Module ImportFrom alias alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ClassDef bases NameLoad body Pass decorator_list ClassDef bases NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore AttributeLoad NameLoad attr FunctionDef arguments args NameParam defaults body Assign AttributeStore NameLoad attr Dict Expr Call AttributeLoad NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr NameLoad Expr Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body TryExcept body Expr Call NameLoad NameLoad NameLoad Call NameLoad NameLoad NameLoad handlers ExceptHandler type NameLoad body Pass decorator_list Assign NameStore NameLoad Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Print TupleLoad Str NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Raise Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If Call NameLoad NameLoad Str body Return AttributeLoad NameLoad attr Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If Call NameLoad NameLoad Str body Return AttributeLoad NameLoad attr Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults kwarg body Return UnaryOpUSub Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults kwarg body Return BinOpAdd Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults kwarg body Return BinOpSub Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults kwarg body Return BinOpMult Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults kwarg body Return BinOpDiv Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad NameLoad body If NameLoad body If NameLoad body Return Call NameLoad GeneratorExp BinOpPow Call NameLoad NameLoad Num comprehension NameStore NameLoad AttributeLoad NameLoad attr Return Call NameLoad GeneratorExp Call NameLoad NameLoad comprehension NameStore NameLoad AttributeLoad NameLoad attr If NameLoad body Return Call NameLoad GeneratorExp BinOpPow NameLoad Num comprehension NameStore NameLoad AttributeLoad NameLoad attr Return Call NameLoad NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad NameLoad body If CompareIsNot NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad NameLoad If NameLoad body Assign NameStore AttributeLoad NameLoad attr Return Call NameLoad GeneratorExp BinOpMult NameLoad Call NameLoad NameLoad comprehension TupleStore NameStore NameStore NameLoad AttributeLoad NameLoad attr orelse Return Call NameLoad GeneratorExp BinOpMult NameLoad NameLoad comprehension TupleStore NameStore NameStore NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore AttributeLoad NameLoad attr For NameStore NameLoad body AugAssignMult NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num kwarg body Expr Str Print Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str If CompareIs NameLoad NameLoad body Assign NameStore BinOpMult Num AttributeLoad NameLoad attr TryExcept body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad If CompareLt Call NameLoad NameLoad NameLoad body Return AttributeLoad NameLoad attr If Call AttributeLoad NameLoad attr NameLoad body Assign NameStore Call NameLoad NameLoad BinOpMult NameLoad NameLoad If CompareLt Call NameLoad AttributeLoad NameLoad attr NameLoad body Return AttributeLoad NameLoad attr If CompareLt Call NameLoad AttributeLoad NameLoad attr NameLoad body Return Call AttributeLoad NameLoad attr Num AttributeLoad NameLoad attr handlers ExceptHandler type NameLoad body If Call NameLoad NameLoad AttributeLoad NameLoad attr body Return Call AttributeLoad NameLoad attr Lambda arguments args NameParam defaults Call AttributeLoad NameLoad attr NameLoad NameLoad If Call NameLoad NameLoad Str body Return ListComp Call AttributeLoad NameLoad attr NameLoad NameLoad comprehension NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad If BoolOpAnd CompareIs NameLoad NameLoad CompareIs NameLoad NameLoad body Assign NameStore NameStore Call AttributeLoad NameLoad attr Num BinOpAdd UnaryOpUSub AttributeLoad NameLoad attr Num If CompareIs NameLoad NameLoad body Assign NameStore NameLoad orelse If CompareIs NameLoad NameLoad body Assign NameStore NameLoad Assign NameStore Call NameLoad BinOpSub NameLoad NameLoad If CompareLtE NameLoad NameLoad body Return NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareLt NameLoad NameLoad body Assign NameStore BinOpDiv NameLoad NameLoad orelse Assign NameStore BinOpDiv NameLoad NameLoad Return CompareLtE NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults vararg body Expr Str If UnaryOpNot CompareLtE Call NameLoad NameLoad Num body