Source code for sympy.polys.domains.expressiondomain

"""Implementation of :class:`ExpressionDomain` class. """

from __future__ import print_function, division

from sympy.polys.domains.field import Field
from sympy.polys.domains.simpledomain import SimpleDomain
from sympy.polys.domains.characteristiczero import CharacteristicZero

from sympy.core import sympify, SympifyError
from sympy.utilities import public
from sympy.polys.polyutils import PicklableWithSlots

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