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 a b}
... is translated to the CAS output ...
Semantic latex: \cpi a b
Confidence: 0
Mathematica
Translation: Pi*a*b
Information
Sub Equations
- Pi*a*b
Free variables
- a
- b
Symbol info
- Pi was translated to: Pi
Tests
Symbolic
Numeric
SymPy
Translation: pi*a*b
Information
Sub Equations
- pi*a*b
Free variables
- a
- b
Symbol info
- Pi was translated to: pi
Tests
Symbolic
Numeric
Maple
Translation: Pi*a*b
Information
Sub Equations
- Pi*a*b
Free variables
- a
- b
Symbol info
- Pi was translated to: Pi
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- ellipse
- area formula
- area
- factor
- circle of radius
- stretch
- area by the same factor
- circumference
- length
- radius
- length of the semi-major axis
- exact infinite series
- Bessel
- close approximation for the circumference
- expression
- James Ivory
- series
- Srinivasa Ramanujan
- term
- minor axis
- radius of the large circle
- sum
- complete elliptic integral of the second kind
- eccentricity
- elementary function
- canonical ellipse
- concentric circle
- endpoint
- endpoint of the ellipse 's major axis
- perimeter
- rhombus with vertex
- upper bound on the circumference
- strip of paper
- substrip of length
- function
- circle with center
- device
- method
- point
- strip
- first method
- observation that the midpoint
- paper strip
- variation of the paper strip method
Complete translation information:
{
"id" : "FORMULA_925a02b5b92511788528f78c729d799e",
"formula" : "\\pi a b",
"semanticFormula" : "\\cpi a b",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Pi*a*b",
"translationInformation" : {
"subEquations" : [ "Pi*a*b" ],
"freeVariables" : [ "a", "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*a*b",
"translationInformation" : {
"subEquations" : [ "pi*a*b" ],
"freeVariables" : [ "a", "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*a*b",
"translationInformation" : {
"subEquations" : [ "Pi*a*b" ],
"freeVariables" : [ "a", "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" : 3
} ],
"includes" : [ "b", "a", "\\pi" ],
"isPartOf" : [ "a - b", "a + b", "\\tfrac{a + b}{2}", "a/b", "\\pi b^2(a/b) = \\pi a b", "2\\pi / \\sqrt{4AC - B^2}", "C \\,=\\, 4a\\int_0^{\\pi/2}\\sqrt {1 - e^2 \\sin^2\\theta}\\ d\\theta \\,=\\, 4 a \\,E(e)", "E(e) \\,=\\, \\int_0^{\\pi/2}\\sqrt {1 - e^2 \\sin^2\\theta}\\ d\\theta", "\\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}", "h = (a-b)^2 / (a+b)^2", "\\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]", "C\\approx\\pi\\left(a+b\\right)\\left(1+\\frac{3h}{10+\\sqrt{4-3h}}\\right)", "\\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}" ],
"definiens" : [ {
"definition" : "ellipse",
"score" : 0.7803166466345224
}, {
"definition" : "area formula",
"score" : 0.722
}, {
"definition" : "area",
"score" : 0.7089336197972064
}, {
"definition" : "factor",
"score" : 0.694495238095238
}, {
"definition" : "circle of radius",
"score" : 0.6584038577190456
}, {
"definition" : "stretch",
"score" : 0.6185699173880385
}, {
"definition" : "area by the same factor",
"score" : 0.5930849375172879
}, {
"definition" : "circumference",
"score" : 0.4217547148891849
}, {
"definition" : "length",
"score" : 0.35068571428571427
}, {
"definition" : "radius",
"score" : 0.35068571428571427
}, {
"definition" : "length of the semi-major axis",
"score" : 0.3414396566832059
}, {
"definition" : "exact infinite series",
"score" : 0.34128947089398726
}, {
"definition" : "Bessel",
"score" : 0.3412843203980455
}, {
"definition" : "close approximation for the circumference",
"score" : 0.3412843203980455
}, {
"definition" : "expression",
"score" : 0.3412843203980455
}, {
"definition" : "James Ivory",
"score" : 0.3412843203980455
}, {
"definition" : "series",
"score" : 0.3412843203980455
}, {
"definition" : "Srinivasa Ramanujan",
"score" : 0.3412843203980455
}, {
"definition" : "term",
"score" : 0.3412843203980455
}, {
"definition" : "minor axis",
"score" : 0.3412842247769864
}, {
"definition" : "radius of the large circle",
"score" : 0.3412842247769857
}, {
"definition" : "sum",
"score" : 0.3412842247769857
}, {
"definition" : "complete elliptic integral of the second kind",
"score" : 0.31474976581574204
}, {
"definition" : "eccentricity",
"score" : 0.31474976581574204
}, {
"definition" : "elementary function",
"score" : 0.31474976581574204
}, {
"definition" : "canonical ellipse",
"score" : 0.3145943339095225
}, {
"definition" : "concentric circle",
"score" : 0.3145943339095225
}, {
"definition" : "endpoint",
"score" : 0.3145943339095225
}, {
"definition" : "endpoint of the ellipse 's major axis",
"score" : 0.3145943339095225
}, {
"definition" : "perimeter",
"score" : 0.3145943339095225
}, {
"definition" : "rhombus with vertex",
"score" : 0.3145943339095225
}, {
"definition" : "upper bound on the circumference",
"score" : 0.3145943339095225
}, {
"definition" : "strip of paper",
"score" : 0.31459433390952196
}, {
"definition" : "substrip of length",
"score" : 0.31459433390952196
}, {
"definition" : "function",
"score" : 0.27491582548473487
}, {
"definition" : "circle with center",
"score" : 0.27476039357851473
}, {
"definition" : "device",
"score" : 0.22750321381914684
}, {
"definition" : "method",
"score" : 0.22750321381914684
}, {
"definition" : "point",
"score" : 0.22750321381914684
}, {
"definition" : "strip",
"score" : 0.22750321381914684
}, {
"definition" : "first method",
"score" : 0.17878095238095237
}, {
"definition" : "observation that the midpoint",
"score" : 0.13359313986716373
}, {
"definition" : "paper strip",
"score" : 0.13359313986716373
}, {
"definition" : "variation of the paper strip method",
"score" : 0.13359313986716373
} ]
}