def unify(K0, K1, symbols=None): """ Construct a minimal domain that contains elements of ``K0`` and ``K1``. Known domains (from smallest to largest): - ``GF(p)`` - ``ZZ`` - ``QQ`` - ``RR(prec, tol)`` - ``CC(prec, tol)`` - ``ALG(a, b, c)`` - ``K[x, y, z]`` - ``K(x, y, z)`` - ``EX`` """ if symbols is not None: return K0.unify_with_symbols(K1, symbols) if K0 == K1: return K0 if K0.is_EX: return K0 if K1.is_EX: return K1 if K0.is_Composite or K1.is_Composite: K0_ground = K0.dom if K0.is_Composite else K0 K1_ground = K1.dom if K1.is_Composite else K1 K0_symbols = K0.symbols if K0.is_Composite else () K1_symbols = K1.symbols if K1.is_Composite else () domain = K0_ground.unify(K1_ground) symbols = _unify_gens(K0_symbols, K1_symbols) order = K0.order if K0.is_Composite else K1.order if ((K0.is_FractionField and K1.is_PolynomialRing or K1.is_FractionField and K0.is_PolynomialRing) and (not K0_ground.has_Field or not K1_ground.has_Field) and domain.has_Field): domain = domain.get_ring() if K0.is_Composite and (not K1.is_Composite or K0.is_FractionField or K1.is_PolynomialRing): cls = K0.__class__ else: cls = K1.__class__ return cls(domain, symbols, order) def mkinexact(cls, K0, K1): prec = max(K0.precision, K1.precision) tol = max(K0.tolerance, K1.tolerance) return cls(prec=prec, tol=tol) if K0.is_ComplexField and K1.is_ComplexField: return mkinexact(K0.__class__, K0, K1) if K0.is_ComplexField and K1.is_RealField: return mkinexact(K0.__class__, K0, K1) if K0.is_RealField and K1.is_ComplexField: return mkinexact(K1.__class__, K1, K0) if K0.is_RealField and K1.is_RealField: return mkinexact(K0.__class__, K0, K1) if K0.is_ComplexField or K0.is_RealField: return K0 if K1.is_ComplexField or K1.is_RealField: return K1 if K0.is_AlgebraicField and K1.is_AlgebraicField: return K0.__class__(K0.dom.unify(K1.dom), *_unify_gens(K0.orig_ext, K1.orig_ext)) elif K0.is_AlgebraicField: return K0 elif K1.is_AlgebraicField: return K1 if K0.is_RationalField: return K0 if K1.is_RationalField: return K1 if K0.is_IntegerRing: return K0 if K1.is_IntegerRing: return K1 if K0.is_FiniteField and K1.is_FiniteField: return K0.__class__(max(K0.mod, K1.mod, key=default_sort_key)) from sympy.polys.domains import EX return EX
def test__unify_gens(): assert _unify_gens([], []) == () assert _unify_gens([x], [x]) == (x,) assert _unify_gens([y], [y]) == (y,) assert _unify_gens([x, y], [x]) == (x, y) assert _unify_gens([x], [x, y]) == (x, y) assert _unify_gens([x, y], [x, y]) == (x, y) assert _unify_gens([y, x], [y, x]) == (y, x) assert _unify_gens([x], [y]) == (x, y) assert _unify_gens([y], [x]) == (y, x) assert _unify_gens([x], [y, x]) == (y, x) assert _unify_gens([y, x], [x]) == (y, x) assert _unify_gens([x, y, z], [x, y, z]) == (x, y, z) assert _unify_gens([z, y, x], [x, y, z]) == (z, y, x) assert _unify_gens([x, y, z], [z, y, x]) == (x, y, z) assert _unify_gens([z, y, x], [z, y, x]) == (z, y, x) assert _unify_gens([x, y, z], [t, x, p, q, z]) == (t, x, y, p, q, z)
