Module Expr Str ImportFrom alias alias ImportFrom alias alias ImportFrom alias ImportFrom alias ImportFrom alias alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam defaults vararg kwarg body Assign NameStore Call AttributeLoad NameLoad attr Str SubscriptLoad NameLoad Index Num If Call NameLoad SubscriptLoad NameLoad Index Num body If BoolOpAnd Call NameLoad SubscriptLoad NameLoad Index Num NameLoad UnaryOpNot NameLoad body Return SubscriptLoad NameLoad Index Num Assign NameStore SubscriptLoad NameLoad Index Num Assign NameStore Call NameLoad NameLoad If Call NameLoad GeneratorExp BoolOpAnd AttributeLoad NameLoad attr Call NameLoad NameLoad comprehension NameStore NameLoad body Raise Call NameLoad Str If NameLoad body Assign NameStore Call AttributeLoad NameLoad attr Call NameLoad ListComp TupleLoad NameLoad Call NameLoad Call NameLoad NameLoad keyword NameLoad comprehension NameStore Call AttributeLoad NameLoad attr NameLoad If CompareEq Call NameLoad NameLoad Num body Return Call NameLoad NameLoad NameLoad If CompareEq Call NameLoad NameLoad Num body Return Call NameLoad NameLoad NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Return CompareEq NameLoad NameLoad decorator_list FunctionDef arguments args defaults vararg body Assign NameStore Call NameLoad Call NameLoad NameLoad If UnaryOpNot Call NameLoad GeneratorExp Call NameLoad NameLoad NameLoad comprehension NameStore NameLoad body Raise Call NameLoad Str Return Call AttributeLoad SubscriptLoad NameLoad Index Num attr SubscriptLoad NameLoad Slice Num decorator_list FunctionDef arguments args defaults vararg body Expr Str Assign NameStore Call NameLoad Call NameLoad NameLoad If UnaryOpNot Call NameLoad GeneratorExp Call NameLoad NameLoad NameLoad comprehension NameStore NameLoad body Raise Call NameLoad Str If CompareEq Call NameLoad NameLoad Num body Return NameLoad If CompareLtE Call NameLoad NameLoad Num body Return NameLoad Assign NameStore ListComp BinOpSub NameLoad SubscriptLoad NameLoad Index Num comprehension NameStore SubscriptLoad NameLoad Slice Num For NameStore SubscriptLoad NameLoad Slice Num body If UnaryOpNot Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num NameLoad body Return NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad ListLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return CompareLt Call AttributeLoad NameLoad attr keyword NameLoad Num decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return Call NameLoad BinOpMult ListLoad Num Call NameLoad NameLoad decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return Call NameLoad GeneratorExp CompareEq NameLoad AttributeLoad NameLoad attr comprehension NameStore AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return Call NameLoad NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str Return Call NameLoad Call NameLoad ListComp BinOpPow BinOpSub NameLoad NameLoad Num comprehension TupleStore NameStore NameStore Call NameLoad AttributeLoad NameLoad attr IfExp Call NameLoad NameLoad NameLoad AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Return Call NameLoad GeneratorExp Call NameLoad BinOpSub NameLoad NameLoad comprehension TupleStore NameStore NameStore Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return Call NameLoad ListComp Call NameLoad BinOpMult BinOpAdd NameLoad NameLoad AttributeLoad NameLoad attr comprehension TupleStore NameStore NameStore Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad kwarg body Expr Str Assign NameStore ListComp Call AttributeLoad NameLoad attr NameLoad NameLoad comprehension NameStore AttributeLoad NameLoad attr Return Call NameLoad keyword NameLoad NameLoad decorator_list Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str If Call NameLoad NameLoad NameLoad body If CompareNotEq Call NameLoad NameLoad Call NameLoad NameLoad body Raise Call NameLoad Str If CompareEq NameLoad NameLoad body Return ListLoad NameLoad Return ListLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Return Call NameLoad ListComp BinOpMult NameLoad NameLoad comprehension TupleStore NameStore NameStore Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If BoolOpOr UnaryOpNot Call NameLoad NameLoad NameLoad CompareNotEq Call NameLoad AttributeLoad NameLoad attr Call NameLoad AttributeLoad NameLoad attr body Return NameLoad Return Call NameLoad GeneratorExp Call AttributeLoad NameLoad attr NameLoad comprehension TupleStore NameStore NameStore Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return Call NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr decorator_list FunctionDef arguments args NameParam NameParam defaults body If BoolOpOr UnaryOpNot Call NameLoad NameLoad NameLoad CompareNotEq Call NameLoad AttributeLoad NameLoad attr Call NameLoad AttributeLoad NameLoad attr body Return NameLoad Return CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return Call NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Return SubscriptLoad AttributeLoad NameLoad attr Index NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If BoolOpAnd Call NameLoad NameLoad CompareEq Call NameLoad NameLoad Call NameLoad NameLoad body Return Call NameLoad ListComp Call NameLoad BinOpAdd NameLoad NameLoad comprehension TupleStore NameStore NameStore Call NameLoad NameLoad NameLoad orelse Raise Call NameLoad Str decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return BinOpAdd NameLoad UnaryOpUSub NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Return Call NameLoad ListComp Call NameLoad BinOpMult NameLoad NameLoad comprehension NameStore AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Return Call NameLoad ListComp Call NameLoad BinOpDiv NameLoad NameLoad comprehension NameStore AttributeLoad NameLoad attr decorator_list Assign NameStore NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return Call NameLoad ListComp UnaryOpUSub NameLoad comprehension NameStore AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call NameLoad BinOpMult ListLoad Num Call NameLoad NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam defaults vararg kwarg body Assign NameStore Call AttributeLoad NameLoad attr Str SubscriptLoad NameLoad Index Num Assign NameStore NameLoad If Call NameLoad SubscriptLoad NameLoad Index Num NameLoad body If UnaryOpNot NameLoad body Return SubscriptLoad NameLoad Index Num Assign NameStore AttributeLoad SubscriptLoad NameLoad Index Num attr Assign NameStore NameLoad orelse If Call NameLoad SubscriptLoad NameLoad Index Num body Assign NameStore SubscriptLoad NameLoad Index Num If