Module ImportFrom alias alias ImportFrom alias alias alias alias alias alias ImportFrom alias alias alias alias ImportFrom alias ImportFrom alias alias ImportFrom alias ImportFrom alias ImportFrom alias ClassDef bases NameLoad body Expr Str Assign NameStore NameLoad Assign NameStore ListLoad FunctionDef arguments args NameParam NameParam defaults vararg kwarg body Assign NameStore Call NameLoad NameLoad If UnaryOpNot NameLoad body If AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr Assign NameStore AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore BinOpMult ListLoad AttributeLoad NameLoad attr Call NameLoad NameLoad orelse Assign NameStore Call NameLoad IfExp Call NameLoad NameLoad NameLoad ListLoad NameLoad Assign TupleStore NameStore NameStore TupleLoad ListLoad ListLoad If Call NameLoad SubscriptLoad NameLoad Index Num body For NameStore NameLoad body Assign TupleStore NameStore NameStore Call NameLoad Call NameLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr NameLoad orelse Assign NameStore Call NameLoad Call NameLoad NameLoad NameLoad Assign NameStore BinOpMult ListLoad AttributeLoad NameLoad attr Call NameLoad NameLoad If UnaryOpNot Call NameLoad GeneratorExp Call NameLoad NameLoad NameLoad comprehension NameStore NameLoad body Raise Call NameLoad BinOpMod Str NameLoad If CompareNotEq Call NameLoad Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad body Raise Call NameLoad BinOpMod Str NameLoad If AttributeLoad NameLoad attr body Assign NameStore Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad Call NameLoad NameLoad NameLoad For TupleStore NameStore NameStore Call AttributeLoad NameLoad attr body If CompareIn NameLoad Call AttributeLoad NameLoad attr body If CompareNotEq NameLoad SubscriptLoad NameLoad Index NameLoad body Raise Call NameLoad Str orelse Assign SubscriptStore NameLoad Index NameLoad NameLoad If CompareEq Call NameLoad Call AttributeLoad NameLoad attr Call NameLoad Call AttributeLoad NameLoad attr body Return NameLoad orelse Assign NameStore Call NameLoad Call AttributeLoad NameLoad attr Assign NameStore ListComp SubscriptLoad NameLoad Index NameLoad comprehension NameStore NameLoad If CompareIs NameLoad AttributeLoad NameLoad attr body Return AttributeLoad NameLoad attr If Call NameLoad GeneratorExp CompareIn NameLoad AttributeLoad NameLoad attr comprehension NameStore NameLoad comprehension NameStore NameLoad body Raise Call NameLoad BinOpMod Str NameLoad If NameLoad body If Call NameLoad GeneratorExp CompareNotEq NameLoad SubscriptLoad NameLoad Index Num comprehension NameStore NameLoad body Raise NameLoad If CompareIs SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr body Assign NameStore DictComp NameLoad BinOpDiv Num Call NameLoad comprehension NameStore NameLoad Assign NameStore DictComp BinOpDiv Num NameLoad BinOpDiv Num NameLoad comprehension TupleStore NameStore NameStore Call AttributeLoad NameLoad attr orelse If CompareIsNot SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr body Assign NameStore Call NameLoad GeneratorExp TupleLoad NameLoad BinOpAdd Call NameLoad SubscriptLoad NameLoad Index Num comprehension NameStore NameLoad Assign NameStore Call NameLoad GeneratorExp TupleLoad BinOpSub NameLoad SubscriptLoad NameLoad Index Num BinOpSub NameLoad SubscriptLoad NameLoad Index Num comprehension TupleStore NameStore NameStore Call AttributeLoad NameLoad attr orelse Assign NameStore TupleLoad Assign NameStore TupleLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad If AttributeLoad NameLoad attr body ImportFrom alias Assign NameStore Call NameLoad NameLoad If NameLoad body Assign NameStore Call NameLoad ListComp SubscriptLoad NameLoad Index Num comprehension NameStore Call AttributeLoad NameLoad attr orelse Assign NameStore Call NameLoad NameLoad If CompareGt Call NameLoad NameLoad Num body Assign NameStore Call AttributeLoad NameLoad attr If AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad ListComp AttributeLoad NameLoad attr comprehension TupleStore NameStore NameStore NameLoad orelse If NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore SubscriptLoad Call AttributeLoad NameLoad attr keyword NameLoad NameLoad Index Num Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareEq Call NameLoad NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num Assign NameStore Call NameLoad Call AttributeLoad NameLoad attr SubscriptLoad Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Index Num For TupleStore NameStore NameStore Call NameLoad NameLoad body If AttributeLoad NameLoad attr body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If BoolOpAnd CompareIn NameLoad TupleLoad NameLoad UnaryOpUSub NameLoad AttributeLoad NameLoad attr UnaryOpNot Call AttributeLoad NameLoad attr NameLoad body Assign SubscriptStore NameLoad Index NameLoad BinOpPow NameLoad NameLoad orelse If BoolOpAnd AttributeLoad NameLoad attr UnaryOpNot Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If BoolOpAnd CompareIn NameLoad TupleLoad NameLoad UnaryOpUSub NameLoad AttributeLoad NameLoad attr body