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
- Failed to parse (syntax error): {\displaystyle a \ge b > 0 \}
- Failed to parse (syntax error): {\displaystyle \frac{\left(x_1 + su\right)^2}{a^2} + \frac{\left(y_1 + sv\right)^2}{b^2} = 1\ \quad\Longrightarrow\quad 2s\left(\frac{x_1u}{a^2} + \frac{y_1v}{b^2}\right) + s^2\left(\frac{u^2}{a^2} + \frac{v^2}{b^2}\right) = 0\}
- Failed to parse (syntax error): {\displaystyle \frac{\left(x - x_\circ\right)^2}{a^2} + \frac{\left(y - y_\circ\right)^2}{b^2} = 1 \}
- Failed to parse (syntax error): {\displaystyle (x,\, y) = (a \cos t,\, b \sin t),\ 0 \le t < 2\pi\}
- Failed to parse (syntax error): {\displaystyle \frac{(x - a)^2}{a^2} + \frac{y^2}{b^2} = 1\}
- Failed to parse (syntax error): {\displaystyle \left|\vec c_1\right|^2 + \left|\vec c_2\right|^2 = \cdots = a^2 + b^2\}
- Failed to parse (syntax error): {\displaystyle \tfrac{a^2}{b}\}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa = \frac{1}{a^2 b^2}\left(\frac{x^2}{a^4}+\frac{y^2}{b^4}\right)^{-\frac{3}{2}}\}
- Failed to parse (syntax error): {\displaystyle \rho = a^2 b^2 \left(\frac{x^{2}}{a^4} + \frac{y^{2}}{b^4}\right)^\frac{3}{2} = \frac{1}{a^4 b^4} \sqrt{\left(a^4 y^{2} + b^4 x^{2}\right)^3} \}
- Failed to parse (syntax error): {\displaystyle \rho_0 = \frac{b^2}{a}=p\ , \qquad \left(\pm\frac{c^2}{a}\,\bigg|\,0\right)\}
- Failed to parse (syntax error): {\displaystyle \rho_1 = \frac{a^2}{b}\ , \qquad \left(0\,\bigg|\,\pm\frac{c^2}{b}\right)\}
Description
- semi-minor axis
- length
- circle of radius
- substrip of length
- focus
- equation of a standard ellipse
- height
- origin with width
- standard parametric equation
- ellipse
- point
- equation
- line
- parametric representation
- radius of curvature
- eccentricity
- co-vertex
- circle
- parameter
- center
- expression
- axis
- center of the ellipse
- point of the ellipse
- semi-major axis
- term
- center of curvature
- conjugate diameter
- vertex
- area
- diagram
- length of the semi-major axis
- Metric property
- circumference
- proof
- area formula
- bottom point
- canonical ellipse equation
- factor
- height parameter
- major/minor semi axis
- new parameter
- perpendicular vector
- radii
- radius
- above-mentioned eccentricity
- tangent at a point
- trigonometric formula
- paper strip
- affine transformation of the coordinate
- angle from the positive horizontal axis
- angle of the slope
- arc length
- Bessel
- canonical equation
- canonical form parameter
- canonical form with parametric equation
- case
- close approximation for the circumference
- coordinate
- coordinate equation
- derivative of the standard representation
- distance from the center
- ellipse 's major axis
- ellipse with equation
- equation of an ellipse
- equation of the tangent
- formula
- general equation 's coefficient
- general form coefficient by the equation
- harmonic mean
- James Ivory
- left vertex
- minor axis
- origin at the center
- other word
- parametric representation of the standard ellipse
- polar coordinate
- radius of the large circle
- rotation angle
- series
- Srinivasa Ramanujan
- standard equation of the ellipse
- stretch
- sum
- tangent vector at point
- vector parametric equation of the tangent
- width
- yield
- constant ratio
- angle of slope
- angular coordinate
- arithmetic mean
- auxiliary point
- axis as major axis
- axis of the ellipse
- calculation
- canonical ellipse
- center of the osculating circle
- closest distance
- concentric circle
- constant area
- curvature
- easy way
- ellipse 's equation
- ellipse point
- ellipse with equal axis
- ellipse with semi-axis
- elliptical orbit
- endpoint
- endpoint of the ellipse 's major axis
- farthest distance
- generation of point
- geometric mean
- half
- help of trigonometric formula
- i.e.