CompareNotEq Call NameLoad NameLoad Num body Raise Call NameLoad Str Assign NameStore Call NameLoad NameLoad If NameLoad body If Call NameLoad GeneratorExp BoolOpAnd AttributeLoad NameLoad attr Call NameLoad NameLoad comprehension NameStore NameLoad body Raise Call NameLoad Str If NameLoad body Assign NameStore Call AttributeLoad NameLoad attr Call NameLoad ListComp TupleLoad NameLoad Call NameLoad Call NameLoad NameLoad keyword NameLoad comprehension NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return CompareEq NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return TupleLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args defaults vararg body Expr Str If CompareEq Call NameLoad NameLoad Num body Return NameLoad If CompareLtE Call NameLoad NameLoad Num body Return NameLoad Assign NameStore ListComp Call NameLoad NameLoad comprehension NameStore NameLoad If CompareEq Call NameLoad NameLoad Num body Return UnaryOpNot Call AttributeLoad NameLoad attr NameLoad TryExcept body ImportFrom alias Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num For NameStore SubscriptLoad NameLoad Slice Num body If CompareNotIn NameLoad NameLoad body Return NameLoad Return NameLoad handlers ExceptHandler type NameLoad body Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str ImportFrom alias alias alias Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore NameLoad If CompareIsNot NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad AugAssignSub NameStore NameLoad Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Assign NameStore Call NameLoad BinOpSub BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpAdd BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad If CompareIsNot NameLoad NameLoad body AugAssignAdd NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num Num NameLoad body Expr Str If NameLoad body Assign NameStore Call NameLoad NameLoad Return Call AttributeLoad Call AttributeLoad Call AttributeLoad NameLoad attr AttributeLoad UnaryOpUSub NameLoad attr attr NameLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num Num body Expr Str Return Call NameLoad BinOpAdd AttributeLoad NameLoad attr NameLoad BinOpAdd AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str TryExcept body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Assign NameStore BoolOpAnd AttributeLoad NameLoad attr CompareEq NameLoad Num handlers ExceptHandler type NameLoad body Assign NameStore NameLoad If UnaryOpNot NameLoad body Raise Call NameLoad BinOpAdd Str Str Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Return Call NameLoad SubscriptLoad SubscriptLoad Call AttributeLoad BinOpMult Call NameLoad Num Num ListLoad NameLoad NameLoad Num NameLoad attr Index Num Slice Num decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam defaults vararg kwarg body Assign NameStore Call AttributeLoad NameLoad attr Str SubscriptLoad NameLoad Index Num If Call NameLoad SubscriptLoad NameLoad Index Num TupleLoad NameLoad NameLoad body If UnaryOpNot NameLoad body Return SubscriptLoad NameLoad Index Num Assign NameStore AttributeLoad SubscriptLoad NameLoad Index Num attr orelse If Call NameLoad SubscriptLoad NameLoad Index Num body Assign NameStore SubscriptLoad NameLoad Index Num If CompareNotIn Call NameLoad NameLoad TupleLoad Num Num body Raise Call NameLoad Str Assign NameStore Call NameLoad NameLoad If CompareEq Call NameLoad NameLoad Num body AugAssignAdd NameStore TupleLoad AttributeLoad NameLoad attr If NameLoad body Assign NameStore Call AttributeLoad NameLoad attr Call NameLoad ListComp TupleLoad NameLoad Call NameLoad Call NameLoad NameLoad keyword NameLoad comprehension NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return CompareEq NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str Return ListLoad BinOpSub AttributeLoad NameLoad attr AttributeLoad NameLoad attr BinOpSub AttributeLoad NameLoad attr AttributeLoad NameLoad attr BinOpSub AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad Call NameLoad GeneratorExp BinOpPow NameLoad Num comprehension NameStore NameLoad Return ListLoad BinOpDiv BinOpSub AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad BinOpDiv BinOpSub AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad BinOpDiv BinOpSub AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args defaults vararg body Expr Str Return Call AttributeLoad NameLoad attr NameLoad decorator_list NameLoad FunctionDef arguments args defaults vararg body Expr Str ImportFrom alias Assign NameStore Call NameLoad Call NameLoad NameLoad If CompareLt Call NameLoad NameLoad Num body Raise Call NameLoad Str Assign TupleStore NameStore NameStore SubscriptLoad NameLoad Slice Num For TupleStore NameStore NameStore Call NameLoad SubscriptLoad NameLoad Slice Num body TryExcept body Assign NameStore Call NameLoad NameLoad NameLoad NameLoad For NameStore TupleLoad Num Num NameLoad body Expr Call AttributeLoad NameLoad attr NameLoad Return Call NameLoad GeneratorExp Call AttributeLoad NameLoad attr NameLoad comprehension NameStore NameLoad handlers ExceptHandler type NameLoad body Pass Raise Call NameLoad Str decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str If Call NameLoad NameLoad NameLoad body If CompareEq NameLoad NameLoad body Return ListLoad NameLoad Return ListLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults Num Num Num NameLoad body Expr Str If NameLoad body Assign NameStore Call NameLoad NameLoad Return Call AttributeLoad Call AttributeLoad Call AttributeLoad NameLoad attr AttributeLoad UnaryOpUSub NameLoad attr attr NameLoad NameLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad BinOpMult AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num Num Num body Expr Str Return Call NameLoad BinOpAdd AttributeLoad NameLoad attr NameLoad BinOpAdd AttributeLoad NameLoad attr NameLoad BinOpAdd AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str TryExcept body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Assign NameStore BoolOpAnd AttributeLoad NameLoad attr CompareEq NameLoad Num handlers ExceptHandler type NameLoad body Assign NameStore NameLoad If UnaryOpNot NameLoad body Raise Call NameLoad BinOpAdd Str Str ImportFrom alias Assign TupleStore NameStore NameStore NameStore AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad Return Call NameLoad SubscriptLoad SubscriptLoad Call AttributeLoad BinOpMult Call NameLoad Num Num ListLoad NameLoad NameLoad NameLoad Num NameLoad attr Index Num Slice Num decorator_list decorator_list
N/A N/A Geometrical Points.