Raise Call NameLoad BinOpMod Str Call NameLoad NameLoad If UnaryOpNot CompareGtE Call NameLoad NameLoad Num body Raise Call NameLoad BinOpMod Str Call NameLoad NameLoad Assign NameStore Num Assign NameStore Num If CompareEq Call NameLoad NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num orelse If CompareGtE Call NameLoad NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num Assign NameStore SubscriptLoad NameLoad Index Num If CompareEq Call NameLoad NameLoad Num body Assign NameStore SubscriptLoad NameLoad Index Num Assign TupleStore NameStore NameStore NameStore TupleLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Assert CompareNotEq BinOpAdd NameLoad NameLoad NameLoad Str If CompareGt NameLoad NameLoad body If CompareGt NameLoad Num body Return ListLoad Assign NameStore NameLoad orelse If CompareLt NameLoad Num body Return ListLoad Assign NameStore NameLoad Assign NameStore ListLoad Assign NameStore Num Assign NameStore NameLoad While Num body Assign NameStore BinOpAdd NameLoad BinOpMult NameLoad NameLoad AugAssignAdd NameStore Num If Call NameLoad NameLoad NameLoad body Expr Call AttributeLoad NameLoad attr NameLoad orelse Break Return NameLoad decorator_list FunctionDef arguments args NameParam defaults vararg kwarg body Expr Str If CompareEq Call NameLoad NameLoad Num body Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Num orelse If CompareEq Call NameLoad NameLoad Num body Assert Call NameLoad SubscriptLoad NameLoad Index Num Str Assign NameStore AttributeLoad SubscriptLoad NameLoad Index Num attr Assign NameStore AttributeLoad SubscriptLoad NameLoad Index Num attr Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Num orelse Raise Call NameLoad BinOpMod Str Call NameLoad NameLoad If CompareLt NameLoad Num body Raise Call NameLoad Str If BoolOpOr UnaryOpNot CompareIn Str NameLoad SubscriptLoad NameLoad Index Str body If CompareEq NameLoad Num body Return ListLoad Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpDiv BinOpSub NameLoad NameLoad Call AttributeLoad NameLoad attr BinOpSub NameLoad Num Assign NameStore ListComp BinOpAdd BinOpMult NameLoad NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad Assign SubscriptStore NameLoad Index Num NameLoad orelse Assign NameStore BinOpDiv BinOpSub NameLoad NameLoad Call AttributeLoad NameLoad attr NameLoad Assign NameStore ListComp BinOpAdd BinOpMult NameLoad NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults kwarg body Return TupleLoad Call AttributeLoad NameLoad attr NameLoad NameLoad Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults kwarg body Return TupleLoad Call AttributeLoad NameLoad attr NameLoad NameLoad Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call NameLoad BinOpAdd BinOpMult Num BinOpPow NameLoad Num BinOpMult Num NameLoad decorator_list Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad AttributeLoad NameLoad attr FunctionDef arguments args NameParam NameParam NameParam defaults Num body Assign NameStore AttributeLoad NameLoad attr TryFinally body Assign NameStore Num While Num body Assign AttributeStore NameLoad attr BinOpAdd BinOpAdd NameLoad NameLoad Num Assign NameStore AttributeLoad NameLoad attr Assign NameStore AttributeLoad NameLoad attr Assign NameStore Num For NameStore Call NameLoad body AugAssignAdd NameStore NameLoad If BoolOpAnd UnaryOpNot BinOpMod NameLoad NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareGt BinOpSub NameLoad NameLoad AttributeLoad NameLoad attr body Break AugAssignAdd NameStore Num Assign NameStore BinOpSub NameLoad NameLoad If CompareNotEq NameLoad NameLoad body Break If BoolOpOr CompareLt NameLoad NameLoad AttributeLoad NameLoad attr body Break AugAssignAdd NameStore Call NameLoad AttributeLoad NameLoad attr NameLoad Return NameLoad finalbody Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num body Assign NameStore AttributeLoad NameLoad attr TryFinally body Assign NameStore Num While Num body Assign AttributeStore NameLoad attr BinOpAdd BinOpAdd NameLoad NameLoad Num Assign NameStore AttributeLoad NameLoad attr Assign NameStore AttributeLoad NameLoad attr Assign NameStore NameLoad Assign NameStore Num For NameStore Call NameLoad body AugAssignMult NameStore NameLoad Assign NameStore BinOpSub NameLoad NameLoad If UnaryOpNot BinOpMod NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr BinOpSub NameLoad NameLoad If CompareGt UnaryOpUSub NameLoad AttributeLoad NameLoad attr body Break AugAssignAdd NameStore Num Assign NameStore