# Source code for sympy.polys.domains.fractionfield

"""Implementation of :class:FractionField class. """

from __future__ import print_function, division

from sympy.polys.domains.field import Field
from sympy.polys.domains.compositedomain import CompositeDomain

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

[docs]@public
class FractionField(Field, CompositeDomain):
"""A class for representing multivariate rational function fields. """

is_FractionField = is_Frac = True

has_assoc_Ring = True
has_assoc_Field = True

def __init__(self, domain_or_field, symbols=None, order=None):
from sympy.polys.fields import FracField

if isinstance(domain_or_field, FracField) and symbols is None and order is None:
field = domain_or_field
else:
field = FracField(symbols, domain_or_field, order)

self.field = field
self.dtype = field.dtype

self.gens = field.gens
self.ngens = field.ngens
self.symbols = field.symbols
self.domain = field.domain

# TODO: remove this
self.dom = self.domain

def new(self, element):
return self.field.field_new(element)

@property
def zero(self):
return self.field.zero

@property
def one(self):
return self.field.one

@property
def order(self):
return self.field.order

def __str__(self):
return str(self.domain) + '(' + ','.join(map(str, self.symbols)) + ')'

def __hash__(self):
return hash((self.__class__.__name__, self.dtype.field, self.domain, self.symbols))

def __eq__(self, other):
"""Returns True if two domains are equivalent. """
return isinstance(other, FractionField) and \
(self.dtype.field, self.domain, self.symbols) ==\
(other.dtype.field, 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.field.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 K1.new(a)
except (CoercionFailed, GeneratorsError):
return None

[docs]    def from_FractionField(K1, a, K0):
"""Convert a rational function to dtype. """
try:
return a.set_field(K1.field)
except (CoercionFailed, GeneratorsError):
return None

[docs]    def get_ring(self):
"""Returns a field associated with self. """
return self.field.to_ring().to_domain()

[docs]    def is_positive(self, a):
"""Returns True if LC(a) is positive. """
return self.domain.is_positive(a.numer.LC)

[docs]    def is_negative(self, a):
"""Returns True if LC(a) is negative. """
return self.domain.is_negative(a.numer.LC)

[docs]    def is_nonpositive(self, a):
"""Returns True if LC(a) is non-positive. """
return self.domain.is_nonpositive(a.numer.LC)

[docs]    def is_nonnegative(self, a):
"""Returns True if LC(a) is non-negative. """
return self.domain.is_nonnegative(a.numer.LC)

[docs]    def numer(self, a):
"""Returns numerator of a. """
return a.numer

[docs]    def denom(self, a):
"""Returns denominator of a. """
return a.denom

[docs]    def factorial(self, a):
"""Returns factorial of a. """
return self.dtype(self.domain.factorial(a))