Contains
========
Point
Point2D
Point3D

 __future__ division print_function sympy.core S sympify sympy.core.compatibility iterable sympy.core.containers Tuple sympy.simplify nsimplify simplify sympy.geometry.exceptions GeometryError sympy.functions.elementary.miscellaneous sqrt sympy.functions.elementary.complexes im sympy.matrices Matrix sympy.core.numbers Float sympy.core.evaluate global_evaluate sympy.core.add Add entity GeometryEntity Point N/A GeometryEntity N/A N/A A point in a n-dimensional Euclidean space.

    Parameters
    ==========

    coords : sequence of n-coordinate values. In the special
    case where n=2 or 3, a Point2D or Point3D will be created
    as appropriate.

    Attributes
    ==========

    length
    origin: A `Point` representing the origin of the
        appropriately-dimensioned space.

    Raises
    ======

    TypeError
        When trying to add or subtract points with different dimensions.
        When `intersection` is called with object other than a Point.

    See Also
    ========

    sympy.geometry.line.Segment : Connects two Points

    Examples
    ========

    >>> from sympy.geometry import Point
    >>> from sympy.abc import x
    >>> Point(1, 2, 3)
    Point3D(1, 2, 3)
    >>> Point([1, 2])
    Point2D(1, 2)
    >>> Point(0, x)
    Point2D(0, x)

    Floats are automatically converted to Rational unless the
    evaluate flag is False:

    >>> Point(0.5, 0.25)
    Point2D(1/2, 1/4)
    >>> Point(0.5, 0.25, evaluate=False)
    Point2D(0.5, 0.25)

     __new__ N/A N/A cls N/A args kwargs N/A N/A evaluate N/A N/A kwargs get evaluate N/A global_evaluate N/A 0 N/A N/A iterable N/A args N/A 0 N/A N/A N/A N/A isinstance N/A args N/A 0 Point N/A evaluate N/A N/A N/A args N/A 0 N/A args N/A args N/A 0 N/A coords N/A Tuple args N/A N/A any N/A N/A N/A a is_number N/A im a N/A a coords N/A N/A N/A ValueError Imaginary coordinates not permitted. N/A evaluate N/A N/A coords N/A N/A coords xreplace N/A dict N/A N/A f N/A simplify N/A nsimplify f rational True N/A f N/A N/A coords atoms Float N/A N/A N/A len coords 2 N/A N/A N/A Point2D coords kwargs N/A N/A N/A len coords 3 N/A N/A N/A Point3D coords kwargs N/A N/A N/A GeometryEntity __new__ cls coords N/A N/A is_Point True __contains__ N/A N/A self item N/A N/A N/A N/A item self N/A is_concyclic N/A N/A N/A args N/A N/A args N/A list N/A set args N/A N/A N/A all N/A N/A isinstance p Point N/A p args N/A N/A N/A TypeError Must pass only Point objects N/A N/A N/A N/A args N/A 0 is_concyclic N/A args N/A 1 N/A is_collinear N/A N/A N/A args N/A N/A Is a sequence of points collinear?

        Test whether or not a set of points are collinear. Returns True if
        the set of points are collinear, or False otherwise.