BinOpSub NameLoad NameLoad If CompareNotEq NameLoad NameLoad body Break If BoolOpOr CompareLt NameLoad NameLoad AttributeLoad NameLoad attr body Break AugAssignAdd NameStore Call NameLoad AttributeLoad NameLoad attr NameLoad Return NameLoad finalbody Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Return BinOpPow Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore ListLoad Num FunctionDef arguments args defaults vararg kwarg body AugAssignAdd SubscriptStore NameLoad Index Num Num If CompareGt SubscriptLoad NameLoad Index Num NameLoad body Raise Call AttributeLoad NameLoad attr BinOpMod Str NameLoad Return Call NameLoad NameLoad NameLoad decorator_list Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Dict FunctionDef arguments args defaults vararg kwarg body If NameLoad body Assign NameStore TupleLoad NameLoad Call NameLoad Call AttributeLoad NameLoad attr orelse Assign NameStore NameLoad Assign NameStore AttributeLoad NameLoad attr If CompareIn NameLoad NameLoad body Assign TupleStore NameStore NameStore SubscriptLoad NameLoad Index NameLoad If CompareGtE NameLoad NameLoad body Return UnaryOpUAdd NameLoad Assign NameStore Call NameLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index NameLoad TupleLoad NameLoad NameLoad Return NameLoad decorator_list Assign AttributeStore NameLoad attr AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr AttributeLoad NameLoad attr Return NameLoad decorator_list decorator_list
N/A operator gt lt libmp.backend xrange functions.functions SpecialFunctions functions.rszeta RSCache calculus.quadrature QuadratureMethods calculus.calculus CalculusMethods calculus.optimization OptimizationMethods calculus.odes ODEMethods matrices.matrices MatrixMethods matrices.calculus MatrixCalculusMethods matrices.linalg LinearAlgebraMethods matrices.eigen Eigen identification IdentificationMethods visualization VisualizationMethods N/A libmp Context N/A object N/A N/A N/A StandardBaseContext N/A Context SpecialFunctions RSCache QuadratureMethods CalculusMethods MatrixMethods MatrixCalculusMethods LinearAlgebraMethods Eigen IdentificationMethods OptimizationMethods ODEMethods VisualizationMethods N/A N/A NoConvergence N/A libmp NoConvergence N/A ComplexResult N/A libmp ComplexResult __init__ N/A N/A ctx N/A N/A N/A N/A ctx _aliases N/A N/A N/A N/A SpecialFunctions __init__ ctx N/A N/A N/A RSCache __init__ ctx N/A N/A N/A QuadratureMethods __init__ ctx N/A N/A N/A CalculusMethods __init__ ctx N/A N/A N/A MatrixMethods __init__ ctx N/A _init_aliases N/A N/A ctx N/A N/A N/A N/A alias value N/A N/A N/A ctx _aliases items N/A N/A N/A N/A N/A setattr ctx alias N/A getattr ctx value N/A N/A N/A AttributeError N/A N/A N/A N/A _fixed_precision False N/A verbose False warn N/A N/A ctx msg N/A N/A N/A N/A Warning: msg N/A bad_domain N/A N/A ctx msg N/A N/A N/A N/A ValueError msg N/A _re N/A N/A ctx x N/A N/A N/A N/A hasattr x real N/A N/A N/A x real N/A x N/A _im N/A N/A ctx x N/A N/A N/A N/A hasattr x imag N/A N/A N/A x imag N/A N/A ctx zero N/A _as_points N/A N/A ctx x N/A N/A N/A x N/A fneg N/A N/A ctx x N/A kwargs N/A N/A N/A N/A N/A ctx convert x N/A fadd N/A N/A ctx x y N/A kwargs N/A N/A N/A N/A N/A ctx convert x N/A N/A ctx convert y N/A fsub N/A N/A ctx x y N/A kwargs N/A N/A N/A N/A N/A ctx convert x N/A N/A ctx convert y N/A fmul N/A N/A ctx x y N/A kwargs N/A N/A N/A N/A N/A ctx convert x N/A N/A ctx convert y N/A fdiv N/A N/A ctx x y N/A kwargs N/A N/A N/A N/A N/A ctx convert x N/A N/A ctx convert y N/A fsum N/A N/A ctx args absolute squared N/A False False N/A N/A absolute N/A N/A squared N/A N/A N/A sum N/A N/A N/A abs x 2 N/A x args N/A ctx zero N/A N/A sum N/A N/A abs x N/A x args N/A ctx zero N/A squared N/A N/A N/A sum N/A N/A x 2 N/A x args N/A ctx zero N/A N/A sum args N/A ctx zero N/A fdot N/A N/A ctx xs ys conjugate N/A None False N/A N/A N/A ys None N/A N/A xs N/A zip xs ys N/A conjugate N/A N/A cf N/A ctx conj N/A N/A sum N/A N/A x N/A cf y N/A N/A x y xs N/A ctx zero N/A N/A N/A sum N/A N/A x y N/A N/A x y xs N/A ctx zero N/A fprod N/A N/A ctx args N/A N/A N/A prod N/A ctx one N/A arg args N/A N/A prod arg N/A prod N/A nprint N/A N/A ctx x n N/A 6 kwargs N/A N/A 
        Equivalent to ``print(nstr(x, n))``.
         N/A N/A N/A ctx nstr x n kwargs N/A chop N/A N/A ctx x tol N/A None N/A N/A 
        Chops off small real or imaginary parts, or converts
        numbers close to zero to exact zeros. The input can be a
        single number or an iterable::

