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