LaTeX to CAS translator
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 e}
... is translated to the CAS output ...
Semantic latex: e
Confidence: 0
Mathematica
Translation: e
Information
Sub Equations
- e
Free variables
- e
Symbol info
- You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].
We keep it like it is! But you should know that Mathematica uses E for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \expe
Tests
Symbolic
Numeric
SymPy
Translation: e
Information
Sub Equations
- e
Free variables
- e
Symbol info
- You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].
We keep it like it is! But you should know that SymPy uses E for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \expe
Tests
Symbolic
Numeric
Maple
Translation: e
Information
Sub Equations
- e
Free variables
- e
Symbol info
- You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].
We keep it like it is! But you should know that Maple uses exp(1) for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \expe
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
- Failed to parse (syntax error): {\displaystyle \frac{\left|PF_1\right|}{\left|Pl_1\right|} = \frac{\left|PF_2\right|}{\left|Pl_2\right|} = e = \frac{c}{a}\}
- Failed to parse (syntax error): {\displaystyle \left(x - f_1\right)^2 + \left(y - f_2\right)^2 = e^2 \frac{\left(ux + vy + w\right)^2}{u^2 + v^2}\}
Description
- eccentricity
- real number
- ellipse
- case of a circle
- elongation of an ellipse
- parabola
- case of infinite elongation
- number
- equation
- directrix
- length of the semi-major axis
- line
- focus
- choice
- semi-latus rectum
- hyperbola
- point
- term
- quotient of the distance
- angular coordinate
- ellipse 's equation
- center
- equation of an ellipse
- major axis
- semi-minor axis
- quotient
- relation
- yield
- diagram
- above-mentioned eccentricity
- circumference
- converse
- definition of a parabola
- distance
- eccentricity of a circle
- exact infinite series
- general case of an ellipse
- harmonic mean
- locus of point
- manner
- numerator of these formula
- origin at the center
- parameter
- polar coordinate
- polar form
- substitution
- constant ratio
- area
- arithmetic mean
- calculation
- closest distance
- complete elliptic integral of the second kind
- context
- direction
- elementary function
- elliptical orbit
- farthest distance
- geometric mean
- minor axis
- new parameter
- other focus at angular coordinate
- point on the curve
- point towards the center
- polar coordinate with the origin
- proof
- radical by suitable squaring
- radius at apoapsis
- radius at periapsis
- reference direction
- semi-major axis
- sign in the denominator
- term of eccentricity
- useful relation
- arbitrary point
- circumference of the ellipse
- focus at the origin
- function
- General ellipse If the focus
- iterative method
- axis as major axis
- ellipse equation
- family of ellipsis
- major/minor semi axis
- standard equation of the ellipse
- Gauss 's arithmetic-geometric mean
- directrix of the ellipse
- section
Complete translation information:
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"formula" : "e",
"semanticFormula" : "e",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
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"translationInformation" : {
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"freeVariables" : [ "e" ],
"tokenTranslations" : {
"e" : "You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].\nWe keep it like it is! But you should know that Mathematica uses E for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\expe\n"
}
},
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"SymPy" : {
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"translationInformation" : {
"subEquations" : [ "e" ],
"freeVariables" : [ "e" ],
"tokenTranslations" : {
"e" : "You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].\nWe keep it like it is! But you should know that SymPy uses E for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\expe\n"
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},
"Maple" : {
"translation" : "e",
"translationInformation" : {
"subEquations" : [ "e" ],
"freeVariables" : [ "e" ],
"tokenTranslations" : {
"e" : "You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].\nWe keep it like it is! But you should know that Maple uses exp(1) for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\expe\n"
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"word" : 10
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"includes" : [ ],
"isPartOf" : [ "e = \\frac{c}{a} = \\sqrt{1 - \\frac{b^2}{a^2}}", "e=\\tfrac{c}{a}", "y = \\pm\\frac{b}{a}\\sqrt{a^2 - x^2} = \\pm \\sqrt{\\left(a^2 - x^2\\right)\\left(1 - e^2\\right)}", "e = \\frac{c}{a} = \\sqrt{1 - \\left(\\frac{b}{a}\\right)^2}", "\\ell = \\frac{b^2}a = a \\left(1 - e^2\\right)", "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=\\frac{a (1-e^2)}{1 - e\\cos(\\theta - \\phi)}", "\\ell=a (1-e^2)", "d = \\frac{a^2}{c} = \\frac{a}{e}", "\\frac{\\left|PF_1\\right|}{\\left|Pl_1\\right|} = \\frac{\\left|PF_2\\right|}{\\left|Pl_2\\right|} = e = \\frac{c}{a}\\", "0 < e < 1", "E = \\left\\{P\\ \\left|\\ \\frac{|PF|}{|Pl|} = e\\right.\\right\\}", "e = 0", "e = 1", "e > 1", "F = (f,\\, 0),\\ e > 0", "x = -\\tfrac{f}{e}", "|PF|^2 = e^2|Pl|^2", "(x - f)^2 + y^2 = e^2\\left(x + \\frac{f}{e}\\right)^2 = (ex + f)^2", "x^2\\left(e^2 - 1\\right) + 2xf(1 + e) - y^2 = 0", "p = f(1 + e)", "x^2\\left(e^2 - 1\\right) + 2px - y^2 = 0", "e < 1", "1 - e^2 = \\tfrac{b^2}{a^2}, \\text{ and }\\ p = \\tfrac{b^2}{a}", "\\left(x - f_1\\right)^2 + \\left(y - f_2\\right)^2 = e^2 \\frac{\\left(ux + vy + w\\right)^2}{u^2 + v^2}\\", "{\\color{blue}q} = \\frac{a^2}{b^2} = \\frac{1}{1 - e^2}", "a^2\\pi\\sqrt{1-e^2}", "C \\,=\\, 4a\\int_0^{\\pi/2}\\sqrt {1 - e^2 \\sin^2\\theta}\\ d\\theta \\,=\\, 4 a \\,E(e)", "e=\\sqrt{1 - b^2/a^2}", "E(e) \\,=\\, \\int_0^{\\pi/2}\\sqrt {1 - e^2 \\sin^2\\theta}\\ d\\theta", "E(e)", "\\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} 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}" ],
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}