def unify(K0, K1, symbols=None): """ Construct a minimal domain that contains elements of ``K0`` and ``K1``. Known domains (from smallest to largest): - ``GF(p)`` - ``ZZ`` - ``QQ`` - ``RR(prec, tol)`` - ``CC(prec, tol)`` - ``ALG(a, b, c)`` - ``K[x, y, z]`` - ``K(x, y, z)`` - ``EX`` """ if symbols is not None: return K0.unify_with_symbols(K1, symbols) if K0 == K1: return K0 if K0.is_EX: return K0 if K1.is_EX: return K1 if K0.is_FiniteExtension or K1.is_FiniteExtension: if K1.is_FiniteExtension: K0, K1 = K1, K0 if K1.is_FiniteExtension: # Unifying two extensions. # Try to ensure that K0.unify(K1) == K1.unify(K0) if list(ordered([K0.modulus, K1.modulus]))[1] == K0.modulus: K0, K1 = K1, K0 return K1.set_domain(K0) else: # Drop the generator from other and unify with the base domain K1 = K1.drop(K0.symbol) K1 = K0.domain.unify(K1) return K0.set_domain(K1) if K0.is_Composite or K1.is_Composite: K0_ground = K0.dom if K0.is_Composite else K0 K1_ground = K1.dom if K1.is_Composite else K1 K0_symbols = K0.symbols if K0.is_Composite else () K1_symbols = K1.symbols if K1.is_Composite else () domain = K0_ground.unify(K1_ground) symbols = _unify_gens(K0_symbols, K1_symbols) order = K0.order if K0.is_Composite else K1.order if ((K0.is_FractionField and K1.is_PolynomialRing or K1.is_FractionField and K0.is_PolynomialRing) and (not K0_ground.is_Field or not K1_ground.is_Field) and domain.is_Field and domain.has_assoc_Ring): domain = domain.get_ring() if K0.is_Composite and (not K1.is_Composite or K0.is_FractionField or K1.is_PolynomialRing): cls = K0.__class__ else: cls = K1.__class__ from sympy.polys.domains.old_polynomialring import GlobalPolynomialRing if cls == GlobalPolynomialRing: return cls(domain, symbols) return cls(domain, symbols, order) def mkinexact(cls, K0, K1): prec = max(K0.precision, K1.precision) tol = max(K0.tolerance, K1.tolerance) return cls(prec=prec, tol=tol) if K1.is_ComplexField: K0, K1 = K1, K0 if K0.is_ComplexField: if K1.is_ComplexField or K1.is_RealField: return mkinexact(K0.__class__, K0, K1) else: return K0 if K1.is_RealField: K0, K1 = K1, K0 if K0.is_RealField: if K1.is_RealField: return mkinexact(K0.__class__, K0, K1) elif K1.is_GaussianRing or K1.is_GaussianField: from sympy.polys.domains.complexfield import ComplexField return ComplexField(prec=K0.precision, tol=K0.tolerance) else: return K0 if K1.is_AlgebraicField: K0, K1 = K1, K0 if K0.is_AlgebraicField: if K1.is_GaussianRing: K1 = K1.get_field() if K1.is_GaussianField: K1 = K1.as_AlgebraicField() if K1.is_AlgebraicField: return K0.__class__(K0.dom.unify(K1.dom), *_unify_gens(K0.orig_ext, K1.orig_ext)) else: return K0 if K0.is_GaussianField: return K0 if K1.is_GaussianField: return K1 if K0.is_GaussianRing: if K1.is_RationalField: K0 = K0.get_field() return K0 if K1.is_GaussianRing: if K0.is_RationalField: K1 = K1.get_field() return K1 if K0.is_RationalField: return K0 if K1.is_RationalField: return K1 if K0.is_IntegerRing: return K0 if K1.is_IntegerRing: return K1 if K0.is_FiniteField and K1.is_FiniteField: return K0.__class__(max(K0.mod, K1.mod, key=default_sort_key)) from sympy.polys.domains import EX return EX