontal axis
- canonical equation
- canonical form parameter
- center
- constant area
- diagram
- ellipse 's major axis
- ellipse point
- ellipse with semi-axis
- formula
- general equation 's coefficient
- general form coefficient by the equation
- half
- help of trigonometric formula
- intersection point of orthogonal tangent
- parallelogram of tangent
- rotation angle
- semi-major axis
- semi-minor axis
- triangle
- interval
- radius
- complete elliptic integral of the second kind
- function
- elementary function
Complete translation information:
{
"id" : "FORMULA_9a91ffb098821ed202708ca41ae6a8cc",
"formula" : "\\pi b^2",
"semanticFormula" : "\\cpi b^2",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Pi*(b)^(2)",
"translationInformation" : {
"subEquations" : [ "Pi*(b)^(2)" ],
"freeVariables" : [ "b" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi"
}
},
"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" : "pi*(b)**(2)",
"translationInformation" : {
"subEquations" : [ "pi*(b)**(2)" ],
"freeVariables" : [ "b" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: pi"
}
},
"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" : "Pi*(b)^(2)",
"translationInformation" : {
"subEquations" : [ "Pi*(b)^(2)" ],
"freeVariables" : [ "b" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi"
}
},
"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" : 36,
"sentence" : 1,
"word" : 19
} ],
"includes" : [ "b", "\\pi", "\\pi a^2" ],
"isPartOf" : [ "\\cos t = \\frac{\\cot t}{\\pm\\sqrt{1 + \\cot^2t}} = \\frac{-ma}{\\pm\\sqrt{m^2 a^2 + b^2}}\\ ,\\quad\\quad\\sin t = \\frac{1}{\\pm\\sqrt{1 + \\cot^2t}} = \\frac{b}{\\pm\\sqrt{m^2 a^2 + b^2}}", "c = \\sqrt{a^2-b^2}", "\\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}", "y = mx \\pm\\sqrt{m^2 a^2 + b^2}\\;", "c_1^2 + c_2^2 = a^2 + b^2", "c = \\sqrt{a^2 - b^2}", "x^2+y^2=a^2+b^2", "\\pi b^2(a/b) = \\pi a b", "\\pi a^2", "e=\\sqrt{1 - b^2/a^2}", "\\begin{align} C &= 2\\pi a \\left[{1 - \\left(\\frac{1}{2}\\right)^2e^2 - \\left(\\frac{1\\cdot 3}{2\\cdot 4}\\right)^2\\frac{e^4}{3} - \\left(\\frac{1\\cdot 3\\cdot 5}{2\\cdot 4\\cdot 6}\\right)^2\\frac{e^6}{5} - \\cdots}\\right] \\\\ &= 2\\pi a \\left[1 - \\sum_{n=1}^\\infty \\left(\\frac{(2n-1)!!}{(2n)!!}\\right)^2 \\frac{e^{2n}}{2n-1}\\right] \\\\ &= -2\\pi a \\sum_{n=0}^\\infty \\left(\\frac{(2n-1)!!}{(2n)!!}\\right)^2 \\frac{e^{2n}}{2n-1},\\end{align}", "\\begin{align} C &= \\pi (a+b) \\sum_{n=0}^\\infty \\left(\\frac{(2n-3)!!}{2^n n!}\\right)^2 h^n \\\\ &= \\pi (a+b) \\left[1 + \\frac{h}{4} + \\sum_{n=2}^\\infty \\left(\\frac{(2n-3)!!}{2^n n!}\\right)^2 h^n\\right] \\\\ &= \\pi (a+b) \\left[1 + \\sum_{n=1}^\\infty \\left(\\frac{(2n-1)!!}{2^n n!}\\right)^2 \\frac{h^n}{(2n-1)^2}\\right].\\end{align}", "C \\approx \\pi \\biggl[3(a + b) - \\sqrt{(3a + b)(a + 3b)} \\biggr] = \\pi \\biggl[3(a + b) - \\sqrt{10ab + 3\\left(a^2 + b^2\\right)}\\biggr]", "x^2/a^2 + y^2/b^2 = 1", "\\begin{align} 2\\pi b &\\le C \\le 2\\pi a, \\\\ \\pi (a+b) &\\le C \\le 4(a+b), \\\\ 4\\sqrt{a^2+b^2} &\\le C \\le \\sqrt{2} \\pi \\sqrt{a^2+b^2} .\\end{align}", "4\\sqrt{a^2+b^2}" ],
"definiens" : [ {
"definition" : "ellipse",
"score" : 0.7433793077947476
}, {
"definition" : "area",
"score" : 0.6896778755706364
}, {
"definition" : "stretch",
"score" : 0.6896778755706364
}, {
"definition" : "circle of radius",
"score" : 0.6629879847031728
}, {
"definition" : "factor",
"score" : 0.6629879847031728
}, {
"definition" : "area formula",
"score" : 0.6231540443721655
}, {
"definition" : "area by the same factor",
"score" : 0.5976690645014149
}, {
"definition" : "expression",
"score" : 0.43286208957350525
}, {
"definition" : "conjugate diameter",
"score" : 0.40617210308498164
}, {
"definition" : "focus",
"score" : 0.3970721724437041
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"definition" : "area of the ellipse",
"score" : 0.3960013259619435
}, {
"definition" : "circumference",
"score" : 0.38631193544518344
}, {
