255 lines
6.8 KiB
Python
255 lines
6.8 KiB
Python
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"""Implementation of :class:`ExpressionDomain` class. """
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from sympy.core import sympify, SympifyError
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from sympy.polys.domains.characteristiczero import CharacteristicZero
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from sympy.polys.domains.field import Field
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from sympy.polys.domains.simpledomain import SimpleDomain
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from sympy.polys.polyutils import PicklableWithSlots
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from sympy.utilities import public
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eflags = {"deep": False, "mul": True, "power_exp": False, "power_base": False,
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"basic": False, "multinomial": False, "log": False}
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@public
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class ExpressionDomain(Field, CharacteristicZero, SimpleDomain):
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"""A class for arbitrary expressions. """
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is_SymbolicDomain = is_EX = True
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class Expression(PicklableWithSlots):
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"""An arbitrary expression. """
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__slots__ = ('ex',)
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def __init__(self, ex):
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if not isinstance(ex, self.__class__):
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self.ex = sympify(ex)
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else:
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self.ex = ex.ex
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def __repr__(f):
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return 'EX(%s)' % repr(f.ex)
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def __str__(f):
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return 'EX(%s)' % str(f.ex)
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def __hash__(self):
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return hash((self.__class__.__name__, self.ex))
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def as_expr(f):
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return f.ex
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def numer(f):
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return f.__class__(f.ex.as_numer_denom()[0])
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def denom(f):
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return f.__class__(f.ex.as_numer_denom()[1])
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def simplify(f, ex):
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return f.__class__(ex.cancel().expand(**eflags))
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def __abs__(f):
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return f.__class__(abs(f.ex))
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def __neg__(f):
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return f.__class__(-f.ex)
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def _to_ex(f, g):
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try:
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return f.__class__(g)
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except SympifyError:
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return None
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def __add__(f, g):
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g = f._to_ex(g)
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if g is None:
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return NotImplemented
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elif g == EX.zero:
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return f
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elif f == EX.zero:
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return g
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else:
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return f.simplify(f.ex + g.ex)
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def __radd__(f, g):
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return f.simplify(f.__class__(g).ex + f.ex)
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def __sub__(f, g):
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g = f._to_ex(g)
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if g is None:
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return NotImplemented
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elif g == EX.zero:
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return f
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elif f == EX.zero:
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return -g
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else:
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return f.simplify(f.ex - g.ex)
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def __rsub__(f, g):
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return f.simplify(f.__class__(g).ex - f.ex)
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def __mul__(f, g):
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g = f._to_ex(g)
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if g is None:
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return NotImplemented
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if EX.zero in (f, g):
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return EX.zero
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elif f.ex.is_Number and g.ex.is_Number:
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return f.__class__(f.ex*g.ex)
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return f.simplify(f.ex*g.ex)
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def __rmul__(f, g):
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return f.simplify(f.__class__(g).ex*f.ex)
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def __pow__(f, n):
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n = f._to_ex(n)
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if n is not None:
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return f.simplify(f.ex**n.ex)
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else:
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return NotImplemented
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def __truediv__(f, g):
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g = f._to_ex(g)
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if g is not None:
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return f.simplify(f.ex/g.ex)
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else:
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return NotImplemented
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def __rtruediv__(f, g):
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return f.simplify(f.__class__(g).ex/f.ex)
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def __eq__(f, g):
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return f.ex == f.__class__(g).ex
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def __ne__(f, g):
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return not f == g
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def __bool__(f):
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return not f.ex.is_zero
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def gcd(f, g):
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from sympy.polys import gcd
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return f.__class__(gcd(f.ex, f.__class__(g).ex))
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def lcm(f, g):
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from sympy.polys import lcm
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return f.__class__(lcm(f.ex, f.__class__(g).ex))
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dtype = Expression
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zero = Expression(0)
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one = Expression(1)
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rep = 'EX'
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has_assoc_Ring = False
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has_assoc_Field = True
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def __init__(self):
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pass
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def to_sympy(self, a):
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"""Convert ``a`` to a SymPy object. """
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return a.as_expr()
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def from_sympy(self, a):
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"""Convert SymPy's expression to ``dtype``. """
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return self.dtype(a)
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def from_ZZ(K1, a, K0):
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"""Convert a Python ``int`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_ZZ_python(K1, a, K0):
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"""Convert a Python ``int`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_QQ(K1, a, K0):
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"""Convert a Python ``Fraction`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_QQ_python(K1, a, K0):
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"""Convert a Python ``Fraction`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_ZZ_gmpy(K1, a, K0):
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"""Convert a GMPY ``mpz`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_QQ_gmpy(K1, a, K0):
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"""Convert a GMPY ``mpq`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_GaussianIntegerRing(K1, a, K0):
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"""Convert a ``GaussianRational`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_GaussianRationalField(K1, a, K0):
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"""Convert a ``GaussianRational`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_RealField(K1, a, K0):
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"""Convert a mpmath ``mpf`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_PolynomialRing(K1, a, K0):
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"""Convert a ``DMP`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_FractionField(K1, a, K0):
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"""Convert a ``DMF`` object to ``dtype``. """
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return K1(K0.to_sympy(a))
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def from_ExpressionDomain(K1, a, K0):
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"""Convert a ``EX`` object to ``dtype``. """
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return a
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def get_ring(self):
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"""Returns a ring associated with ``self``. """
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return self # XXX: EX is not a ring but we don't have much choice here.
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def get_field(self):
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"""Returns a field associated with ``self``. """
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return self
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def is_positive(self, a):
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"""Returns True if ``a`` is positive. """
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return a.ex.as_coeff_mul()[0].is_positive
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def is_negative(self, a):
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"""Returns True if ``a`` is negative. """
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return a.ex.could_extract_minus_sign()
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def is_nonpositive(self, a):
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"""Returns True if ``a`` is non-positive. """
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return a.ex.as_coeff_mul()[0].is_nonpositive
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def is_nonnegative(self, a):
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"""Returns True if ``a`` is non-negative. """
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return a.ex.as_coeff_mul()[0].is_nonnegative
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def numer(self, a):
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"""Returns numerator of ``a``. """
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return a.numer()
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def denom(self, a):
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"""Returns denominator of ``a``. """
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return a.denom()
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def gcd(self, a, b):
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return self(1)
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def lcm(self, a, b):
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return a.lcm(b)
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EX = ExpressionDomain()
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