Source code for

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

from __future__ import print_function, division

from import Field
from import CompositeDomain

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

[docs]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 @property def one(self): return @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
[docs] def from_PolynomialRing(K1, a, K0): """Convert a polynomial to ``dtype``. """ try: return 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))