            >>> from mpmath import *
            >>> mp.dps = 15; mp.pretty = False
            >>> chop(5+1e-10j, tol=1e-9)
            mpf('5.0')
            >>> nprint(chop([1.0, 1e-20, 3+1e-18j, -4, 2]))
            [1.0, 0.0, 3.0, -4.0, 2.0]

        The tolerance defaults to ``100*eps``.
         N/A N/A tol None N/A N/A tol N/A 100 N/A ctx eps N/A N/A N/A x N/A N/A ctx convert x N/A absx N/A abs x N/A N/A N/A abs x tol N/A N/A N/A ctx zero N/A N/A N/A ctx _is_complex_type x N/A N/A part_tol N/A max tol N/A absx tol N/A N/A N/A abs N/A x imag part_tol N/A N/A N/A x real N/A N/A N/A abs N/A x real part_tol N/A N/A N/A N/A ctx mpc 0 N/A x imag N/A N/A N/A TypeError N/A N/A N/A isinstance x N/A ctx matrix N/A N/A N/A N/A x apply N/A N/A N/A a N/A N/A N/A ctx chop a tol N/A N/A hasattr x __iter__ N/A N/A N/A N/A N/A ctx chop a tol N/A a x N/A x N/A almosteq N/A N/A ctx s t rel_eps abs_eps N/A None None N/A N/A 
        Determine whether the difference between `s` and `t` is smaller
        than a given epsilon, either relatively or absolutely.