        Parameters
        ==========

        points : sequence of Point

        Returns
        =======

        is_collinear : boolean

        Notes
        =====

        Slope is preserved everywhere on a line, so the slope between
        any two points on the line should be the same. Take the first
        two points, p1 and p2, and create a translated point v1
        with p1 as the origin. Now for every other point we create
        a translated point, vi with p1 also as the origin. Note that
        these translations preserve slope since everything is
        consistently translated to a new origin of p1. Since slope
        is preserved then we have the following equality:

              * v1_slope = vi_slope
              * v1.y/v1.x = vi.y/vi.x (due to translation)
              * v1.y*vi.x = vi.y*v1.x
              * v1.y*vi.x - vi.y*v1.x = 0           (*)

        Hence, if we have a vi such that the equality in (*) is False
        then the points are not collinear. We do this test for every
        point in the list, and if all pass then they are collinear.

        See Also
        ========

        sympy.geometry.line.Line

        Examples
        ========

        >>> from sympy import Point
        >>> from sympy.abc import x
        >>> p1, p2 = Point(0, 0), Point(1, 1)
        >>> p3, p4, p5 = Point(2, 2), Point(x, x), Point(1, 2)
        >>> Point.is_collinear(p1, p2, p3, p4)
        True
        >>> Point.is_collinear(p1, p2, p3, p5)
        False

         N/A args N/A list N/A set args N/A N/A N/A all N/A N/A isinstance p Point N/A p args N/A N/A N/A TypeError Must pass only Point objects N/A N/A N/A len args 0 N/A N/A False N/A N/A N/A len args 2 N/A N/A True N/A points N/A N/A p N/A args N/A 0 N/A p N/A args N/A 1 N/A p N/A points N/A 1 N/A N/A N/A N/A N/A Point is_scalar_multiple N/A points N/A 0 p N/A N/A False N/A True N/A is_scalar_multiple N/A N/A p1 p2 N/A N/A N/A Returns whether `p1` and `p2` are scalar multiples
        of eachother.
         N/A m N/A Matrix N/A N/A p1 args N/A p2 args N/A N/A N/A N/A m rank simplify True 2 N/A length N/A N/A self N/A N/A N/A 
        Treating a Point as a Line, this returns 0 for the length of a Point.

        Examples
        ========

        >>> from sympy import Point
        >>> p = Point(0, 1)
        >>> p.length
        0
         N/A N/A S Zero N/A property origin N/A N/A self N/A N/A N/A A point of all zeros of the same ambient dimension
        as the current point N/A N/A Point N/A N/A 0 N/A len self N/A property is_zero N/A N/A self N/A N/A N/A True if every coordinate is zero, otherwise False. N/A N/A all N/A N/A x N/A S Zero N/A x N/A self args N/A property ambient_dimension N/A N/A self N/A N/A N/A The dimension of the ambient space the point is in.
        I.e., if the point is in R^n, the ambient dimension
        will be n N/A N/A len self N/A property distance N/A N/A self p N/A N/A N/A The Euclidean distance from self to point p.

        Parameters
        ==========

        p : Point

        Returns
        =======

        distance : number or symbolic expression.

        See Also
        ========

        sympy.geometry.line.Segment.length

        Examples
        ========

        >>> from sympy.geometry import Point
        >>> p1, p2 = Point(1, 1), Point(4, 5)
        >>> p1.distance(p2)
        5

        >>> from sympy.abc import x, y
        >>> p3 = Point(x, y)
        >>> p3.distance(Point(0, 0))
        sqrt(x**2 + y**2)

         N/A N/A sqrt N/A sum N/A N/A N/A a b 2 N/A N/A a b N/A zip N/A self args N/A N/A isinstance p Point N/A p args p N/A taxicab_distance N/A N/A self p N/A N/A N/A The Taxicab Distance from self to point p.

        Returns the sum of the horizontal and vertical distances to point p.

        Parameters
        ==========

        p : Point

        Returns
        =======

        taxicab_distance : The sum of the horizontal
        and vertical distances to point p.

        See Also
        ========

        sympy.geometry.Point.distance

        Examples
        ========

        >>> from sympy.geometry import Point
        >>> p1, p2 = Point(1, 1), Point(4, 5)
        >>> p1.taxicab_distance(p2)
        7

         N/A p N/A Point p N/A N/A sum N/A N/A abs N/A a b N/A N/A a b N/A zip N/A self args N/A p args N/A midpoint N/A N/A self p N/A N/A N/A The midpoint between self and point p.

        Parameters
        ==========

        p : Point

        Returns
        =======

        midpoint : Point

        See Also
        ========

        sympy.geometry.line.Segment.midpoint

        Examples
        ========

        >>> from sympy.geometry import Point
        >>> p1, p2 = Point(1, 1), Point(13, 5)
        >>> p1.midpoint(p2)
        Point2D(7, 3)

         N/A N/A Point N/A N/A simplify N/A N/A a b N/A S Half N/A N/A a b N/A zip N/A self args N/A p args N/A evalf N/A N/A self prec N/A None options N/A N/A Evaluate the coordinates of the point.

        This method will, where possible, create and return a new Point
        where the coordinates are evaluated as floating point numbers to
        the precision indicated (default=15).