Assign SubscriptStore NameLoad Index NameLoad BinOpPow NameLoad BinOpMult NameLoad NameLoad orelse If BoolOpAnd AttributeLoad NameLoad attr CompareIs SubscriptLoad AttributeLoad NameLoad attr Index Num AttributeLoad NameLoad attr body Assign NameStore UnaryOpUSub NameLoad If BoolOpAnd AttributeLoad NameLoad attr UnaryOpNot Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If BoolOpAnd CompareIn NameLoad TupleLoad NameLoad UnaryOpUSub NameLoad AttributeLoad NameLoad attr body Assign SubscriptStore NameLoad Index NameLoad BinOpPow NameLoad BinOpMult NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareIs NameLoad AttributeLoad NameLoad attr body Return NameLoad If AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr If UnaryOpNot Call AttributeLoad NameLoad attr NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore Call NameLoad Call NameLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr keyword NameLoad Assign NameStore ListComp SubscriptLoad NameLoad Index NameLoad comprehension NameStore NameLoad Assign NameStore BinOpAdd TupleLoad NameLoad Call NameLoad Call NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Return NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list NameLoad FunctionDef arguments args NameParam defaults body If SubscriptLoad AttributeLoad NameLoad attr Slice Num body Return Call NameLoad GeneratorExp SubscriptLoad NameLoad Index Num comprehension NameStore SubscriptLoad AttributeLoad NameLoad attr Slice Num orelse Return TupleLoad decorator_list NameLoad FunctionDef arguments args NameParam defaults body If SubscriptLoad AttributeLoad NameLoad attr Slice Num body Return Call NameLoad GeneratorExp SubscriptLoad NameLoad Index Num comprehension NameStore SubscriptLoad AttributeLoad NameLoad attr Slice Num orelse Return TupleLoad decorator_list NameLoad FunctionDef arguments args NameParam defaults body Return BinOpBitOr AttributeLoad AttributeLoad NameLoad attr attr Call NameLoad AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body If BoolOpAnd AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return Call AttributeLoad NameLoad attr BinOpPow AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num If CompareEq NameLoad Call NameLoad Num body Return NameLoad Return decorator_list FunctionDef arguments args NameParam NameParam defaults body If CompareIs NameLoad NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Slice Num orelse If BoolOpAnd UnaryOpNot Call NameLoad GeneratorExp CompareEq SubscriptLoad NameLoad Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num comprehension NameStore NameLoad UnaryOpNot Call NameLoad GeneratorExp CompareEq NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num comprehension NameStore AttributeLoad NameLoad attr body Raise Call NameLoad BinOpMod Str NameLoad If BoolOpAnd NameLoad CompareNotEq SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad Str Assign NameStore Call NameLoad NameLoad For TupleStore NameStore NameStore Call AttributeLoad Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num attr body If CompareNotIn NameLoad Call AttributeLoad NameLoad attr body Assign SubscriptStore NameLoad Index NameLoad NameLoad Assign NameStore Call NameLoad Call AttributeLoad NameLoad attr keyword Lambda arguments args NameParam defaults Call NameLoad SubscriptLoad NameLoad Index Num Return TupleLoad AttributeLoad NameLoad attr Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str ImportFrom alias If CompareIs NameLoad AttributeLoad NameLoad attr body Return NameLoad If CompareIs NameLoad AttributeLoad NameLoad attr body Return NameLoad If AttributeLoad NameLoad attr body If BoolOpAnd UnaryOpNot Call NameLoad GeneratorExp CompareEq NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num comprehension NameStore AttributeLoad NameLoad attr UnaryOpNot Call NameLoad GeneratorExp CompareEq NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num comprehension NameStore AttributeLoad NameLoad attr body Raise Call NameLoad BinOpMod Str NameLoad orelse If Call NameLoad GeneratorExp UnaryOpNot NameLoad comprehension NameStore ListLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Assign NameStore BinOpAdd AttributeLoad NameLoad attr AttributeLoad NameLoad attr If NameLoad body Assign NameStore SubscriptLoad NameLoad Index Num orelse Assign NameStore AttributeLoad NameLoad attr orelse Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return Call NameLoad ListComp CompareIn NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num comprehension NameStore SubscriptLoad AttributeLoad NameLoad attr Slice Num If AttributeLoad AttributeLoad NameLoad attr attr body Return Call NameLoad ListComp Call AttributeLoad NameLoad attr NameLoad comprehension NameStore AttributeLoad AttributeLoad NameLoad attr attr If AttributeLoad AttributeLoad NameLoad attr attr body Return Call NameLoad ListComp Call AttributeLoad Call AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num attr NameLoad comprehension NameStore AttributeLoad AttributeLoad NameLoad attr attr If BoolOpAnd AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Assign NameStore Call NameLoad ListComp NameLoad comprehension NameStore AttributeLoad NameLoad attr CompareIn NameLoad AttributeLoad NameLoad attr orelse If AttributeLoad NameLoad attr body Assign NameStore AttributeLoad NameLoad attr orelse Assign NameStore AttributeLoad NameLoad attr If UnaryOpNot NameLoad body Return NameLoad If BoolOpAnd AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad AttributeLoad NameLoad attr attr attr AttributeLoad AttributeLoad AttributeLoad NameLoad attr attr attr body If BoolOpAnd AttributeLoad AttributeLoad NameLoad attr attr CompareEq AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr body Return UnaryOpNot AttributeLoad BinOpSub AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr attr If AttributeLoad AttributeLoad NameLoad attr attr body For NameStore AttributeLoad AttributeLoad NameLoad attr attr body If BoolOpAnd AttributeLoad NameLoad attr CompareEq AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad BinOpDiv AttributeLoad NameLoad attr NameLoad attr body Assign NameStore AttributeLoad BinOpSub AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr attr If UnaryOpNot CompareIs NameLoad NameLoad body Return UnaryOpNot NameLoad Assign NameStore NameLoad Assign NameStore BinOpDiv AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad keyword NameLoad keyword Str For NameStore NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad ImportFrom alias If UnaryOpNot Call NameLoad NameLoad NameLoad body Assign NameStore CompareNotEq NameLoad Num orelse Assign NameStore NameLoad If CompareIs NameLoad NameLoad body Assign NameStore NameLoad orelse If CompareNotEq NameLoad NameLoad body Return Return NameLoad If BoolOpAnd AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad AttributeLoad NameLoad attr attr attr AttributeLoad AttributeLoad AttributeLoad NameLoad attr attr attr body If BoolOpAnd AttributeLoad NameLoad attr CompareEq AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr body Return UnaryOpNot AttributeLoad BinOpSub AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr attr If AttributeLoad NameLoad attr body For NameStore AttributeLoad NameLoad attr body If BoolOpAnd AttributeLoad NameLoad attr CompareEq AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad BinOpDiv NameLoad NameLoad attr body Assign NameStore AttributeLoad BinOpSub AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr attr If UnaryOpNot CompareIs NameLoad NameLoad body Return UnaryOpNot NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num Return Call AttributeLoad NameLoad attr NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareIs NameLoad NameLoad body Raise Call NameLoad Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body If CompareIn NameLoad AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr If AttributeLoad NameLoad attr body Assign SubscriptStore NameLoad Index NameLoad NameLoad orelse Assign NameStore AttributeLoad NameLoad attr If BoolOpOr CompareEq Call NameLoad NameLoad Num CompareIn NameLoad NameLoad body If CompareIn NameLoad NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad orelse Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Index NameLoad If CompareNotEq NameLoad SubscriptLoad AttributeLoad NameLoad attr Index NameLoad body ImportFrom alias Assign NameStore Call NameLoad Assign NameStore Call NameLoad BinOpSub NameLoad Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad If Call NameLoad NameLoad NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore BinOpSub Call NameLoad NameLoad Call NameLoad NameLoad Assign NameStore ListLoad Call NameLoad Call NameLoad TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign SubscriptStore NameLoad Index NameLoad NameLoad Assign SubscriptStore NameLoad Index NameLoad NameLoad orelse If CompareNotIn NameLoad NameLoad body Delete SubscriptDel NameLoad Index NameLoad SubscriptDel NameLoad Index NameLoad If BoolOpAnd UnaryOpNot NameLoad CompareEq NameLoad SubscriptLoad AttributeLoad NameLoad attr Index NameLoad body Expr Call AttributeLoad NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr BinOpMult ListLoad AttributeLoad NameLoad attr Call NameLoad NameLoad orelse Return Return Call NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr If CompareIsNot NameLoad NameLoad body Return Call AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Return BoolOpOr Call AttributeLoad NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr If CompareIsNot NameLoad NameLoad body Return Call AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad Call NameLoad Num attr decorator_list decorator_list Assign NameStore NameLoad
N/A __future__ print_function division sympy.core S sympify Expr Rational Symbol Dummy sympy.core Add Mul expand_power_base expand_log sympy.core.cache cacheit sympy.core.compatibility default_sort_key is_sequence sympy.core.containers Tuple sympy.utilities.iterables uniq sympy.sets.sets Complement Order N/A Expr N/A N/A  Represents the limiting behavior of some function