        Both a maximum relative difference and a maximum difference
        ('epsilons') may be specified. The absolute difference is
        defined as `|s-t|` and the relative difference is defined
        as `|s-t|/\max(|s|, |t|)`.

        If only one epsilon is given, both are set to the same value.
        If none is given, both epsilons are set to `2^{-p+m}` where
        `p` is the current working precision and `m` is a small
        integer. The default setting typically allows :func:`~mpmath.almosteq`
        to be used to check for mathematical equality
        in the presence of small rounding errors.

        **Examples**

            >>> from mpmath import *
            >>> mp.dps = 15
            >>> almosteq(3.141592653589793, 3.141592653589790)
            True
            >>> almosteq(3.141592653589793, 3.141592653589700)
            False
            >>> almosteq(3.141592653589793, 3.141592653589700, 1e-10)
            True
            >>> almosteq(1e-20, 2e-20)
            True
            >>> almosteq(1e-20, 2e-20, rel_eps=0, abs_eps=0)
            False

         N/A t N/A N/A ctx convert t N/A N/A N/A abs_eps None N/A rel_eps None N/A N/A rel_eps abs_eps N/A N/A ctx ldexp 1 N/A N/A N/A ctx prec 4 N/A N/A abs_eps None N/A N/A abs_eps rel_eps N/A N/A N/A rel_eps None N/A N/A rel_eps abs_eps N/A diff N/A abs N/A s t N/A N/A diff abs_eps N/A N/A True N/A abss N/A abs s N/A abst N/A abs t N/A N/A abss abst N/A N/A err N/A diff abst N/A N/A err N/A diff abss N/A N/A err rel_eps N/A arange N/A N/A ctx N/A args N/A N/A 
        This is a generalized version of Python's :func:`~mpmath.range` function
        that accepts fractional endpoints and step sizes and
        returns a list of ``mpf`` instances. Like :func:`~mpmath.range`,
        :func:`~mpmath.arange` can be called with 1, 2 or 3 arguments:

        ``arange(b)``
            `[0, 1, 2, \ldots, x]`
        ``arange(a, b)``
            `[a, a+1, a+2, \ldots, x]`
        ``arange(a, b, h)``
            `[a, a+h, a+h, \ldots, x]`

        where `b-1 \le x < b` (in the third case, `b-h \le x < b`).

        Like Python's :func:`~mpmath.range`, the endpoint is not included. To
        produce ranges where the endpoint is included, :func:`~mpmath.linspace`
        is more convenient.

        **Examples**

            >>> from mpmath import *
            >>> mp.dps = 15; mp.pretty = False
            >>> arange(4)
            [mpf('0.0'), mpf('1.0'), mpf('2.0'), mpf('3.0')]
            >>> arange(1, 2, 0.25)
            [mpf('1.0'), mpf('1.25'), mpf('1.5'), mpf('1.75')]
            >>> arange(1, -1, -0.75)
            [mpf('1.0'), mpf('0.25'), mpf('-0.5')]

         N/A N/A N/A N/A len args 3 N/A N/A N/A TypeError N/A arange expected at most 3 arguments, got %i N/A len args N/A N/A N/A N/A len args 1 N/A N/A N/A TypeError N/A arange expected at least 1 argument, got %i N/A len args N/A a 0 N/A dt 1 N/A N/A N/A len args 1 N/A N/A b N/A args N/A 0 N/A N/A N/A N/A len args 2 N/A N/A a N/A args N/A 0 N/A b N/A args N/A 1 N/A N/A N/A len args 3 N/A N/A dt N/A args N/A 2 N/A N/A a b dt N/A N/A N/A ctx mpf a N/A N/A ctx mpf b N/A N/A ctx mpf dt N/A N/A N/A a dt a dt is too small and would cause an infinite loop N/A N/A a b N/A N/A N/A dt 0 N/A N/A N/A N/A op gt N/A N/A N/A dt 0 N/A N/A N/A N/A op lt N/A result N/A N/A i 0 N/A t a N/A 1 N/A N/A t N/A a N/A dt i N/A i 1 N/A N/A op t b N/A N/A N/A N/A result append t N/A N/A N/A result N/A linspace N/A N/A ctx N/A args kwargs N/A N/A 
        ``linspace(a, b, n)`` returns a list of `n` evenly spaced
        samples from `a` to `b`. The syntax ``linspace(mpi(a,b), n)``
        is also valid.

