186 lines
6.0 KiB
Python
186 lines
6.0 KiB
Python
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"""Implementation of :class:`FractionField` class. """
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from sympy.polys.domains.field import Field
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from sympy.polys.domains.compositedomain import CompositeDomain
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from sympy.polys.domains.characteristiczero import CharacteristicZero
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from sympy.polys.polyclasses import DMF
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from sympy.polys.polyerrors import GeneratorsNeeded
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from sympy.polys.polyutils import dict_from_basic, basic_from_dict, _dict_reorder
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from sympy.utilities import public
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@public
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class FractionField(Field, CharacteristicZero, CompositeDomain):
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"""A class for representing rational function fields. """
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dtype = DMF
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is_FractionField = is_Frac = True
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has_assoc_Ring = True
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has_assoc_Field = True
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def __init__(self, dom, *gens):
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if not gens:
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raise GeneratorsNeeded("generators not specified")
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lev = len(gens) - 1
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self.ngens = len(gens)
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self.zero = self.dtype.zero(lev, dom, ring=self)
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self.one = self.dtype.one(lev, dom, ring=self)
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self.domain = self.dom = dom
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self.symbols = self.gens = gens
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def new(self, element):
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return self.dtype(element, self.dom, len(self.gens) - 1, ring=self)
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def __str__(self):
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return str(self.dom) + '(' + ','.join(map(str, self.gens)) + ')'
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def __hash__(self):
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return hash((self.__class__.__name__, self.dtype, self.dom, self.gens))
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def __eq__(self, other):
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"""Returns ``True`` if two domains are equivalent. """
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return isinstance(other, FractionField) and \
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self.dtype == other.dtype and self.dom == other.dom and self.gens == other.gens
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def to_sympy(self, a):
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"""Convert ``a`` to a SymPy object. """
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return (basic_from_dict(a.numer().to_sympy_dict(), *self.gens) /
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basic_from_dict(a.denom().to_sympy_dict(), *self.gens))
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def from_sympy(self, a):
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"""Convert SymPy's expression to ``dtype``. """
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p, q = a.as_numer_denom()
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num, _ = dict_from_basic(p, gens=self.gens)
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den, _ = dict_from_basic(q, gens=self.gens)
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for k, v in num.items():
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num[k] = self.dom.from_sympy(v)
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for k, v in den.items():
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den[k] = self.dom.from_sympy(v)
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return self((num, den)).cancel()
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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(K1.dom.convert(a, K0))
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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(K1.dom.convert(a, K0))
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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(K1.dom.convert(a, K0))
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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(K1.dom.convert(a, K0))
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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(K1.dom.convert(a, K0))
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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(K1.dom.convert(a, K0))
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def from_GlobalPolynomialRing(K1, a, K0):
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"""Convert a ``DMF`` object to ``dtype``. """
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if K1.gens == K0.gens:
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if K1.dom == K0.dom:
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return K1(a.rep)
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else:
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return K1(a.convert(K1.dom).rep)
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else:
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monoms, coeffs = _dict_reorder(a.to_dict(), K0.gens, K1.gens)
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if K1.dom != K0.dom:
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coeffs = [ K1.dom.convert(c, K0.dom) for c in coeffs ]
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return K1(dict(zip(monoms, coeffs)))
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def from_FractionField(K1, a, K0):
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"""
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Convert a fraction field element to another fraction field.
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Examples
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========
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>>> from sympy.polys.polyclasses import DMF
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>>> from sympy.polys.domains import ZZ, QQ
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>>> from sympy.abc import x
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>>> f = DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(1)]), ZZ)
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>>> QQx = QQ.old_frac_field(x)
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>>> ZZx = ZZ.old_frac_field(x)
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>>> QQx.from_FractionField(f, ZZx)
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(x + 2)/(x + 1)
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"""
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if K1.gens == K0.gens:
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if K1.dom == K0.dom:
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return a
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else:
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return K1((a.numer().convert(K1.dom).rep,
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a.denom().convert(K1.dom).rep))
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elif set(K0.gens).issubset(K1.gens):
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nmonoms, ncoeffs = _dict_reorder(
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a.numer().to_dict(), K0.gens, K1.gens)
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dmonoms, dcoeffs = _dict_reorder(
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a.denom().to_dict(), K0.gens, K1.gens)
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if K1.dom != K0.dom:
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ncoeffs = [ K1.dom.convert(c, K0.dom) for c in ncoeffs ]
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dcoeffs = [ K1.dom.convert(c, K0.dom) for c in dcoeffs ]
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return K1((dict(zip(nmonoms, ncoeffs)), dict(zip(dmonoms, dcoeffs))))
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def get_ring(self):
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"""Returns a ring associated with ``self``. """
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from sympy.polys.domains import PolynomialRing
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return PolynomialRing(self.dom, *self.gens)
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def poly_ring(self, *gens):
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"""Returns a polynomial ring, i.e. `K[X]`. """
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raise NotImplementedError('nested domains not allowed')
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def frac_field(self, *gens):
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"""Returns a fraction field, i.e. `K(X)`. """
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raise NotImplementedError('nested domains not allowed')
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def is_positive(self, a):
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"""Returns True if ``a`` is positive. """
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return self.dom.is_positive(a.numer().LC())
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def is_negative(self, a):
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"""Returns True if ``a`` is negative. """
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return self.dom.is_negative(a.numer().LC())
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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 self.dom.is_nonpositive(a.numer().LC())
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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 self.dom.is_nonnegative(a.numer().LC())
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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 factorial(self, a):
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"""Returns factorial of ``a``. """
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return self.dtype(self.dom.factorial(a))
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