    The order of a function characterizes the function based on the limiting
    behavior of the function as it goes to some limit. Only taking the limit
    point to be a number is currently supported. This is expressed in
    big O notation [1]_.

    The formal definition for the order of a function `g(x)` about a point `a`
    is such that `g(x) = O(f(x))` as `x \rightarrow a` if and only if for any
    `\delta > 0` there exists a `M > 0` such that `|g(x)| \leq M|f(x)|` for
    `|x-a| < \delta`.  This is equivalent to `\lim_{x \rightarrow a}
    \sup |g(x)/f(x)| < \infty`.

    Let's illustrate it on the following example by taking the expansion of
    `\sin(x)` about 0:

    .. math ::
        \sin(x) = x - x^3/3! + O(x^5)

    where in this case `O(x^5) = x^5/5! - x^7/7! + \cdots`. By the definition
    of `O`, for any `\delta > 0` there is an `M` such that:

    .. math ::
        |x^5/5! - x^7/7! + ....| <= M|x^5| \text{ for } |x| < \delta

    or by the alternate definition:

    .. math ::
        \lim_{x \rightarrow 0} | (x^5/5! - x^7/7! + ....) / x^5| < \infty

    which surely is true, because

    .. math ::
        \lim_{x \rightarrow 0} | (x^5/5! - x^7/7! + ....) / x^5| = 1/5!


