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polys: Moved old PolynomialRing and FractionField to old_* files
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,185 @@ | ||
| """Implementation of :class:`FractionField` class. """ | ||
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| from sympy.polys.domains.field import Field | ||
| from sympy.polys.domains.compositedomain import CompositeDomain | ||
| from sympy.polys.domains.characteristiczero import CharacteristicZero | ||
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| from sympy.polys.polyclasses import DMF | ||
| from sympy.polys.polyerrors import GeneratorsNeeded | ||
| from sympy.polys.polyutils import dict_from_basic, basic_from_dict, _dict_reorder | ||
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| class FractionField(Field, CharacteristicZero, CompositeDomain): | ||
| """A class for representing rational function fields. """ | ||
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| dtype = DMF | ||
| is_Frac = True | ||
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| has_assoc_Ring = True | ||
| has_assoc_Field = True | ||
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| def __init__(self, dom, *gens): | ||
| if not gens: | ||
| raise GeneratorsNeeded("generators not specified") | ||
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| lev = len(gens) - 1 | ||
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| self.zero = self.dtype.zero(lev, dom, ring=self) | ||
| self.one = self.dtype.one(lev, dom, ring=self) | ||
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| self.dom = dom | ||
| self.gens = gens | ||
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| def __str__(self): | ||
| return str(self.dom) + '(' + ','.join(map(str, self.gens)) + ')' | ||
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| def __hash__(self): | ||
| return hash((self.__class__.__name__, self.dtype, self.dom, self.gens)) | ||
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| def __call__(self, a): | ||
| """Construct an element of ``self`` domain from ``a``. """ | ||
| return DMF(a, self.dom, len(self.gens) - 1, ring=self) | ||
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| def __eq__(self, other): | ||
| """Returns ``True`` if two domains are equivalent. """ | ||
| if not isinstance(other, FractionField): | ||
| return False | ||
| return self.dtype == other.dtype and self.dom == other.dom and self.gens == other.gens | ||
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| def __ne__(self, other): | ||
| """Returns ``False`` if two domains are equivalent. """ | ||
| return not self.__eq__(other) | ||
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| def to_sympy(self, a): | ||
| """Convert ``a`` to a SymPy object. """ | ||
| return (basic_from_dict(a.numer().to_sympy_dict(), *self.gens) / | ||
| basic_from_dict(a.denom().to_sympy_dict(), *self.gens)) | ||
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| def from_sympy(self, a): | ||
| """Convert SymPy's expression to ``dtype``. """ | ||
| p, q = a.as_numer_denom() | ||
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| num, _ = dict_from_basic(p, gens=self.gens) | ||
| den, _ = dict_from_basic(q, gens=self.gens) | ||
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| for k, v in num.iteritems(): | ||
| num[k] = self.dom.from_sympy(v) | ||
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| for k, v in den.iteritems(): | ||
| den[k] = self.dom.from_sympy(v) | ||
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| return self((num, den)).cancel() | ||
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| def from_ZZ_python(K1, a, K0): | ||
| """Convert a Python ``int`` object to ``dtype``. """ | ||
| return K1(K1.dom.convert(a, K0)) | ||
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| def from_QQ_python(K1, a, K0): | ||
| """Convert a Python ``Fraction`` object to ``dtype``. """ | ||
| return K1(K1.dom.convert(a, K0)) | ||
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| def from_ZZ_gmpy(K1, a, K0): | ||
| """Convert a GMPY ``mpz`` object to ``dtype``. """ | ||
| return K1(K1.dom.convert(a, K0)) | ||
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| def from_QQ_gmpy(K1, a, K0): | ||
| """Convert a GMPY ``mpq`` object to ``dtype``. """ | ||
| return K1(K1.dom.convert(a, K0)) | ||
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| def from_RR_mpmath(K1, a, K0): | ||
| """Convert a mpmath ``mpf`` object to ``dtype``. """ | ||
| return K1(K1.dom.convert(a, K0)) | ||
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| def from_GlobalPolynomialRing(K1, a, K0): | ||
| """Convert a ``DMF`` object to ``dtype``. """ | ||
| if K1.gens == K0.gens: | ||
| if K1.dom == K0.dom: | ||
| return K1(a.rep) | ||
| else: | ||
| return K1(a.convert(K1.dom).rep) | ||
| else: | ||
| monoms, coeffs = _dict_reorder(a.to_dict(), K0.gens, K1.gens) | ||
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| if K1.dom != K0.dom: | ||
| 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): | ||
| """ | ||
| Convert a fraction field element to another fraction field. | ||
| Examples | ||
| ======== | ||
| >>> from sympy.polys.polyclasses import DMF | ||
| >>> from sympy.polys.domains import ZZ, QQ | ||
| >>> from sympy.abc import x | ||
| >>> f = DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(1)]), ZZ) | ||
| >>> QQx = QQ.frac_field(x) | ||
| >>> ZZx = ZZ.frac_field(x) | ||
| >>> QQx.from_FractionField(f, ZZx) | ||
| (x + 2)/(x + 1) | ||
| """ | ||
| if K1.gens == K0.gens: | ||
| if K1.dom == K0.dom: | ||
| return a | ||
| else: | ||
| return K1((a.numer().convert(K1.dom).rep, | ||
| a.denom().convert(K1.dom).rep)) | ||
| elif set(K0.gens).issubset(K1.gens): | ||
| nmonoms, ncoeffs = _dict_reorder( | ||
| a.numer().to_dict(), K0.gens, K1.gens) | ||
| dmonoms, dcoeffs = _dict_reorder( | ||
| a.denom().to_dict(), K0.gens, K1.gens) | ||
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| if K1.dom != K0.dom: | ||
| ncoeffs = [ K1.dom.convert(c, K0.dom) for c in ncoeffs ] | ||
| 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): | ||
| """Returns a ring associated with ``self``. """ | ||
| from sympy.polys.domains import PolynomialRing | ||
| return PolynomialRing(self.dom, *self.gens) | ||
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| def poly_ring(self, *gens): | ||
| """Returns a polynomial ring, i.e. `K[X]`. """ | ||
| raise NotImplementedError('nested domains not allowed') | ||
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| def frac_field(self, *gens): | ||
| """Returns a fraction field, i.e. `K(X)`. """ | ||
| raise NotImplementedError('nested domains not allowed') | ||
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| def is_positive(self, a): | ||
| """Returns True if ``a`` is positive. """ | ||
| return self.dom.is_positive(a.numer().LC()) | ||
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| def is_negative(self, a): | ||
| """Returns True if ``a`` is negative. """ | ||
| return self.dom.is_negative(a.numer().LC()) | ||
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| def is_nonpositive(self, a): | ||
| """Returns True if ``a`` is non-positive. """ | ||
| return self.dom.is_nonpositive(a.numer().LC()) | ||
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| def is_nonnegative(self, a): | ||
| """Returns True if ``a`` is non-negative. """ | ||
| return self.dom.is_nonnegative(a.numer().LC()) | ||
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| def numer(self, a): | ||
| """Returns numerator of ``a``. """ | ||
| return a.numer() | ||
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| def denom(self, a): | ||
| """Returns denominator of ``a``. """ | ||
| return a.denom() | ||
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| def factorial(self, a): | ||
| """Returns factorial of ``a``. """ | ||
| return self.dtype(self.dom.factorial(a)) |
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