Source code for sympy.polys.domains.polynomialring

"""Implementation of :class:`PolynomialRing` class. """

from __future__ import print_function, division

from sympy.polys.domains.ring import Ring
from sympy.polys.domains.compositedomain import CompositeDomain

from sympy.polys.polyerrors import CoercionFailed, GeneratorsError
from sympy.utilities import public

@public
[docs]class PolynomialRing(Ring, CompositeDomain): """A class for representing multivariate polynomial rings. """ is_PolynomialRing = is_Poly = True has_assoc_Ring = True has_assoc_Field = True def __init__(self, domain_or_ring, symbols=None, order=None): from sympy.polys.rings import PolyRing if isinstance(domain_or_ring, PolyRing) and symbols is None and order is None: ring = domain_or_ring else: ring = PolyRing(symbols, domain_or_ring, order) self.ring = ring self.dtype = ring.dtype self.gens = ring.gens self.ngens = ring.ngens self.symbols = ring.symbols self.domain = ring.domain if symbols: if ring.domain.is_Field and ring.domain.is_Exact and len(symbols)==1: self.is_PID = True # TODO: remove this self.dom = self.domain def new(self, element): return self.ring.ring_new(element) @property def zero(self): return self.ring.zero @property def one(self): return self.ring.one @property def order(self): return self.ring.order def __str__(self): return str(self.domain) + '[' + ','.join(map(str, self.symbols)) + ']' def __hash__(self): return hash((self.__class__.__name__, self.dtype.ring, self.domain, self.symbols)) def __eq__(self, other): """Returns `True` if two domains are equivalent. """ return isinstance(other, PolynomialRing) and \ (self.dtype.ring, self.domain, self.symbols) == \ (other.dtype.ring, other.domain, other.symbols)
[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.ring.from_expr(a)
[docs] def from_ZZ_python(K1, a, K0): """Convert a Python `int` object to `dtype`. """ return K1(K1.domain.convert(a, K0))
[docs] def from_QQ_python(K1, a, K0): """Convert a Python `Fraction` object to `dtype`. """ return K1(K1.domain.convert(a, K0))
[docs] def from_ZZ_gmpy(K1, a, K0): """Convert a GMPY `mpz` object to `dtype`. """ return K1(K1.domain.convert(a, K0))
[docs] def from_QQ_gmpy(K1, a, K0): """Convert a GMPY `mpq` object to `dtype`. """ return K1(K1.domain.convert(a, K0))
[docs] def from_RealField(K1, a, K0): """Convert a mpmath `mpf` object to `dtype`. """ return K1(K1.domain.convert(a, K0))
[docs] def from_AlgebraicField(K1, a, K0): """Convert an algebraic number to ``dtype``. """ if K1.domain == K0: return K1.new(a)
[docs] def from_PolynomialRing(K1, a, K0): """Convert a polynomial to ``dtype``. """ try: return a.set_ring(K1.ring) except (CoercionFailed, GeneratorsError): return None
[docs] def from_FractionField(K1, a, K0): """Convert a rational function to ``dtype``. """ q, r = K0.numer(a).div(K0.denom(a)) if r.is_zero: return K1.from_PolynomialRing(q, K0.field.ring.to_domain()) else: return None
[docs] def get_field(self): """Returns a field associated with `self`. """ return self.ring.to_field().to_domain()
[docs] def is_positive(self, a): """Returns True if `LC(a)` is positive. """ return self.domain.is_positive(a.LC)
[docs] def is_negative(self, a): """Returns True if `LC(a)` is negative. """ return self.domain.is_negative(a.LC)
[docs] def is_nonpositive(self, a): """Returns True if `LC(a)` is non-positive. """ return self.domain.is_nonpositive(a.LC)
[docs] def is_nonnegative(self, a): """Returns True if `LC(a)` is non-negative. """ return self.domain.is_nonnegative(a.LC)
[docs] def gcdex(self, a, b): """Extended GCD of `a` and `b`. """ return a.gcdex(b)
[docs] def gcd(self, a, b): """Returns GCD of `a` and `b`. """ return a.gcd(b)
[docs] def lcm(self, a, b): """Returns LCM of `a` and `b`. """ return a.lcm(b)
[docs] def factorial(self, a): """Returns factorial of `a`. """ return self.dtype(self.domain.factorial(a))