        Returns
        =======

        point : Point

        Examples
        ========

        >>> from sympy import Point, Rational
        >>> p1 = Point(Rational(1, 2), Rational(3, 2))
        >>> p1
        Point2D(1/2, 3/2)
        >>> p1.evalf()
        Point2D(0.5, 1.5)

         N/A coords N/A N/A N/A x evalf prec options N/A x N/A self args N/A N/A Point evaluate False coords N/A N/A n evalf intersection N/A N/A self o N/A N/A N/A The intersection between this point and another point.

        Parameters
        ==========

        other : Point

        Returns
        =======

        intersection : list of Points

        Notes
        =====

        The return value will either be an empty list if there is no
        intersection, otherwise it will contain this point.

        Examples
        ========

        >>> from sympy import Point
        >>> p1, p2, p3 = Point(0, 0), Point(1, 1), Point(0, 0)
        >>> p1.intersection(p2)
        []
        >>> p1.intersection(p3)
        [Point2D(0, 0)]

         N/A N/A isinstance o Point N/A N/A N/A N/A len self N/A len o N/A N/A N/A ValueError Points must be of the same dimension to intersect N/A N/A self o N/A N/A N/A self N/A N/A N/A N/A N/A o intersection self N/A dot N/A N/A self p2 N/A N/A N/A Return dot product of self with another Point. N/A p2 N/A Point p2 N/A N/A Add N/A N/A a b N/A N/A a b N/A zip self p2 N/A equals N/A N/A self other N/A N/A N/A Returns whether the coordinates of self and other agree. N/A N/A N/A N/A isinstance other Point N/A N/A len N/A self args N/A len N/A other args N/A N/A False N/A N/A all N/A N/A N/A a equals b N/A N/A a b N/A zip N/A self args N/A other args N/A __len__ N/A N/A self N/A N/A N/A N/A len N/A self args N/A __iter__ N/A N/A self N/A N/A N/A N/A N/A N/A self args __iter__ N/A __eq__ N/A N/A self other N/A N/A N/A N/A N/A N/A isinstance other Point N/A N/A len N/A self args N/A len N/A other args N/A N/A False N/A N/A N/A self args N/A other args N/A __hash__ N/A N/A self N/A N/A N/A N/A hash N/A self args N/A __getitem__ N/A N/A self key N/A N/A N/A N/A N/A self args N/A key N/A __add__ N/A N/A self other N/A N/A N/A Add other to self by incrementing self's coordinates by those of other.

        See Also
        ========

        sympy.geometry.entity.translate

         N/A N/A N/A iterable other N/A N/A len other N/A len self N/A N/A N/A Point N/A N/A simplify N/A a b N/A N/A a b N/A zip self other N/A N/A N/A ValueError Points must have the same number of dimensions N/A __sub__ N/A N/A self other N/A N/A N/A Subtract two points, or subtract a factor from this point's
        coordinates. N/A N/A self N/A other N/A __mul__ N/A N/A self factor N/A N/A N/A Multiply point's coordinates by a factor. N/A factor N/A sympify factor N/A N/A Point N/A N/A simplify N/A x factor N/A x N/A self args N/A __div__ N/A N/A self divisor N/A N/A N/A Divide point's coordinates by a factor. N/A divisor N/A sympify divisor N/A N/A Point N/A N/A simplify N/A x divisor N/A x N/A self args N/A N/A __truediv__ __div__ __neg__ N/A N/A self N/A N/A N/A Negate the point. N/A N/A Point N/A N/A x N/A x N/A self args N/A __abs__ N/A N/A self N/A N/A N/A Returns the distance between this point and the origin. N/A origin N/A Point N/A N/A 0 N/A len self N/A N/A N/A Point distance origin self N/A N/A Point2D N/A Point N/A N/A A point in a 2-dimensional Euclidean space.

    Parameters
    ==========

    coords : sequence of 2 coordinate values.

    Attributes
    ==========

    x
    y
    length

    Raises
    ======

    TypeError
        When trying to add or subtract points with different dimensions.
        When trying to create a point with more than two dimensions.
        When `intersection` is called with object other than a Point.

    See Also
    ========

    sympy.geometry.line.Segment : Connects two Points

    Examples
    ========

    >>> from sympy.geometry import Point2D
    >>> from sympy.abc import x
    >>> Point2D(1, 2)
    Point2D(1, 2)
    >>> Point2D([1, 2])
    Point2D(1, 2)
    >>> Point2D(0, x)
    Point2D(0, x)

    Floats are automatically converted to Rational unless the
    evaluate flag is False:

    >>> Point2D(0.5, 0.25)
    Point2D(1/2, 1/4)
    >>> Point2D(0.5, 0.25, evaluate=False)
    Point2D(0.5, 0.25)

     __new__ N/A N/A cls N/A args kwargs N/A N/A eval N/A N/A kwargs get evaluate N/A global_evaluate N/A 0 N/A check True N/A N/A isinstance N/A args N/A 0 Point2D N/A N/A N/A eval N/A N/A N/A args N/A 0 N/A args N/A N/A args N/A 0 args N/A check False N/A N/A N/A iterable N/A args N/A 0 N/A N/A args N/A args N/A 0 N/A N/A N/A len args 2 N/A N/A N/A ValueError Only two dimensional points currently supported N/A coords N/A Tuple args N/A check N/A N/A N/A any N/A N/A N/A a is_number N/A im a N/A a coords N/A N/A N/A ValueError Imaginary args not permitted. N/A eval N/A N/A coords N/A N/A coords xreplace N/A dict N/A N/A f N/A simplify N/A nsimplify f rational True N/A f N/A N/A coords atoms Float N/A N/A N/A GeometryEntity __new__ cls coords N/A __contains__ N/A N/A self item N/A N/A N/A N/A item self N/A x N/A N/A self N/A N/A N/A 
        Returns the X coordinate of the Point.

