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# mypy: allow-untyped-defs
import mpmath.libmp as mlib # type: ignore[import-untyped]
import sympy
from sympy import Expr
from sympy.core.decorators import _sympifyit
from sympy.core.expr import AtomicExpr
from sympy.core.numbers import Number
from sympy.core.parameters import global_parameters
from sympy.core.singleton import S, Singleton
class IntInfinity(Number, metaclass=Singleton):
r"""Positive integer infinite quantity.
Integer infinity is a value in an extended integers which
is greater than all other integers. We distinguish it from
sympy's existing notion of infinity in that it reports that
it is_integer.
Infinity is a singleton, and can be accessed by ``S.IntInfinity``,
or can be imported as ``int_oo``.
"""
# NB: We can't actually mark this as infinite, as integer and infinite are
# inconsistent assumptions in sympy. We also report that we are complex,
# different from sympy.oo
is_integer = True
is_commutative = True
is_number = True
is_extended_real = True
is_comparable = True
is_extended_positive = True
is_prime = False
# Ensure we get dispatched to before plain numbers
_op_priority = 100.0
__slots__ = ()
def __new__(cls):
return AtomicExpr.__new__(cls)
def _sympystr(self, printer):
return "int_oo"
def _eval_subs(self, old, new):
if self == old:
return new
# We could do these, not sure about it
"""
def _eval_evalf(self, prec=None):
return Float('inf')
def evalf(self, prec=None, **options):
return self._eval_evalf(prec)
"""
@_sympifyit("other", NotImplemented)
def __add__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other in (S.Infinity, S.NegativeInfinity):
return other
if other in (S.NegativeIntInfinity, S.NaN):
return S.NaN
return self
return Number.__add__(self, other)
__radd__ = __add__
@_sympifyit("other", NotImplemented)
def __sub__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other is S.Infinity:
return S.NegativeInfinity
if other is S.NegativeInfinity:
return S.Infinity
if other in (S.IntInfinity, S.NaN):
return S.NaN
return self
return Number.__sub__(self, other)
@_sympifyit("other", NotImplemented)
def __rsub__(self, other):
return (-self).__add__(other)
@_sympifyit("other", NotImplemented)
def __mul__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other.is_zero or other is S.NaN:
return S.NaN
if other.is_extended_positive:
return self
return S.NegativeIntInfinity
return Number.__mul__(self, other)
__rmul__ = __mul__
@_sympifyit("other", NotImplemented)
def __truediv__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other in (
S.Infinity,
S.IntInfinity,
S.NegativeInfinity,
S.NegativeIntInfinity,
S.NaN,
):
return S.NaN
if other.is_extended_nonnegative:
return S.Infinity # truediv produces float
return S.NegativeInfinity # truediv produces float
return Number.__truediv__(self, other)
def __abs__(self):
return S.IntInfinity
def __neg__(self):
return S.NegativeIntInfinity
def _eval_power(self, expt):
if expt.is_extended_positive:
return S.IntInfinity
if expt.is_extended_negative:
return S.Zero
if expt is S.NaN:
return S.NaN
if expt is S.ComplexInfinity:
return S.NaN
if expt.is_extended_real is False and expt.is_number:
from sympy.functions.elementary.complexes import re
expt_real = re(expt)
if expt_real.is_positive:
return S.ComplexInfinity
if expt_real.is_negative:
return S.Zero
if expt_real.is_zero:
return S.NaN
return self ** expt.evalf()
def _as_mpf_val(self, prec):
return mlib.finf
def __hash__(self):
return super().__hash__()
def __eq__(self, other):
return other is S.IntInfinity
def __ne__(self, other):
return other is not S.IntInfinity
def __gt__(self, other):
if other is S.Infinity:
return sympy.false # sympy.oo > int_oo
elif other is S.IntInfinity:
return sympy.false # consistency with sympy.oo
else:
return sympy.true
def __ge__(self, other):
if other is S.Infinity:
return sympy.false # sympy.oo > int_oo
elif other is S.IntInfinity:
return sympy.true # consistency with sympy.oo
else:
return sympy.true
def __lt__(self, other):
if other is S.Infinity:
return sympy.true # sympy.oo > int_oo
elif other is S.IntInfinity:
return sympy.false # consistency with sympy.oo
else:
return sympy.false
def __le__(self, other):
if other is S.Infinity:
return sympy.true # sympy.oo > int_oo
elif other is S.IntInfinity:
return sympy.true # consistency with sympy.oo
else:
return sympy.false
@_sympifyit("other", NotImplemented)
def __mod__(self, other):
if not isinstance(other, Expr):
return NotImplemented
return S.NaN
__rmod__ = __mod__
def floor(self):
return self
def ceiling(self):
return self
int_oo = S.IntInfinity
class NegativeIntInfinity(Number, metaclass=Singleton):
"""Negative integer infinite quantity.