- incomplete elliptic integral of the second kind
- intersection point of orthogonal tangent
- intersection point of this line
- inverse function
- line segment
- parallelogram of tangent
- parameter name
- perimeter
- principle
- radical by suitable squaring
- radius at apoapsis
- radius at periapsis
- representation
- rhombus with vertex
- section parametric representation
- semi axis
- semi-latus rectum
- simple method
- standard ellipse
- strip of paper
- suitable coordinate system by an equation
- tangent direction
- tangent line
- tracing point
- triangle
- trigonometric function
- upper bound on the circumference
- upper co-vertex of the ellipse
- upper half of an ellipse
- useful relation
- method
- area by the same factor
- article
- cases center
- circle with center
- complete elliptic integral of the second kind
- family of ellipsis
- strip
- variable name
- device
- ellipse equation
- fact
- function
- major axis
- pencil at the vertex
- proof for the pair
- rational parametric equation of an ellipse
- standard representation yield
- vector equation
- arbitrary point
- first method
- line 's equation into the ellipse equation
- origin
- real number
- section
- slope
- substitution
- form
- observation that the midpoint
- standard form
- variation of the paper strip method
- elementary function
Complete translation information:
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"formula" : "b",
"semanticFormula" : "b",
"confidence" : 0.0,
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"SymPy" : {
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"freeVariables" : [ "b" ]
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},
"Maple" : {
"translation" : "b",
"translationInformation" : {
"subEquations" : [ "b" ],
"freeVariables" : [ "b" ]
},
"numericResults" : {
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}
}
},
"positions" : [ {
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"sentence" : 4,
"word" : 19
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"section" : 3,
"sentence" : 0,
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"includes" : [ ],
"isPartOf" : [ "\\frac{x^2}{a^2}+\\frac{y^2}{b^2} = 1", "a\\geq b", "c = \\sqrt{a^2-b^2}", "(x,y) = (a\\cos(t),b\\sin(t)) \\quad \\text{for} \\quad 0\\leq t\\leq 2\\pi", "e = \\frac{c}{a} = \\sqrt{1 - \\frac{b^2}{a^2}}", "b^2 = a^2-c^2", "\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1", "y = \\pm\\frac{b}{a}\\sqrt{a^2 - x^2} = \\pm \\sqrt{\\left(a^2 - x^2\\right)\\left(1 - e^2\\right)}", "a,\\; b", "V_3 = (0,\\, b),\\; V_4 = (0,\\, -b)", "a \\ge b > 0 \\", "\\tfrac{x^2}{a^2} + \\tfrac{y^2}{b^2} = 1", "a < b", "c = \\sqrt{a^2 - b^2}", "e = \\frac{c}{a} = \\sqrt{1 - \\left(\\frac{b}{a}\\right)^2}", "a > b", "a = b", "\\ell = \\frac{b^2}a = a \\left(1 - e^2\\right)", "\\frac{x_1}{a^2}x + \\frac{y_1}{b^2}y = 1", "\\vec x = \\begin{pmatrix}x_1 \\\\ y_1\\end{pmatrix} + s\\begin{pmatrix} \\;\\! -y_1 a^2 \\\\ \\;\\ \\ \\ x_1 b^2\\end{pmatrix}", "\\frac{\\left(x_1 + su\\right)^2}{a^2} + \\frac{\\left(y_1 + sv\\right)^2}{b^2} = 1\\ \\quad\\Longrightarrow\\quad 2s\\left(\\frac{x_1u}{a^2} + \\frac{y_1v}{b^2}\\right) + s^2\\left(\\frac{u^2}{a^2} + \\frac{v^2}{b^2}\\right) = 0\\", "\\frac{x_1}{a^2}u + \\frac{y_1}{b^2}v = 