        Examples
        ========

        >>> from sympy import Point2D
        >>> p = Point2D(0, 1)
        >>> p.x
        0
         N/A N/A N/A self args N/A 0 N/A property y N/A N/A self N/A N/A N/A 
        Returns the Y coordinate of the Point.

        Examples
        ========

        >>> from sympy import Point2D
        >>> p = Point2D(0, 1)
        >>> p.y
        1
         N/A N/A N/A self args N/A 1 N/A property bounds N/A N/A self N/A N/A N/A Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
        rectangle for the geometric figure.

         N/A N/A N/A self x N/A self y N/A self x N/A self y N/A property is_concyclic N/A N/A N/A points N/A N/A Is a sequence of points concyclic?

        Test whether or not a sequence of points are concyclic (i.e., they lie
        on a circle).

        Parameters
        ==========

        points : sequence of Points

        Returns
        =======

        is_concyclic : boolean
            True if points are concyclic, False otherwise.

        See Also
        ========

        sympy.geometry.ellipse.Circle

        Notes
        =====

        No points are not considered to be concyclic. One or two points
        are definitely concyclic and three points are conyclic iff they
        are not collinear.

        For more than three points, create a circle from the first three
        points. If the circle cannot be created (i.e., they are collinear)
        then all of the points cannot be concyclic. If the circle is created
        successfully then simply check the remaining points for containment
        in the circle.

        Examples
        ========

        >>> from sympy.geometry import Point
        >>> p1, p2 = Point(-1, 0), Point(1, 0)
        >>> p3, p4 = Point(0, 1), Point(-1, 2)
        >>> Point.is_concyclic(p1, p2, p3)
        True
        >>> Point.is_concyclic(p1, p2, p3, p4)
        False

         N/A N/A N/A len points 0 N/A N/A False N/A N/A N/A len points 2 N/A N/A True N/A points N/A N/A Point p N/A p points N/A N/A N/A len points 3 N/A N/A N/A N/A N/A Point is_collinear points N/A N/A ellipse Circle N/A c N/A Circle N/A points N/A 0 N/A points N/A 1 N/A points N/A 2 N/A point N/A points N/A 3 N/A N/A N/A point c N/A N/A False N/A True N/A N/A N/A GeometryError N/A N/A False N/A rotate N/A N/A self angle pt N/A None N/A N/A Rotate ``angle`` radians counterclockwise about Point ``pt``.

        See Also
        ========

        rotate, scale

        Examples
        ========

        >>> from sympy import Point2D, pi
        >>> t = Point2D(1, 0)
        >>> t.rotate(pi/2)
        Point2D(0, 1)
        >>> t.rotate(pi/2, (2, 0))
        Point2D(2, -1)

         sympy cos sin Point N/A c N/A cos angle N/A s N/A sin angle N/A rv self N/A N/A pt None N/A N/A pt N/A Point pt N/A rv pt N/A N/A x y N/A rv args N/A rv N/A Point N/A N/A c x N/A s y N/A N/A s x N/A c y N/A N/A pt None N/A N/A rv pt N/A rv N/A scale N/A N/A self x y pt N/A 1 1 None N/A N/A Scale the coordinates of the Point by multiplying by
        ``x`` and ``y`` after subtracting ``pt`` -- default is (0, 0) --
        and then adding ``pt`` back again (i.e. ``pt`` is the point of
        reference for the scaling).

        See Also
        ========

        rotate, translate

        Examples
        ========

        >>> from sympy import Point2D
        >>> t = Point2D(1, 1)
        >>> t.scale(2)
        Point2D(2, 1)
        >>> t.scale(2, 2)
        Point2D(2, 2)

         N/A pt N/A N/A pt N/A Point pt N/A N/A N/A N/A N/A N/A N/A self translate N/A N/A pt args scale x y translate N/A pt args N/A N/A Point N/A N/A self x x N/A N/A self y y N/A translate N/A N/A self x y N/A 0 0 N/A N/A Shift the Point by adding x and y to the coordinates of the Point.

        See Also
        ========

        rotate, scale

        Examples
        ========

        >>> from sympy import Point2D
        >>> t = Point2D(0, 1)
        >>> t.translate(2)
        Point2D(2, 1)
        >>> t.translate(2, 2)
        Point2D(2, 3)
        >>> t + Point2D(2, 2)
        Point2D(2, 3)

         N/A N/A Point N/A N/A self x x N/A N/A self y y N/A transform N/A N/A self matrix N/A N/A N/A Return the point after applying the transformation described
        by the 3x3 Matrix, ``matrix``.