    As it is usually used, the order of a function can be intuitively thought
    of representing all terms of powers greater than the one specified. For
    example, `O(x^3)` corresponds to any terms proportional to `x^3,
    x^4,\ldots` and any higher power. For a polynomial, this leaves terms
    proportional to `x^2`, `x` and constants.

    Examples
    ========

    >>> from sympy import O, oo, cos, pi
    >>> from sympy.abc import x, y

    >>> O(x + x**2)
    O(x)
    >>> O(x + x**2, (x, 0))
    O(x)
    >>> O(x + x**2, (x, oo))
    O(x**2, (x, oo))

    >>> O(1 + x*y)
    O(1, x, y)
    >>> O(1 + x*y, (x, 0), (y, 0))
    O(1, x, y)
    >>> O(1 + x*y, (x, oo), (y, oo))
    O(x*y, (x, oo), (y, oo))

    >>> O(1) in O(1, x)
    True
    >>> O(1, x) in O(1)
    False
    >>> O(x) in O(1, x)
    True
    >>> O(x**2) in O(x)
    True

    >>> O(x)*x
    O(x**2)
    >>> O(x) - O(x)
    O(x)
    >>> O(cos(x))
    O(1)
    >>> O(cos(x), (x, pi/2))
    O(x - pi/2, (x, pi/2))

    References
    ==========

    .. [1] `Big O notation <http://en.wikipedia.org/wiki/Big_O_notation>`_

    Notes
    =====

    In ``O(f(x), x)`` the expression ``f(x)`` is assumed to have a leading
    term.  ``O(f(x), x)`` is automatically transformed to
    ``O(f(x).as_leading_term(x),x)``.

        ``O(expr*f(x), x)`` is ``O(f(x), x)``

        ``O(expr, x)`` is ``O(1)``

        ``O(0, x)`` is 0.

    Multivariate O is also supported:

        ``O(f(x, y), x, y)`` is transformed to
        ``O(f(x, y).as_leading_term(x,y).as_leading_term(y), x, y)``

    In the multivariate case, it is assumed the limits w.r.t. the various
    symbols commute.

    If no symbols are passed then all symbols in the expression are used
    and the limit point is assumed to be zero.