"definition" : "area of a circle",
"score" : 0.36931143509447967
}, {
"definition" : "integral",
"score" : 0.36931143509447967
}, {
"definition" : "circle",
"score" : 0.3552698412698413
}, {
"definition" : "eccentricity",
"score" : 0.34602378366733294
}, {
"definition" : "exact infinite series",
"score" : 0.3458735978781142
}, {
"definition" : "Bessel",
"score" : 0.34586844738217254
}, {
"definition" : "close approximation for the circumference",
"score" : 0.34586844738217254
}, {
"definition" : "James Ivory",
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"definition" : "series",
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"definition" : "Srinivasa Ramanujan",
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"definition" : "term",
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"definition" : "minor axis",
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"definition" : "coordinate",
"score" : 0.34586835176111275
}, {
"definition" : "distance from the center",
"score" : 0.34586835176111275
}, {
"definition" : "second integral",
"score" : 0.32947749476347243
}, {
"definition" : "length of the semi-major axis",
"score" : 0.319333892799869
}, {
"definition" : "canonical ellipse",
"score" : 0.31917846089364954
}, {
"definition" : "concentric circle",
"score" : 0.31917846089364954
}, {
"definition" : "endpoint",
"score" : 0.31917846089364954
}, {
"definition" : "endpoint of the ellipse 's major axis",
"score" : 0.31917846089364954
}, {
"definition" : "perimeter",
"score" : 0.31917846089364954
}, {
"definition" : "rhombus with vertex",
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}, {
"definition" : "upper bound on the circumference",
"score" : 0.31917846089364954
}, {
"definition" : "affine transformation of the coordinate",
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}, {
"definition" : "angle from the positive horizontal axis",
"score" : 0.31917846089364893
}, {
"definition" : "canonical equation",
"score" : 0.31917846089364893
}, {
"definition" : "canonical form parameter",
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"definition" : "center",
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}, {
"definition" : "constant area",
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}, {
"definition" : "diagram",
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}, {
"definition" : "ellipse 's major axis",
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}, {
"definition" : "ellipse point",
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}, {
"definition" : "ellipse with semi-axis",
"score" : 0.31917846089364893
}, {
"definition" : "formula",
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}, {
"definition" : "general equation 's coefficient",
"score" : 0.31917846089364893
}, {
"definition" : "general form coefficient by the equation",
"score" : 0.31917846089364893
}, {
"definition" : "half",
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}, {
"definition" : "help of trigonometric formula",
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}, {
"definition" : "intersection point of orthogonal tangent",
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}, {
"definition" : "parallelogram of tangent",
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}, {
"definition" : "rotation angle",
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}, {
"definition" : "semi-major axis",
"score" : 0.31917846089364893
}, {
"definition" : "semi-minor axis",
"score" : 0.31917846089364893
}, {
"definition" : "triangle",
"score" : 0.31917846089364893
}, {
"definition" : "interval",
"score" : 0.28222031500410455
}, {
"definition" : "radius",
"score" : 0.28222031500410455
}, {
"definition" : "complete elliptic integral of the second kind",
"score" : 0.27949995246886183
}, {
"definition" : "function",
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"definition" : "elementary function",
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} ]
}