        See Also
        ========
        geometry.entity.rotate
        geometry.entity.scale
        geometry.entity.translate
         N/A N/A N/A N/A col row N/A matrix shape N/A valid_matrix N/A N/A matrix is_square N/A col 3 N/A N/A N/A AttributeError N/A N/A valid_matrix False N/A N/A valid_matrix N/A N/A N/A ValueError N/A The argument to the transform function must be  a 3x3 matrix N/A N/A x y N/A self args N/A N/A Point N/A N/A N/A N/A N/A N/A Matrix 1 3 N/A x y 1 matrix tolist N/A 0 N/A 2 N/A N/A Point3D N/A Point N/A N/A A point in a 3-dimensional Euclidean space.

    Parameters
    ==========

    coords : sequence of 3 coordinate values.

    Attributes
    ==========

    x
    y
    z
    length

    Raises
    ======

    TypeError
        When trying to add or subtract points with different dimensions.
        When `intersection` is called with object other than a Point.

    Notes
    =====

    Currently only 2-dimensional and 3-dimensional points are supported.

    Examples
    ========

    >>> from sympy import Point3D
    >>> from sympy.abc import x
    >>> Point3D(1, 2, 3)
    Point3D(1, 2, 3)
    >>> Point3D([1, 2, 3])
    Point3D(1, 2, 3)
    >>> Point3D(0, x, 3)
    Point3D(0, x, 3)

    Floats are automatically converted to Rational unless the
    evaluate flag is False:

    >>> Point3D(0.5, 0.25, 2)
    Point3D(1/2, 1/4, 2)
    >>> Point3D(0.5, 0.25, 3, evaluate=False)
    Point3D(0.5, 0.25, 3)

     __new__ N/A N/A cls N/A args kwargs N/A N/A eval N/A N/A kwargs get evaluate N/A global_evaluate N/A 0 N/A N/A isinstance N/A args N/A 0 N/A Point Point3D N/A N/A N/A eval N/A N/A N/A args N/A 0 N/A args N/A N/A args N/A 0 args N/A N/A N/A iterable N/A args N/A 0 N/A N/A args N/A args N/A 0 N/A N/A N/A len args N/A 2 3 N/A N/A N/A TypeError Enter a 2 or 3 dimensional point N/A coords N/A Tuple args N/A N/A N/A len coords 2 N/A N/A coords N/A N/A S Zero N/A eval N/A N/A coords N/A N/A coords xreplace N/A dict N/A N/A f N/A simplify N/A nsimplify f rational True N/A f N/A N/A coords atoms Float N/A N/A N/A GeometryEntity __new__ cls coords N/A __contains__ N/A N/A self item N/A N/A N/A N/A item self N/A x N/A N/A self N/A N/A N/A 
        Returns the X coordinate of the Point.

        Examples
        ========

        >>> from sympy import Point3D
        >>> p = Point3D(0, 1, 3)
        >>> p.x
        0
         N/A N/A N/A self args N/A 0 N/A property y N/A N/A self N/A N/A N/A 
        Returns the Y coordinate of the Point.

        Examples
        ========

        >>> from sympy import Point3D
        >>> p = Point3D(0, 1, 2)
        >>> p.y
        1
         N/A N/A N/A self args N/A 1 N/A property z N/A N/A self N/A N/A N/A 
        Returns the Z coordinate of the Point.

        Examples
        ========

        >>> from sympy import Point3D
        >>> p = Point3D(0, 1, 1)
        >>> p.z
        1
         N/A N/A N/A self args N/A 2 N/A property direction_ratio N/A N/A self point N/A N/A N/A 
        Gives the direction ratio between 2 points

        Parameters
        ==========

        p : Point3D

        Returns
        =======

        list

        Examples
        ========

        >>> from sympy import Point3D
        >>> p1 = Point3D(1, 2, 3)
        >>> p1.direction_ratio(Point3D(2, 3, 5))
        [1, 1, 2]
         N/A N/A N/A N/A point x N/A self x N/A N/A point y N/A self y N/A N/A point z N/A self z N/A direction_cosine N/A N/A self point N/A N/A N/A 
        Gives the direction cosine between 2 points

        Parameters
        ==========

        p : Point3D

        Returns
        =======

        list

        Examples
        ========

        >>> from sympy import Point3D
        >>> p1 = Point3D(1, 2, 3)
        >>> p1.direction_cosine(Point3D(2, 3, 5))
        [sqrt(6)/6, sqrt(6)/6, sqrt(6)/3]
         N/A a N/A N/A self direction_ratio point N/A b N/A sqrt N/A sum N/A N/A i 2 N/A i a N/A N/A N/A N/A N/A point x N/A self x b N/A N/A N/A point y N/A self y b N/A N/A N/A point z N/A self z b N/A are_collinear N/A N/A N/A points N/A N/A Is a sequence of points collinear?

        Test whether or not a set of points are collinear. Returns True if
        the set of points are collinear, or False otherwise.

