Edj)dZddlmZddlmZddlmZmZddlm Z m Z ddl m Z m Z ddlmZmZmZmZmZddlmZdd lmZdd lmZdd lmZGd d e ZdS)z4Parabolic geometrical entity. Contains * Parabola )S)ordered)_symbolsymbols)GeometryEntity GeometrySet)PointPoint2D)LineLine2DRay2D Segment2DLinearEntity3D)Ellipse)sign)simplify)solveceZdZdZddZedZedZedZedZ dd Z ed Z ed Z d Z edZedZdS)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)) Nc |rt|d}ntdd}t|}||rtdt j|||fi|S)N)dimrz*The focus must not be a point of directrix)r r contains ValueErrorr__new__)clsfocus directrixkwargss 7lib/python3.11/site-packages/sympy/geometry/parabola.pyrzParabola.__new__Asy  %Q'''EE!QKKEOO   e $ $ KIJJ J%c5)FFvFFFcdS)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 rselfs r ambient_dimensionzParabola.ambient_dimensionOs &qr!c@|j|jS)aReturn the axis of symmetry of the parabola: a line perpendicular to the directrix passing through the focus. 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)) )rperpendicular_linerr$s r axis_of_symmetryzParabola.axis_of_symmetryds0~00<<>> from sympy import Parabola, Point, Line >>> l1 = Line(Point(5, 8), Point(7, 8)) >>> p1 = Parabola(Point(0, 0), l1) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) argsr$s r rzParabola.directrix~0y|r!ctjS)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. )rOner$s r eccentricityzParabola.eccentricitys Bu r!xyct|d}t|d}|jj}|tjur-d|jz||jjz z}||jjz dz}n|dkr-d|jz||jjz z}||jjz dz}n\|j \}}|jj dd\}} ||z dz||z dzz}|j ||dz|dz| dzzz }||z S)azThe equation of the parabola. Parameters ========== x : str, optional Label for the x-axis. Default value is 'x'. y : str, optional Label for the y-axis. Default value is 'y'. Returns ======= equation : SymPy expression Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.equation() -x**2 - 16*y + 64 >>> p1.equation('f') -f**2 - 16*y + 64 >>> p1.equation(y='z') -x**2 - 16*z + 64 TrealrrN) rrsloperInfinity p_parametervertexr2r3r coefficientsequation) r%r2r3mt1t2abcds r r=zParabola.equations 6 AD ! ! ! AD ! ! ! N   ? @d&'1t{}+<=Bdkm#a'BB !V @d&'1t{}+<=Bdkm#a'BB:DAq>.rr2DAqa%!q1uqj(B((A..11a4!Q$;?BBwr!cN|j|j}|dz }|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%rF focal_lengths r rGzParabola.focal_lengths*<>**4:66z r!c|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) rr,r$s r rzParabola.focus r.r!c &tdd\}}|}ttrQ|vrgSt t dt |g||gDSttrGt| |j df|j dfgdkrgSgStttfrrt |tjdjdg||g}t t fd|DStttfrJt t dt |g||gDStt rt#d t#d ) aThe intersection of the parabola and another geometrical entity `o`. Parameters ========== o : GeometryEntity, LinearEntity Returns ======= intersection : list of GeometryEntity objects Examples ======== >>> from sympy import Parabola, Point, Ellipse, Line, Segment >>> p1 = Point(0,0) >>> l1 = Line(Point(1, -2), Point(-1,-2)) >>> parabola1 = Parabola(p1, l1) >>> parabola1.intersection(Ellipse(Point(0, 0), 2, 5)) [Point2D(-2, 0), Point2D(2, 0)] >>> parabola1.intersection(Line(Point(-7, 3), Point(12, 3))) [Point2D(-4, 3), Point2D(4, 3)] >>> parabola1.intersection(Segment((-12, -65), (14, -68))) [] zx yTr5c,g|]}t|Sr#)r .0is r z)Parabola.intersection..Fs$b$b$b!U1XX$b$b$br!rr+c6g|]}|vt|Sr#r )rLrMos r rNz)Parabola.intersection..Ns( F F FqAv F F F Fr!c,g|]}t|Sr#rPrKs r rNz)Parabola.intersection..Ps ` ` ` ` ` `r!z5Entity must be two dimensional, not three dimensionalzWrong type of argument were put)rr= isinstancerlistrrr rsubs_argsrr r pointsrr TypeError)r%rQr2r3 parabola_eqresults ` r intersectionzParabola.intersection$s8u4(((1mmoo a " " ?Dy es G$b$buk1::<<=X[\^_Z`7a7a$b$b$bccddd 7 # # ? ((1agaj/Aqwqz?)KLLMMQRR s  Iu- . . ?K QXa[)I)I)R)R)T)TUXY[\W]^^F F F F FV F F FGGHH H FG, - - ? ` `UK;VYZ\]X^5_5_ ` ` `aabb b > * * ?STT T=>> >r!c|jj}|tjur5|jjd}t |jjd|z}n{|dkr5|jjd}t |jjd|z}n@|j|j}t |jj |j z }||j zS)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+) rr8rr9r<rrr- projectionr2rG)r%r>r2pr3rDs r r:zParabola.p_parameterVsB N   ? )+A.ATZ_Q'!+,,AA !V )+A.ATZ_Q'!+,,AA))$*55ATZ\AC'((A4$$$r!cP|j}|jj}|tjur/t |jd|jz |jd}nU|dkr/t |jd|jd|jz }n |j |d}|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+) rrr8rr9r r-r:r)r[)r%rr>r;s r r;zParabola.vertexs.  N   ? A5:a=4+;;UZ]KKFF !V A5:a=%*Q-$:J*JKKFF*77==a@F r!)NN)r2r3)__name__ __module__ __qualname____doc__rpropertyr&r)rr1r=rGrr[r:r;r#r!r rrs7**X G G G GX(==X=2X2  X D****X  X DX20?0?0?d*%*%X*%XXr!rN)rc sympy.corersympy.core.sortingrsympy.core.symbolrrsympy.geometry.entityrrsympy.geometry.pointr r sympy.geometry.liner r r rrsympy.geometry.ellipsersympy.functionsrsympy.simplifyrsympy.solvers.solversrrr#r!r ros-&&&&&&........========////////NNNNNNNNNNNNNN****** ######''''''NNNNN{NNNNNr!