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 x}
... is translated to the CAS output ...
Semantic latex: x
Confidence: 0
Mathematica
Translation: x
Information
Sub Equations
- x
Free variables
- x
Tests
Symbolic
Numeric
SymPy
Translation: x
Information
Sub Equations
- x
Free variables
- x
Tests
Symbolic
Numeric
Maple
Translation: x
Information
Sub Equations
- x
Free variables
- x
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
- Failed to parse (syntax error): {\displaystyle \sqrt{(x - c)^2 + y^2} + \sqrt{(x + c)^2 + y^2} = 2a\}
- 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 \vec x = \vec p(t) = \vec f\!_0 + \vec f\!_1 \cos t + \vec f\!_2 \sin t \}
- 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(x - f_1\right)^2 + \left(y - f_2\right)^2 = e^2 \frac{\left(ux + vy + w\right)^2}{u^2 + v^2}\}
- Failed to parse (syntax error): {\displaystyle (x - 1)^2 + \left(y - \tfrac{1}{2}\right)^2 = \tfrac{5}{4}\}
- Failed to parse (syntax error): {\displaystyle \frac{(x_4 - x_1)(x_4 - x_2) + {\color{blue}q}\;(y_4 - y_1)(y_4 - y_2)} {(y_4 - y_1)(x_4 - x_2) - (y_4 - y_2)(x_4 - x_1)} = \frac{(x_3 - x_1)(x_3 - x_2) + {\color{blue}q}\;(y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}\}
- Failed to parse (syntax error): {\displaystyle \frac{({\color{red}x} - x_1)({\color{red}x} - x_2) + {\color{blue}q}\;({\color{red}y} - y_1)({\color{red}y} - y_2)} {({\color{red}y} - y_1)({\color{red}x} - x_2) - ({\color{red}y} - y_2)({\color{red}x} - x_1)} = \frac{(x_3 - x_1)(x_3 - x_2) + {\color{blue}q}\;(y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}\}
- Failed to parse (syntax error): {\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} \}
Description
- point
- axis
- ellipse
- major axis
- arbitrary point
- variable name
- center of the ellipse
- other focus
- distance to the focus
- focus
- origin
- standard form of an ellipse
- vertex
- Cartesian coordinate
- equation
- standard equation of the ellipse
- line
- radical by suitable squaring
- angle
- center
- circle
- implicit representation
- ellipse with equation
- left vertex
- point of the ellipse
- yield
- parameter
- form
- dot product
- example
- tangent
- parametric representation
- diagram
- formula
- vector
- non-colinear point
- directrix
- tangent at a point
- substitution
- distance from a point
- circumference
- canonical ellipse equation
- axis as major axis
- conversion
- coordinate
- directrice
- limit
- perpendicular vector
- three-point form
- consequence
- parameter name
- coordinate equation
- vector parametric equation of the tangent
- affine transformation of the coordinate
- angle from the positive horizontal axis
- arc length
- canonical equation
- canonical form parameter
- case
- center of the circle
- circle with equation
- derivative of the standard representation
- ellipse 's major axis
- equation of a standard ellipse
- equation of an ellipse
- equation of the tangent
- expression
- general equation 's coefficient
- general form coefficient by the equation
- integral
- interval
- minor axis
- pair of point
- parametric representation of the standard ellipse
- point on an ellipse
- point on the upper half
- radius of curvature
- rational parametric equation of an ellipse
- regular matrix
- rotation angle
- semi-major axis
- semi-minor axis
- standard parametric equation
- tangent vector at point
- three-point equation
- top half of the ellipse
- conjugate diameter
- order
- right focus
- line with equation
- quotient
- principle
- affine image of the unit circle
- affine transformation of the Euclidean plane
- area of the ellipse
- canonical ellipse
- column vector of the matrix
- concentric circle
- curvature
- curve
- diameter
- eccentricity
