B [(@sdZddlmZmZddlmZddlmZddlm Z ddl m Z m Z m Z ddlmZmZddlmZmZdd lmZmZmZmZmZdd lmZGd d d eZd S)z4Parabolic geometrical entity. Contains * Parabola )divisionprint_function)S)ordered)_symbol)symbolssimplifysolve)GeometryEntity GeometrySet)PointPoint2D)LineLine2DRay2D Segment2DLinearEntity3D)Ellipsec@seZdZdZdddZeddZeddZed d Zed d Z dddZ eddZ eddZ ddZ eddZeddZdS)ParabolaaA parabolic GeometryEntity. A parabola is declared with a point, that is called 'focus', and a line, that is called 'directrix'. Only vertical or horizontal parabolas are currently supported. Parameters ========== focus : Point Default value is Point(0, 0) directrix : Line Attributes ========== focus directrix axis of symmetry focal length p parameter vertex eccentricity Raises ====== ValueError When `focus` is not a two dimensional point. When `focus` is a point of directrix. NotImplementedError When `directrix` is neither horizontal nor vertical. Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7,8))) >>> p1.focus Point2D(0, 0) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) NcKsf|rt|dd}n tdd}t|}|jdkrB|jtjkrBtd||rTtdtj |||f|S)N)Zdimrz3The directrix must be a horizontal or vertical linez*The focus must not be a point of directrix) r rsloperZInfinityNotImplementedErrorcontains ValueErrorr __new__)clsfocus directrixkwargsr6lib/python3.7/site-packages/sympy/geometry/parabola.pyr@s  zParabola.__new__cCstdS)aXReturns the ambient dimension of parabola. Returns ======= ambient_dimension : integer Examples ======== >>> from sympy import Parabola, Point, Line >>> f1 = Point(0, 0) >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) >>> p1.ambient_dimension 2 r)r)selfrrr ambient_dimensionQszParabola.ambient_dimensioncCs|j|jS)aThe axis of symmetry of the parabola. Returns ======= axis_of_symmetry : Line See Also ======== sympy.geometry.line.Line Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.axis_of_symmetry Line2D(Point2D(0, 0), Point2D(0, 1)) )rZperpendicular_liner)r!rrr axis_of_symmetryfszParabola.axis_of_symmetrycCs |jdS)aThe directrix of the parabola. Returns ======= directrix : Line See Also ======== sympy.geometry.line.Line Examples ======== >>> from sympy import Parabola, Point, Line >>> l1 = Line(Point(5, 8), Point(7, 8)) >>> p1 = Parabola(Point(0, 0), l1) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) )args)r!rrr rszParabola.directrixcCstdS)aThe eccentricity of the parabola. Returns ======= eccentricity : number A parabola may also be characterized as a conic section with an eccentricity of 1. As a consequence of this, all parabolas are similar, meaning that while they can be different sizes, they are all the same shape. See Also ======== https://en.wikipedia.org/wiki/Parabola Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.eccentricity 1 Notes ----- The eccentricity for every Parabola is 1 by definition. r$)r)r!rrr eccentricitys!zParabola.eccentricityxycCszt|dd}t|dd}|jjdkrLd|j||jj}||jjd}n&d|j||jj}||jjd}||S)azThe equation of the parabola. Parameters ========== x : str, optional Label for the x-axis. Default value is 'x'. y : str, optional Label for the y-axis. Default value is 'y'. Returns ======= equation : sympy expression Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.equation() -x**2 - 16*y + 64 >>> p1.equation('f') -f**2 - 16*y + 64 >>> p1.equation(y='z') -x**2 - 16*z + 64 T)realrr)rr#r p_parametervertexr'r()r!r'r(Zt1Zt2rrr equations   zParabola.equationcCs|j|j}|d}|S)aYThe focal length of the parabola. Returns ======= focal_lenght : number or symbolic expression Notes ===== The distance between the vertex and the focus (or the vertex and directrix), measured along the axis of symmetry, is the "focal length". See Also ======== https://en.wikipedia.org/wiki/Parabola Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.focal_length 4 r)rdistancer)r!r. focal_lengthrrr r/szParabola.focal_lengthcCs |jdS)aThe focus of the parabola. Returns ======= focus : Point See Also ======== sympy.geometry.point.Point Examples ======== >>> from sympy import Parabola, Point, Line >>> f1 = Point(0, 0) >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) >>> p1.focus Point2D(0, 0) r)r%)r!rrr rszParabola.focuscsDtddd\}}|}ttrZ|kr0gSttddt|g||gDSnttrt| |j df|j dfgdkrgSgSntt t frt|t jdjdg||g}ttfdd|DStt tfr"ttd dt|g||gDSttr8td ntd d S) aThe intersection of the parabola and another geometrical entity `o`. Parameters ========== o : GeometryEntity, LinearEntity Returns ======= intersection : list of GeometryEntity objects Examples ======== >>> from sympy import Parabola, Point, Ellipse, Line, Segment >>> p1 = Point(0,0) >>> l1 = Line(Point(1, -2), Point(-1,-2)) >>> parabola1 = Parabola(p1, l1) >>> parabola1.intersection(Ellipse(Point(0, 0), 2, 5)) [Point2D(-2, 0), Point2D(2, 0)] >>> parabola1.intersection(Line(Point(-7, 3), Point(12, 3))) [Point2D(-4, 3), Point2D(4, 3)] >>> parabola1.intersection(Segment((-12, -65), (14, -68))) [] zx yT)r)cSsg|] }t|qSr)r ).0irrr Bsz)Parabola.intersection..rr$csg|]}|krt|qSr)r )r0r1)orr r2JscSsg|] }t|qSr)r )r0r1rrr r2Lsz5Entity must be two dimensional, not three dimensionalzWrong type of argument were putN)rr- isinstancerlistrr r rZsubsZ_argsrrrZpointsrr TypeError)r!r3r'r(Z parabola_eqresultr)r3r intersection s$ * *((  zParabola.intersectioncCsn|jjdkr<|jjd }||jjdkr2|j}qj|j }n.|jjd }||jjdkrd|j }n|j}|S)a P is a parameter of parabola. Returns ======= p : number or symbolic expression Notes ===== The absolute value of p is the focal length. The sign on p tells which way the parabola faces. Vertical parabolas that open up and horizontal that open right, give a positive value for p. Vertical parabolas that open down and horizontal that open left, give a negative value for p. See Also ======== http://www.sparknotes.com/math/precalc/conicsections/section2.rhtml Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.p_parameter -4 rrr$)r#rrZ coefficientsrr%r/)r!r'pr(rrr r+Rs!   zParabola.p_parametercCsP|j}|jjdkr0t|jd|j|jd}nt|jd|jd|j}|S)apThe vertex of the parabola. Returns ======= vertex : Point See Also ======== sympy.geometry.point.Point Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.vertex Point2D(0, 4) rr$)rr#rr r%r+)r!rr,rrr r,s  zParabola.vertex)NN)r'r()__name__ __module__ __qualname____doc__rpropertyr"r#rr&r-r/rr8r+r,rrrr rs+     # ' # 2 0rN)r=Z __future__rrZ sympy.corerZsympy.core.compatibilityrZsympy.core.symbolrZsympyrrr Zsympy.geometry.entityr r Zsympy.geometry.pointr r Zsympy.geometry.linerrrrrZsympy.geometry.ellipserrrrrr s