     N/A is_Order True N/A __slots__ N/A __new__ N/A N/A cls expr N/A args kwargs N/A N/A expr N/A sympify expr N/A N/A args N/A N/A N/A expr is_Order N/A N/A variables N/A expr variables N/A point N/A expr point N/A N/A variables N/A list N/A expr free_symbols N/A point N/A N/A N/A S Zero N/A len variables N/A N/A args N/A list N/A N/A is_sequence args args N/A args N/A N/A variables point N/A N/A N/A N/A N/A is_sequence N/A args N/A 0 N/A N/A a args N/A N/A N/A v p N/A list N/A map sympify a N/A N/A N/A variables append v N/A N/A N/A point append p N/A N/A variables N/A list N/A map sympify args N/A point N/A N/A N/A S Zero N/A len variables N/A N/A N/A all N/A N/A isinstance v Symbol N/A v variables N/A N/A N/A TypeError N/A Variables are not symbols, got %s variables N/A N/A N/A len N/A list N/A uniq variables N/A len variables N/A N/A N/A ValueError N/A Variables are supposed to be unique symbols, got %s variables N/A N/A expr is_Order N/A N/A expr_vp N/A dict N/A N/A expr args N/A 1 N/A new_vp N/A dict expr_vp N/A vp N/A dict N/A zip variables point N/A N/A v p N/A N/A vp items N/A N/A N/A v N/A N/A new_vp keys N/A N/A N/A p N/A new_vp N/A v N/A N/A N/A NotImplementedError Mixing Order at different points is not supported. N/A N/A N/A new_vp N/A v p N/A N/A N/A set N/A N/A expr_vp keys N/A set N/A N/A new_vp keys N/A N/A expr N/A N/A variables N/A list N/A N/A new_vp keys N/A point N/A N/A new_vp N/A v N/A v variables N/A N/A expr N/A S NaN N/A N/A N/A S NaN N/A N/A any N/A N/A x N/A p free_symbols N/A x variables N/A p point N/A N/A N/A ValueError N/A Got %s as a point. point N/A variables N/A N/A N/A any N/A N/A p N/A point N/A 0 N/A p point N/A N/A NotImplementedError N/A N/A N/A point N/A 0 N/A S Infinity N/A N/A s N/A k N/A 1 N/A Dummy N/A k variables N/A rs N/A N/A 1 v N/A 1 k N/A N/A k v N/A N/A s items N/A N/A N/A N/A point N/A 0 N/A S Zero N/A N/A s N/A dict N/A N/A k N/A N/A Dummy N/A point N/A 0 N/A k variables N/A rs N/A dict N/A N/A N/A v N/A point N/A 0 N/A k N/A point N/A 0 N/A N/A k v N/A N/A s items N/A N/A s N/A N/A rs N/A N/A expr N/A N/A expr subs s N/A N/A expr is_Add N/A sympy expand_multinomial N/A expr N/A expand_multinomial expr N/A s N/A N/A args N/A tuple N/A N/A r N/A 0 N/A r N/A N/A rs items N/A N/A args N/A tuple variables N/A N/A N/A len variables 1 N/A N/A expr N/A N/A expr expand N/A N/A expr is_Add N/A N/A lst N/A N/A expr extract_leading_order args N/A expr N/A Add N/A N/A f expr N/A N/A e f lst N/A N/A expr N/A N/A expr N/A N/A expr as_leading_term args N/A expr N/A N/A N/A expr as_independent as_Add False args N/A 1 N/A expr N/A expand_power_base expr N/A expr N/A expand_log expr N/A N/A N/A len args 1 N/A N/A x N/A args N/A 0 N/A margs N/A list N/A N/A Mul make_args N/A N/A N/A expr as_independent x as_Add False N/A 1 N/A N/A i t N/A enumerate margs N/A N/A N/A t is_Pow N/A N/A N/A b q N/A t args N/A N/A N/A b N/A x N/A x N/A q is_real N/A N/A N/A q has x N/A N/A N/A margs N/A i N/A x q N/A N/A N/A N/A b is_Pow N/A N/A N/A N/A b exp has x N/A N/A N/A b r N/A b args N/A N/A N/A b N/A x N/A x N/A r is_real N/A N/A N/A margs N/A i N/A x N/A r q N/A N/A N/A N/A b is_Mul N/A N/A N/A b args N/A 0 N/A S NegativeOne N/A N/A b N/A b N/A N/A N/A b is_Pow N/A N/A N/A N/A b exp has x N/A N/A N/A b r N/A b args N/A N/A N/A b N/A x N/A x N/A r is_real N/A N/A N/A margs N/A i N/A x N/A r q N/A expr N/A Mul margs N/A expr N/A N/A expr subs rs N/A N/A expr N/A S Zero N/A N/A