- ellipse equation
- endpoint
- endpoint of the ellipse 's major axis
- equation for the ellipse
- equation of any line
- generation of point
- incomplete elliptic integral of the second kind
- inscribed angle theorem for circle
- intersection point of orthogonal tangent
- major/minor semi axis
- parametric equation for a general ellipse
- perimeter
- real number
- relation
- rhombus with vertex
- simple way
- standard ellipse
- statement
- suitable coordinate system by an equation
- tangent direction
- tangent line
- term of the angle measurement
- trigonometric function
- unit circle
- upper bound on the circumference
- upper half of an ellipse
- vector equation
- family of ellipsis
- standard form
- arbitrary vector
- arc length of a portion
- astronomy
- fact
- function of the angle
- General ellipse If the focus
- geometric meaning
- inverse function
- metric property
- new parameter
- pair
- proof for the pair
- Such ellipsis
- affine transformation
- angle by a degree
- circle case
- coordinate axis
- definition of an ellipse
- determinant
- equation for the circle
- following measurement
- origin with width
- pair of pole
- pencil at the vertex
- sense of the measurement
- area of a circle
- Cramer 's rule
- de La
- incomplete elliptic integral
- line 's equation into the ellipse equation
- section
- slope
- trigonometric formula
- function of the usual angle measure
- height
- measure
- radian
- second integral
- Drawing ellipsis
- q-analog angle measure
- radius
Complete translation information:
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"isPartOf" : [ "\\frac{x^2}{a^2}+\\frac{y^2}{b^2} = 1", "(x,y) = (a\\cos(t),b\\sin(t)) \\quad \\text{for} \\quad 0\\leq t\\leq 2\\pi", "(x,y)", "\\sqrt{(x - c)^2 + y^2 }", "\\sqrt{(x + c)^2 + y^2}", "(x,\\, y)", "\\sqrt{(x - c)^2 + y^2} + \\sqrt{(x + c)^2 + y^2} = 2a\\", "\\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)}", "\\tfrac{x^2}{a^2} + \\tfrac{y^2}{b^2} = 1", "(x_1,\\, y_1)", "\\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}", "\\vec{x} = \\begin{pmatrix}x_1 \\\\ y_1\\end{pmatrix} + s\\begin{pmatrix}u \\\\ v\\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}", "(x_1, y_1)", "\\frac{x_1u}{a^2} + \\tfrac{y_1v}{b^2} = 0", "\\left(x_\\circ,\\, y_\\circ\\right)", "\\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} x &= \\left(X - x_\\circ\\right) \\cos\\theta + \\left(Y - y_\\circ\\right) \\sin\\theta \\\\ y &= -\\left(X - x_\\circ\\right) \\sin\\theta + \\left(Y - y_\\circ\\right) \\cos\\theta.\\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\\", "(x(t),y(t))", "\\begin{align} x(u) &= a\\frac{1 - u^2}{u^2 + 1} \\\\ y(u) &= \\frac{2bu}{u^2 + 1}\\end{align}\\;,\\quad -\\infty < u < \\infty\\;", "\\lim_{u \\to \\pm \\infty} (x(u),\\, y(u)) = (-a,\\, 0)\\;", "\\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}", "x^2 + y^2 = 1", "\\vec x \\mapsto \\vec f\\!_0 + A\\vec x", "\\vec x = \\vec p(t) = \\vec f\\!_0 + \\vec f\\!_1 \\cos t + \\vec f\\!_2 \\sin t \\", "\\det(\\vec x\\!-\\!\\vec f\\!_0,\\vec f\\!_2)^2+\\det(\\vec f\\!_1,\\vec x\\!-\\!\\vec f\\!_0)^2-\\det(\\vec f\\!_1,\\vec f\\!_2)^2=0", "\\left|PF_1\\right|^2 = (x - c)^2 + y^2,\\ \\left|Pl_1\\right|^2 = \\left(x - \\tfrac{a^2}{c}\\right)^2", "y^2 = b^2 - \\tfrac{b^2}{a^2}x^2", "x = -\\tfrac{f}{e}", "P = (x,\\, y)", "(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", "x^2\\left(e^2 - 1\\right) + 2px - y^2 = 0", "\\frac{(x - a)^2}{a^2} + \\frac{y^2}{b^2} = 1\\", "\\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}\\", "\\vec x = \\vec p(t) = \\vec f\\!_0 +\\vec f\\!_1 \\cos t + \\vec f\\!