0", "\\begin{pmatrix}\\frac{x_1}{a^2} & \\frac{y_1}{b^2}\\end{pmatrix}", "\\frac{x_1}{a^2}x + \\tfrac{y_1}{b^2}y = k", "\\frac{x_ 1}{a^2}u + \\frac{y_1}{b^2}v \\ne 0", "\\begin{pmatrix} -y_1a^2 & x_1b^2 \\end{pmatrix}", "\\frac{x_1u}{a^2} + \\tfrac{y_1v}{b^2} = 0", "\\frac{\\left(x - x_\\circ\\right)^2}{a^2} + \\frac{\\left(y - y_\\circ\\right)^2}{b^2} = 1 \\", "\\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}", "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2} = 1", "(x,\\, y) = (a \\cos t,\\, b \\sin t),\\ 0 \\le t < 2\\pi\\", "\\vec x(t) = (a \\cos t,\\, b \\sin t)^\\mathsf{T}", "\\vec x'(t) = (-a\\sin t,\\, b\\cos t)^\\mathsf{T} \\quad \\rightarrow \\quad m = -\\frac{b}{a}\\cot t\\quad \\rightarrow \\quad \\cot t = -\\frac{ma}{b}", "\\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}}", "\\vec c_\\pm(m) = \\left(-\\frac{ma^2}{\\pm\\sqrt{m^2 a^2 + b^2}},\\;\\frac{b^2}{\\pm\\sqrt{m^2a^2 + b^2}}\\right),\\, m \\in \\R", "y = mx \\pm\\sqrt{m^2 a^2 + b^2}\\;", "r(\\theta) = \\frac{ab}{\\sqrt{(b \\cos \\theta)^2 + (a\\sin \\theta)^2}}=\\frac{b}{\\sqrt{1 - (e\\cos\\theta)^2}}", "y^2 = b^2 - \\tfrac{b^2}{a^2}x^2", "a,\\, b", "1 - e^2 = \\tfrac{b^2}{a^2}, \\text{ and }\\ p = \\tfrac{b^2}{a}", "\\frac{(x - a)^2}{a^2} + \\frac{y^2}{b^2} = 1\\", "c_1^2 + c_2^2 = a^2 + b^2", "\\vec p(t) = (a\\cos t,\\, b\\sin t)", "\\vec c_2 = (-a\\sin t,\\, b\\cos t)^\\mathsf{T}", "\\left|\\vec c_1\\right|^2 + \\left|\\vec c_2\\right|^2 = \\cdots = a^2 + b^2\\", "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2}=1", "x^2+y^2=a^2+b^2", "(a\\cos t,\\, b\\sin t)", "a,b", "a + b", "\\tfrac{a + b}{2}", "a - b", "\\tfrac{b^2}{a}", "\\tfrac{a^2}{b}\\", "C_1 = \\left(a - \\tfrac{b^2}{a}, 0\\right),\\, C_3 = \\left(0, b - \\tfrac{a^2}{b}\\right)", "H = (a,\\, b)", "P = (0,\\, b)", "A = (-a,\\, 2b),\\, B = (a,\\,2b)", "\\tfrac{\\left(x - x_\\circ\\right)^2}{a^2} + \\tfrac{\\left(y - y_\\circ\\right)^2}{b^2} = 1", "{\\color{blue}q} = \\frac{a^2}{b^2} = \\frac{1}{1 - e^2}", "\\tfrac{x_1x}{a^2} + \\tfrac{y_1y}{b^2} = 1", "\\tfrac{x_1 x}{a^2} + \\tfrac{y_1 y}{b^2} = 1", "\\left(-\\tfrac{ma^2}{d},\\, \\tfrac{b^2}{d}\\right)", "\\frac{x^2}{a^2}+\\frac{y^2}{b^2}= 1", "\\pi a b", "\\pi b^2", "a/b", "\\pi b^2(a/b) = \\pi a b", "y(x)= b \\sqrt{1 - x^2/a^2}", "e=\\sqrt{1 - b^2/a^2}", "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)", "y=b\\sqrt{1-\\frac{x^{2}}{a^{2}}}", "s = -b\\int_{\\arccos \\frac{x_{1}}{a}}^{\\arccos \\frac{x_{2}}{a}} \\sqrt{1-\\left(1-\\frac{a^{2}}{b^{2}}\\right)\\sin^{2}z} \\, dz", "s = -b\\left[E\\left(z \\;\\Biggl|\\; 1 - \\frac{a^{2}}{b^{2}}\\right)\\right]^{\\arccos \\frac{x_{2}}{a}}_{\\arccos \\frac{x_{1}}{a}}", "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}", "\\kappa = \\frac{1}{a^2 b^2}\\left(\\frac{x^2}{a^4}+\\frac{y^2}{b^4}\\right)^{-\\frac{3}{2}}\\", "\\rho = a^2 b^2 \\left(\\frac{x^{2}}{a^4} + \\frac{y^{2}}{b^4}\\right)^\\frac{3}{2} = \\frac{1}{a^4 b^4} \\sqrt{\\left(a^4 y^{2} + b^4 x^{2}\\right)^3} \\", "\\rho_0 = \\frac{b^2}{a}=p\\ , \\qquad \\left(\\pm\\frac{c^2}{a}\\,\\bigg|\\,0\\right)\\", "(0,\\pm b)", "\\rho_1 = \\frac{a^2}{b}\\ , \\qquad \\left(0\\,\\bigg|\\,\\pm\\frac{c^2}{b}\\right)\\", "\\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}" ],
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