switching to high quality piper tts and added label translations
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Matthias Hinrichs
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"""Implementation of :class:`ModularInteger` class. """
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from __future__ import annotations
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from typing import Any
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import operator
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from sympy.polys.polyutils import PicklableWithSlots
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from sympy.polys.polyerrors import CoercionFailed
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from sympy.polys.domains.domainelement import DomainElement
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from sympy.utilities import public
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from sympy.utilities.exceptions import sympy_deprecation_warning
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@public
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class ModularInteger(PicklableWithSlots, DomainElement):
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"""A class representing a modular integer. """
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mod, dom, sym, _parent = None, None, None, None
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__slots__ = ('val',)
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def parent(self):
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return self._parent
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def __init__(self, val):
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if isinstance(val, self.__class__):
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self.val = val.val % self.mod
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else:
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self.val = self.dom.convert(val) % self.mod
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def modulus(self):
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return self.mod
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def __hash__(self):
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return hash((self.val, self.mod))
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def __repr__(self):
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return "%s(%s)" % (self.__class__.__name__, self.val)
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def __str__(self):
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return "%s mod %s" % (self.val, self.mod)
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def __int__(self):
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return int(self.val)
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def to_int(self):
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sympy_deprecation_warning(
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"""ModularInteger.to_int() is deprecated.
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Use int(a) or K = GF(p) and K.to_int(a) instead of a.to_int().
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""",
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deprecated_since_version="1.13",
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active_deprecations_target="modularinteger-to-int",
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)
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if self.sym:
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if self.val <= self.mod // 2:
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return self.val
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else:
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return self.val - self.mod
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else:
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return self.val
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def __pos__(self):
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return self
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def __neg__(self):
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return self.__class__(-self.val)
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@classmethod
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def _get_val(cls, other):
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if isinstance(other, cls):
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return other.val
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else:
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try:
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return cls.dom.convert(other)
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except CoercionFailed:
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return None
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def __add__(self, other):
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val = self._get_val(other)
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if val is not None:
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return self.__class__(self.val + val)
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else:
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return NotImplemented
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def __radd__(self, other):
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return self.__add__(other)
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def __sub__(self, other):
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val = self._get_val(other)
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if val is not None:
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return self.__class__(self.val - val)
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else:
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return NotImplemented
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def __rsub__(self, other):
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return (-self).__add__(other)
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def __mul__(self, other):
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val = self._get_val(other)
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if val is not None:
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return self.__class__(self.val * val)
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else:
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return NotImplemented
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def __rmul__(self, other):
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return self.__mul__(other)
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def __truediv__(self, other):
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val = self._get_val(other)
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if val is not None:
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return self.__class__(self.val * self._invert(val))
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else:
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return NotImplemented
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def __rtruediv__(self, other):
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return self.invert().__mul__(other)
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def __mod__(self, other):
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val = self._get_val(other)
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if val is not None:
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return self.__class__(self.val % val)
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else:
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return NotImplemented
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def __rmod__(self, other):
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val = self._get_val(other)
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if val is not None:
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return self.__class__(val % self.val)
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else:
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return NotImplemented
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def __pow__(self, exp):
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if not exp:
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return self.__class__(self.dom.one)
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if exp < 0:
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val, exp = self.invert().val, -exp
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else:
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val = self.val
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return self.__class__(pow(val, int(exp), self.mod))
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def _compare(self, other, op):
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val = self._get_val(other)
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if val is None:
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return NotImplemented
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return op(self.val, val % self.mod)
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def _compare_deprecated(self, other, op):
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val = self._get_val(other)
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if val is None:
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return NotImplemented
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sympy_deprecation_warning(
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"""Ordered comparisons with modular integers are deprecated.
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Use e.g. int(a) < int(b) instead of a < b.
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""",
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deprecated_since_version="1.13",
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active_deprecations_target="modularinteger-compare",
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stacklevel=4,
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)
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return op(self.val, val % self.mod)
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def __eq__(self, other):
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return self._compare(other, operator.eq)
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def __ne__(self, other):
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return self._compare(other, operator.ne)
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def __lt__(self, other):
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return self._compare_deprecated(other, operator.lt)
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def __le__(self, other):
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return self._compare_deprecated(other, operator.le)
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def __gt__(self, other):
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return self._compare_deprecated(other, operator.gt)
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def __ge__(self, other):
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return self._compare_deprecated(other, operator.ge)
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def __bool__(self):
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return bool(self.val)
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@classmethod
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def _invert(cls, value):
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return cls.dom.invert(value, cls.mod)
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def invert(self):
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return self.__class__(self._invert(self.val))
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_modular_integer_cache: dict[tuple[Any, Any, Any], type[ModularInteger]] = {}
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def ModularIntegerFactory(_mod, _dom, _sym, parent):
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"""Create custom class for specific integer modulus."""
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try:
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_mod = _dom.convert(_mod)
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except CoercionFailed:
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ok = False
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else:
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ok = True
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if not ok or _mod < 1:
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raise ValueError("modulus must be a positive integer, got %s" % _mod)
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key = _mod, _dom, _sym
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try:
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cls = _modular_integer_cache[key]
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except KeyError:
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class cls(ModularInteger):
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mod, dom, sym = _mod, _dom, _sym
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_parent = parent
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if _sym:
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cls.__name__ = "SymmetricModularIntegerMod%s" % _mod
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else:
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cls.__name__ = "ModularIntegerMod%s" % _mod
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_modular_integer_cache[key] = cls
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return cls
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