_2 \\sin t", "\\tfrac{x^2}{a^2}+\\tfrac{y^2}{b^2}=1", "x^2+y^2=a^2+b^2", "\\left(x - x_\\circ\\right)^2 + \\left(y - y_\\circ\\right)^2 = r^2", "\\left(x_1, y_1\\right),\\; \\left(x_2,\\,y_2\\right),\\; \\left(x_3,\\, y_3\\right)", "x_\\circ,y_\\circ,r", "P_i = \\left(x_i,\\, y_i\\right),\\ i = 1,\\, 2,\\, 3,\\, 4,", "y = m_1x + d_1,\\ y = m_2x + d_2,\\ m_1 \\ne m_2", "\\frac{(x_4 - x_1)(x_4 - x_2) + (y_4 - y_1)(y_4 - y_2)} {(y_4 - y_1)(x_4 - x_2) - (y_4 - y_2)(x_4 - x_1)} = \\frac{(x_3 - x_1)(x_3 - x_2) + (y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}", "P_i = \\left(x_i,\\, y_i\\right)", "\\frac{({\\color{red}x} - x_1)({\\color{red}x} - x_2) + ({\\color{red}y} - y_1)({\\color{red}y} - y_2)} {({\\color{red}y} - y_1)({\\color{red}x} - x_2) - ({\\color{red}y} - y_2)({\\color{red}x} - x_1)} = \\frac{(x_3 - x_1)(x_3 - x_2) + (y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}", "\\frac{(x - 2)x + y(y - 1)}{yx - (y - 1)(x - 2)} = 0", "(x - 1)^2 + \\left(y - \\tfrac{1}{2}\\right)^2 = \\tfrac{5}{4}\\", "\\vec x = (x,\\, y)", "\\frac{\\left({\\color{red}\\vec x} - \\vec x_1\\right) \\cdot \\left({\\color{red}\\vec x} - \\vec x_2\\right)} {\\det\\left({\\color{red}\\vec x} - \\vec x_1,{\\color{red}\\vec x} - \\vec x_2\\right)} = \\frac{\\left(\\vec x_3 - \\vec x_1\\right) \\cdot \\left(\\vec x_3 - \\vec x_2\\right)} {\\det\\left(\\vec x_3 - \\vec x_1, \\vec x_3 - \\vec x_2\\right)}", "\\begin{bmatrix} 1 & \\frac{y_1 - y_2}{x_1 - x_2} \\\\ \\frac{x_1 - x_3}{y_1 - y_3} & 1 \\end{bmatrix} \\begin{bmatrix} x_\\circ \\\\ y_\\circ \\end{bmatrix} = \\begin{bmatrix} \\frac{x_1^2 - x_2^2 + y_1^2 - y_2^2}{2(x_1 - x_2)} \\\\ \\frac{y_1^2 - y_3^2 + x_1^2 - x_3^2}{2(y_1 - y_3)} \\end{bmatrix}", "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}", "\\tfrac{\\left(x - x_\\circ\\right)^2}{a^2} + \\tfrac{\\left(y - y_\\circ\\right)^2}{b^2} = 1", "\\left(x - x_\\circ\\right)^2 + {\\color{blue}q}\\, \\left(y - y_\\circ\\right)^2 = a^2", "x_\\circ,\\, y_\\circ,\\, a", "P_i = \\left(x_i,\\, y_i\\right),\\ i = 1,\\, 2,\\, 3,\\, 4", "(x - x_\\circ)^2 + {\\color{blue}q}\\, (y - y_\\circ)^2 = a^2", "\\frac{(x_4 - x_1)(x_4 - x_2) + {\\color{blue}q}\\;(y_4 - y_1)(y_4 - y_2)} {(y_4 - y_1)(x_4 - x_2) - (y_4 - y_2)(x_4 - x_1)} = \\frac{(x_3 - x_1)(x_3 - x_2) + {\\color{blue}q}\\;(y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}\\", "\\frac{({\\color{red}x} - x_1)({\\color{red}x} - x_2) + {\\color{blue}q}\\;({\\color{red}y} - y_1)({\\color{red}y} - y_2)} {({\\color{red}y} - y_1)({\\color{red}x} - x_2) - ({\\color{red}y} - y_2)({\\color{red}x} - x_1)} = \\frac{(x_3 - x_1)(x_3 - x_2) + {\\color{blue}q}\\;(y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}\\", "\\frac{(x - 2)x + 4y(y - 1)}{yx - (y - 1)(x - 2)} = 0", "\\frac{(x - 1)^2}{2} + \\frac{\\left(y - \\frac{1}{2}\\right)^2}{\\frac{1}{2}} = 1", "\\frac{\\left({\\color{red}\\vec x} - \\vec x_1\\right)*\\left({\\color{red}\\vec x} - \\vec x_2\\right)} {\\det\\left({\\color{red}\\vec x} - \\vec x_1,{\\color{red}\\vec x} - \\vec x_2\\right)} = \\frac{\\left(\\vec x_3 - \\vec x_1\\right)*\\left(\\vec x_3 - \\vec x_2\\right)} {\\det\\left(\\vec x_3 - \\vec x_1, \\vec x_3 - \\vec x_2\\right)}", "\\vec u*\\vec v = u_x v_x + {\\color{blue}q}\\,u_y v_y", "P_1 = \\left(x_1,\\, y_1\\right)", "\\tfrac{x_1x}{a^2} + \\tfrac{y_1y}{b^2} = 1", "P_1 = \\left(x_1,\\, y_1\\right) \\neq (0,\\, 0)", "\\tfrac{x_1 x}{a^2} + \\tfrac{y_1 y}{b^2} = 1", "x = c,\\ c \\ne 0", "x = \\tfrac{a^2}{c}", "x = -\\tfrac{a^2}{c}", "\\frac{x^2}{a^2}+\\frac{y^2}{b^2}= 1", "y(x)= b \\sqrt{1 - x^2/a^2}", "x\\in[-a,a]", "y(x)", "y=b\\sqrt{1-\\frac{x^{2}}{a^{2}}}", "x_{1}", "x_{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", "\\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} \\" ],
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