NegativeInfinity is a singleton, and can be accessed
by ``S.NegativeInfinity``.
See Also
========
IntInfinity
"""
# Ensure we get dispatched to before plain numbers
_op_priority = 100.0
is_integer = True
is_extended_real = True
is_commutative = True
is_comparable = True
is_extended_negative = True
is_number = True
is_prime = False
__slots__ = ()
def __new__(cls):
return AtomicExpr.__new__(cls)
def _eval_subs(self, old, new):
if self == old:
return new
def _sympystr(self, printer):
return "-int_oo"
"""
def _eval_evalf(self, prec=None):
return Float('-inf')
def evalf(self, prec=None, **options):
return self._eval_evalf(prec)
"""
@_sympifyit("other", NotImplemented)
def __add__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other is S.Infinity:
return S.Infinity
if other in (S.IntInfinity, S.NaN):
return S.NaN
return self
return Number.__add__(self, other)
__radd__ = __add__
@_sympifyit("other", NotImplemented)
def __sub__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other is S.NegativeInfinity:
return S.Infinity
if other in (S.NegativeIntInfinity, S.NaN):
return S.NaN
return self
return Number.__sub__(self, other)
@_sympifyit("other", NotImplemented)
def __rsub__(self, other):
return (-self).__add__(other)
@_sympifyit("other", NotImplemented)
def __mul__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other.is_zero or other is S.NaN:
return S.NaN
if other.is_extended_positive:
return self
return S.IntInfinity
return Number.__mul__(self, other)
__rmul__ = __mul__
@_sympifyit("other", NotImplemented)
def __truediv__(self, other):
if isinstance(other, Number) and global_parameters.evaluate:
if other in (
S.Infinity,
S.IntInfinity,
S.NegativeInfinity,
S.NegativeIntInfinity,
S.NaN,
):
return S.NaN
if other.is_extended_nonnegative:
return self
return S.Infinity # truediv returns float
return Number.__truediv__(self, other)
def __abs__(self):
return S.IntInfinity
def __neg__(self):
return S.IntInfinity
def _eval_power(self, expt):
if expt.is_number:
if expt in (
S.NaN,
S.Infinity,
S.NegativeInfinity,
S.IntInfinity,
S.NegativeIntInfinity,
):
return S.NaN
if isinstance(expt, sympy.Integer) and expt.is_extended_positive:
if expt.is_odd:
return S.NegativeIntInfinity
else:
return S.IntInfinity
inf_part = S.IntInfinity**expt
s_part = S.NegativeOne**expt
if inf_part == 0 and s_part.is_finite:
return inf_part
if (
inf_part is S.ComplexInfinity
and s_part.is_finite
and not s_part.is_zero
):
return S.ComplexInfinity
return s_part * inf_part
def _as_mpf_val(self, prec):
return mlib.fninf
def __hash__(self):
return super().__hash__()
def __eq__(self, other):
return other is S.NegativeIntInfinity
def __ne__(self, other):
return other is not S.NegativeIntInfinity
def __gt__(self, other):
if other is S.NegativeInfinity:
return sympy.true # -sympy.oo < -int_oo
elif other is S.NegativeIntInfinity:
return sympy.false # consistency with sympy.oo
else:
return sympy.false
def __ge__(self, other):
if other is S.NegativeInfinity:
return sympy.true # -sympy.oo < -int_oo
elif other is S.NegativeIntInfinity:
return sympy.true # consistency with sympy.oo
else:
return sympy.false
def __lt__(self, other):
if other is S.NegativeInfinity:
return sympy.false # -sympy.oo < -int_oo
elif other is S.NegativeIntInfinity:
return sympy.false # consistency with sympy.oo
else:
return sympy.true
def __le__(self, other):
if other is S.NegativeInfinity:
return sympy.false # -sympy.oo < -int_oo
elif other is S.NegativeIntInfinity:
return sympy.true # consistency with sympy.oo
else:
return sympy.true
@_sympifyit("other", NotImplemented)
def __mod__(self, other):
if not isinstance(other, Expr):
return NotImplemented
return S.NaN
__rmod__ = __mod__
def floor(self):
return self
def ceiling(self):
return self
def as_powers_dict(self):
return {S.NegativeOne: 1, S.IntInfinity: 1}
|