expr N/A N/A expr is_Order N/A N/A expr N/A expr expr N/A N/A N/A N/A expr has variables N/A N/A expr N/A S One N/A vp N/A dict N/A zip variables point N/A N/A N/A variables sort key default_sort_key N/A point N/A N/A vp N/A v N/A v variables N/A args N/A N/A expr N/A Tuple N/A zip variables point N/A obj N/A N/A Expr __new__ cls args N/A obj N/A cacheit _eval_nseries N/A N/A self x n logx N/A N/A N/A self N/A expr N/A N/A self N/A N/A N/A N/A N/A self args N/A 0 N/A property variables N/A N/A self N/A N/A N/A N/A N/A self args N/A 1 N/A N/A N/A tuple N/A N/A x N/A 0 N/A x N/A N/A self args N/A 1 N/A N/A N/A N/A property point N/A N/A self N/A N/A N/A N/A N/A self args N/A 1 N/A N/A N/A tuple N/A N/A x N/A 1 N/A x N/A N/A self args N/A 1 N/A N/A N/A N/A property free_symbols N/A N/A self N/A N/A N/A N/A N/A N/A self expr free_symbols N/A set N/A self variables N/A property _eval_power N/A N/A b e N/A N/A N/A N/A N/A e is_Number N/A e is_nonnegative N/A N/A N/A N/A b func N/A N/A b expr e N/A N/A b args N/A 1 N/A N/A e N/A O 1 N/A N/A b N/A N/A as_expr_variables N/A N/A self order_symbols N/A N/A N/A N/A order_symbols None N/A N/A order_symbols N/A N/A self args N/A 1 N/A N/A N/A N/A N/A all N/A N/A N/A o N/A 1 N/A N/A order_symbols N/A 0 N/A 1 N/A o order_symbols N/A N/A all N/A N/A p N/A N/A self point N/A 0 N/A p N/A self point N/A N/A N/A NotImplementedError N/A Order at points other than 0 or oo not supported, got %s as a point. point N/A N/A order_symbols N/A N/A N/A order_symbols N/A 0 N/A 1 N/A N/A self point N/A 0 N/A N/A N/A NotImplementedError Multiplying Order at different points is not supported. N/A order_symbols N/A dict order_symbols N/A N/A s p N/A N/A N/A dict N/A N/A self args N/A 1 items N/A N/A N/A s N/A N/A order_symbols keys N/A N/A N/A order_symbols N/A s p N/A order_symbols N/A sorted N/A N/A order_symbols items key N/A N/A N/A x N/A N/A default_sort_key N/A x N/A 0 N/A N/A N/A self expr N/A tuple order_symbols N/A removeO N/A N/A self N/A N/A N/A N/A S Zero N/A getO N/A N/A self N/A N/A N/A self N/A contains N/A N/A self expr N/A N/A N/A 
        Return True if expr belongs to Order(self.expr, \*self.variables).
        Return False if self belongs to expr.
        Return None if the inclusion relation cannot be determined
        (e.g. when self and expr have different symbols).
         sympy powsimp N/A N/A expr N/A S Zero N/A N/A True N/A N/A expr N/A S NaN N/A N/A False N/A N/A expr is_Order N/A N/A N/A N/A N/A all N/A N/A p N/A N/A expr point N/A 0 N/A p N/A expr point N/A N/A all N/A N/A p N/A N/A self point N/A 0 N/A p N/A self point N/A N/A N/A NotImplementedError N/A Order at points other than 0 or oo not supported, got %s as a point. point N/A N/A N/A any N/A N/A p N/A p N/A N/A expr point N/A self point N/A N/A point N/A N/A self point N/A expr point N/A point N/A N/A point N/A point N/A 0 N/A N/A point N/A S Zero N/A N/A point N/A N/A self point N/A 0 N/A N/A N/A expr expr N/A self expr N/A N/A N/A all N/A N/A x N/A N/A self args N/A 1 N/A x N/A N/A expr args N/A 1 N/A N/A N/A expr expr is_Add N/A N/A N/A all N/A N/A N/A self contains x N/A x N/A N/A expr expr args N/A N/A N/A self expr is_Add N/A N/A N/A any N/A N/A N/A N/A N/A self func x N/A N/A self args N/A 1 contains expr N/A x N/A N/A self expr args N/A N/A N/A self variables N/A expr variables N/A N/A common_symbols N/A tuple N/A s N/A s N/A self variables N/A s N/A expr variables N/A N/A N/A self variables N/A