        Parameters
        ==========

        points : sequence of Point

        Returns
        =======

        are_collinear : boolean

        See Also
        ========

        sympy.geometry.line3d.Line3D

        Examples
        ========

        >>> from sympy import Point3D, Matrix
        >>> from sympy.abc import x
        >>> p1, p2 = Point3D(0, 0, 0), Point3D(1, 1, 1)
        >>> p3, p4, p5 = Point3D(2, 2, 2), Point3D(x, x, x), Point3D(1, 2, 6)
        >>> Point3D.are_collinear(p1, p2, p3, p4)
        True
        >>> Point3D.are_collinear(p1, p2, p3, p5)
        False
         N/A N/A N/A Point is_collinear points N/A staticmethod are_coplanar N/A N/A N/A points N/A N/A 

        This function tests whether passed points are coplanar or not.
        It uses the fact that the triple scalar product of three vectors
        vanishes if the vectors are coplanar. Which means that the volume
        of the solid described by them will have to be zero for coplanarity.

        Parameters
        ==========

        A set of points 3D points

        Returns
        =======

        boolean

        Examples
        ========

        >>> from sympy import Point3D
        >>> p1 = Point3D(1, 2, 2)
        >>> p2 = Point3D(2, 7, 2)
        >>> p3 = Point3D(0, 0, 2)
        >>> p4 = Point3D(1, 1, 2)
        >>> Point3D.are_coplanar(p1, p2, p3, p4)
        True
        >>> p5 = Point3D(0, 1, 3)
        >>> Point3D.are_coplanar(p1, p2, p3, p5)
        False

         sympy.geometry.plane Plane N/A points N/A list N/A set points N/A N/A N/A len points 3 N/A N/A N/A ValueError At least 3 points are needed to define a plane. N/A N/A a b N/A points N/A 2 N/A N/A i c N/A enumerate N/A points N/A 2 N/A N/A N/A N/A p N/A Plane a b c N/A j N/A 0 1 i N/A N/A N/A N/A points pop j N/A N/A all N/A N/A N/A p is_coplanar i N/A i points N/A N/A N/A ValueError N/A N/A N/A N/A ValueError At least 3 non-collinear points needed to define plane. N/A staticmethod intersection N/A N/A self o N/A N/A N/A The intersection between this point and another point.

        Parameters
        ==========

        other : Point

        Returns
        =======

        intersection : list of Points

        Notes
        =====

        The return value will either be an empty list if there is no
        intersection, otherwise it will contain this point.

        Examples
        ========

        >>> from sympy import Point3D
        >>> p1, p2, p3 = Point3D(0, 0, 0), Point3D(1, 1, 1), Point3D(0, 0, 0)
        >>> p1.intersection(p2)
        []
        >>> p1.intersection(p3)
        [Point3D(0, 0, 0)]

         N/A N/A isinstance o Point3D N/A N/A N/A self o N/A N/A N/A self N/A N/A N/A N/A N/A o intersection self N/A scale N/A N/A self x y z pt N/A 1 1 1 None N/A N/A Scale the coordinates of the Point by multiplying by
        ``x`` and ``y`` after subtracting ``pt`` -- default is (0, 0) --
        and then adding ``pt`` back again (i.e. ``pt`` is the point of
        reference for the scaling).

        See Also
        ========

        translate

        Examples
        ========

        >>> from sympy import Point3D
        >>> t = Point3D(1, 1, 1)
        >>> t.scale(2)
        Point3D(2, 1, 1)
        >>> t.scale(2, 2)
        Point3D(2, 2, 1)

         N/A pt N/A N/A pt N/A Point3D pt N/A N/A N/A N/A N/A N/A N/A self translate N/A N/A pt args scale x y z translate N/A pt args N/A N/A Point3D N/A N/A self x x N/A N/A self y y N/A N/A self z z N/A translate N/A N/A self x y z N/A 0 0 0 N/A N/A Shift the Point by adding x and y to the coordinates of the Point.

        See Also
        ========

        rotate, scale

        Examples
        ========

        >>> from sympy import Point3D
        >>> t = Point3D(0, 1, 1)
        >>> t.translate(2)
        Point3D(2, 1, 1)
        >>> t.translate(2, 2)
        Point3D(2, 3, 1)
        >>> t + Point3D(2, 2, 2)
        Point3D(2, 3, 3)

         N/A N/A Point3D N/A N/A self x x N/A N/A self y y N/A N/A self z z N/A transform N/A N/A self matrix N/A N/A N/A Return the point after applying the transformation described
        by the 4x4 Matrix, ``matrix``.

        See Also
        ========
        geometry.entity.rotate
        geometry.entity.scale
        geometry.entity.translate
         N/A N/A N/A N/A col row N/A matrix shape N/A valid_matrix N/A N/A matrix is_square N/A col 4 N/A N/A N/A AttributeError N/A N/A valid_matrix False N/A N/A valid_matrix N/A N/A N/A ValueError N/A The argument to the transform function must be  a 4x4 matrix sympy.matrices.expressions Transpose N/A N/A x y z N/A self args N/A m N/A Transpose matrix N/A N/A Point3D N/A N/A N/A N/A N/A N/A Matrix 1 4 N/A x y z 1 m tolist N/A 0 N/A 3 N/A N/A