        This function is often more convenient than :func:`~mpmath.arange`
        for partitioning an interval into subintervals, since
        the endpoint is included::

            >>> from mpmath import *
            >>> mp.dps = 15; mp.pretty = False
            >>> linspace(1, 4, 4)
            [mpf('1.0'), mpf('2.0'), mpf('3.0'), mpf('4.0')]

        You may also provide the keyword argument ``endpoint=False``::

            >>> linspace(1, 4, 4, endpoint=False)
            [mpf('1.0'), mpf('1.75'), mpf('2.5'), mpf('3.25')]

         N/A N/A N/A len args 3 N/A N/A a N/A N/A ctx mpf N/A args N/A 0 N/A b N/A N/A ctx mpf N/A args N/A 1 N/A n N/A int N/A args N/A 2 N/A N/A N/A N/A len args 2 N/A N/A N/A hasattr N/A args N/A 0 _mpi_ N/A a N/A N/A args N/A 0 a N/A b N/A N/A args N/A 0 b N/A n N/A int N/A args N/A 1 N/A N/A N/A TypeError N/A linspace expected 2 or 3 arguments, got %i N/A len args N/A N/A n 1 N/A N/A N/A ValueError n must be greater than 0 N/A N/A N/A N/A endpoint kwargs N/A kwargs N/A endpoint N/A N/A N/A n 1 N/A N/A N/A N/A N/A ctx mpf a N/A step N/A N/A b a N/A N/A ctx mpf N/A n 1 N/A y N/A N/A N/A i step a N/A i N/A xrange n N/A N/A y N/A -1 b N/A N/A step N/A N/A b a N/A N/A ctx mpf n N/A y N/A N/A N/A i step a N/A i N/A xrange n N/A y N/A cos_sin N/A N/A ctx z N/A kwargs N/A N/A N/A N/A N/A ctx cos z kwargs N/A N/A ctx sin z kwargs N/A cospi_sinpi N/A N/A ctx z N/A kwargs N/A N/A N/A N/A N/A ctx cospi z kwargs N/A N/A ctx sinpi z kwargs N/A _default_hyper_maxprec N/A N/A ctx p N/A N/A N/A N/A int N/A N/A 1000 N/A p 0.25 N/A 4 p N/A N/A _gcd N/A staticmethod N/A libmp gcd N/A list_primes N/A staticmethod N/A libmp list_primes N/A isprime N/A staticmethod N/A libmp isprime N/A bernfrac N/A staticmethod N/A libmp bernfrac N/A moebius N/A staticmethod N/A libmp moebius N/A _ifac N/A staticmethod N/A libmp ifac N/A _eulernum N/A staticmethod N/A libmp eulernum N/A _stirling1 N/A staticmethod N/A libmp stirling1 N/A _stirling2 N/A staticmethod N/A libmp stirling2 sum_accurately N/A N/A ctx terms check_step N/A 1 N/A N/A prec N/A ctx prec N/A N/A N/A extraprec 10 N/A 1 N/A N/A N/A ctx prec N/A N/A prec extraprec 5 N/A max_mag N/A ctx ninf N/A s N/A ctx zero N/A k 0 N/A term N/A terms N/A N/A s term N/A N/A N/A N/A k check_step term N/A N/A term_mag N/A N/A ctx mag term N/A max_mag N/A max max_mag term_mag N/A sum_mag N/A N/A ctx mag s N/A N/A N/A sum_mag term_mag N/A ctx prec N/A N/A N/A k 1 N/A cancellation N/A max_mag sum_mag N/A N/A cancellation cancellation N/A N/A N/A N/A N/A cancellation extraprec N/A ctx _fixed_precision N/A N/A N/A extraprec N/A min N/A ctx prec cancellation N/A s N/A N/A N/A ctx prec prec N/A mul_accurately N/A N/A ctx factors check_step N/A 1 N/A N/A prec N/A ctx prec N/A N/A N/A extraprec 10 N/A 1 N/A N/A N/A ctx prec N/A N/A prec extraprec 5 N/A max_mag N/A ctx ninf N/A one N/A ctx one N/A s one N/A k 0 N/A factor N/A factors N/A N/A s factor N/A term N/A factor one N/A N/A N/A k check_step N/A N/A term_mag N/A N/A ctx mag term N/A max_mag N/A max max_mag term_mag N/A sum_mag N/A N/A ctx mag N/A s one N/A N/A N/A term_mag N/A ctx prec N/A N/A N/A k 1 N/A cancellation N/A max_mag sum_mag N/A N/A cancellation cancellation N/A N/A N/A N/A N/A cancellation extraprec N/A ctx _fixed_precision N/A N/A N/A extraprec N/A min N/A ctx prec cancellation N/A s N/A N/A N/A ctx prec prec N/A power N/A N/A ctx x y N/A N/A N/A Converts `x` and `y` to mpmath numbers and evaluates
        `x^y = \exp(y \log(x))`::