N/A common_symbols N/A self variables N/A N/A common_symbols N/A expr variables N/A N/A common_symbols N/A N/A None N/A N/A N/A N/A self expr is_Pow N/A N/A N/A self expr base is_Symbol N/A N/A N/A self expr exp is_positive N/A N/A N/A N/A N/A expr expr is_Pow N/A N/A N/A self expr base N/A N/A expr expr base N/A N/A N/A N/A N/A N/A N/A self expr exp N/A N/A expr expr exp is_positive N/A N/A N/A expr expr is_Mul N/A N/A arg N/A N/A expr expr args N/A N/A N/A N/A arg is_Pow N/A N/A N/A self expr base N/A arg base N/A N/A N/A expr expr arg is_number N/A N/A r N/A N/A N/A N/A self expr exp N/A arg exp is_positive N/A N/A N/A r None N/A N/A N/A r N/A r None N/A ratio N/A N/A self expr N/A expr expr N/A ratio N/A powsimp ratio deep True combine exp N/A s common_symbols N/A N/A l N/A N/A ratio limit s point sympy.series.limits Limit N/A N/A N/A isinstance l Limit N/A N/A l N/A l 0 N/A N/A l None N/A N/A r None N/A N/A r l N/A N/A N/A r l N/A N/A N/A r N/A N/A N/A N/A self expr is_Pow N/A N/A N/A self expr base is_Symbol N/A N/A N/A self expr exp is_positive N/A N/A N/A N/A expr is_Pow N/A N/A N/A self expr base N/A expr base N/A N/A N/A N/A N/A N/A N/A self expr exp N/A expr exp is_positive N/A N/A expr is_Mul N/A N/A arg N/A expr args N/A N/A N/A N/A arg is_Pow N/A N/A N/A self expr base N/A arg base N/A N/A expr arg is_number N/A N/A r N/A N/A N/A N/A self expr exp N/A arg exp is_positive N/A N/A N/A r None N/A N/A N/A r N/A obj N/A N/A self func expr N/A N/A self args N/A 1 N/A N/A N/A self contains obj N/A cacheit __contains__ N/A N/A self other N/A N/A N/A result N/A N/A self contains other N/A N/A result None N/A N/A N/A TypeError contains did not evaluate to a bool N/A result N/A _eval_subs N/A N/A self old new N/A N/A N/A N/A old N/A self variables N/A N/A newexpr N/A N/A N/A self expr subs old new N/A i N/A N/A N/A self variables index old N/A newvars N/A list N/A self variables N/A newpt N/A list N/A self point N/A N/A new is_Symbol N/A N/A N/A newvars N/A i new N/A N/A syms N/A new free_symbols N/A N/A N/A N/A len syms 1 N/A old syms N/A N/A N/A old syms N/A N/A var N/A N/A self variables N/A i N/A N/A var N/A N/A syms pop N/A point N/A N/A new subs var N/A N/A self point N/A i N/A N/A point N/A N/A self point N/A i N/A sympy.solvers.solveset solveset N/A d N/A Dummy N/A sol N/A solveset N/A old N/A N/A new subs var d d N/A N/A isinstance sol Complement N/A N/A e1 N/A N/A sol args N/A 0 N/A e2 N/A N/A sol args N/A 1 N/A sol N/A N/A set e1 N/A set e2 N/A res N/A N/A dict N/A zip N/A d sol N/A point N/A N/A N/A N/A d subs N/A res N/A 0 limit old N/A N/A self point N/A i N/A N/A newvars N/A i var N/A N/A newpt N/A i point N/A N/A N/A old syms N/A N/A N/A newvars N/A i N/A newpt N/A i N/A N/A N/A syms N/A new N/A N/A self point N/A i N/A N/A N/A N/A newvars extend syms N/A N/A N/A newpt extend N/A N/A N/A S Zero N/A len syms N/A N/A N/A N/A Order newexpr N/A zip newvars newpt N/A _eval_conjugate N/A N/A self N/A N/A N/A expr N/A N/A N/A self expr _eval_conjugate N/A N/A expr None N/A N/A N/A N/A self func expr N/A N/A self args N/A 1 N/A _eval_derivative N/A N/A self x N/A N/A N/A N/A N/A N/A self func N/A N/A N/A self expr diff x N/A N/A self args N/A 1 self N/A _eval_transpose N/A N/A self N/A N/A N/A expr N/A N/A N/A self expr _eval_transpose N/A N/A expr None N/A N/A N/A N/A self func expr N/A N/A self args N/A 1 N/A _sage_ N/A N/A self N/A N/A N/A N/A N/A N/A Rational 0 _sage_ N/A N/A N/A O Order