            >>> from mpmath import *
            >>> mp.dps = 30; mp.pretty = True
            >>> power(2, 0.5)
            1.41421356237309504880168872421

        This shows the leading few digits of a large Mersenne prime
        (performing the exact calculation ``2**43112609-1`` and
        displaying the result in Python would be very slow)::

            >>> power(2, 43112609)-1
            3.16470269330255923143453723949e+12978188
         N/A N/A N/A N/A ctx convert x N/A N/A ctx convert y N/A _zeta_int N/A N/A ctx n N/A N/A N/A N/A N/A ctx zeta n N/A maxcalls N/A N/A ctx f N N/A N/A N/A 
        Return a wrapped copy of *f* that raises ``NoConvergence`` when *f*
        has been called more than *N* times::

            >>> from mpmath import *
            >>> mp.dps = 15
            >>> f = maxcalls(sin, 10)
            >>> print(sum(f(n) for n in range(10)))
            1.95520948210738
            >>> f(10) # doctest: +IGNORE_EXCEPTION_DETAIL
            Traceback (most recent call last):
              ...
            NoConvergence: maxcalls: function evaluated 10 times

         N/A counter N/A 0 f_maxcalls_wrapped N/A N/A N/A args kwargs N/A N/A N/A counter N/A 0 1 N/A N/A N/A counter N/A 0 N N/A N/A N/A N/A ctx NoConvergence N/A maxcalls: function evaluated %i times N N/A N/A f args kwargs N/A N/A f_maxcalls_wrapped N/A memoize N/A N/A ctx f N/A N/A N/A 
        Return a wrapped copy of *f* that caches computed values, i.e.
        a memoized copy of *f*. Values are only reused if the cached precision
        is equal to or higher than the working precision::

            >>> from mpmath import *
            >>> mp.dps = 15; mp.pretty = True
            >>> f = memoize(maxcalls(sin, 1))
            >>> f(2)
            0.909297426825682
            >>> f(2)
            0.909297426825682
            >>> mp.dps = 25
            >>> f(2) # doctest: +IGNORE_EXCEPTION_DETAIL
            Traceback (most recent call last):
              ...
            NoConvergence: maxcalls: function evaluated 1 times

         N/A f_cache N/A f_cached N/A N/A N/A args kwargs N/A N/A kwargs N/A N/A key N/A args N/A tuple N/A N/A kwargs items N/A N/A key args N/A prec N/A ctx prec N/A N/A key f_cache N/A N/A N/A cprec cvalue N/A f_cache N/A key N/A N/A cprec prec N/A N/A N/A cvalue N/A value N/A f args kwargs N/A N/A f_cache N/A key N/A prec value N/A value N/A N/A N/A f_cached __name__ N/A f __name__ N/A N/A f_cached __doc__ N/A f __doc__ N/A f_cached N/A N/A