def test_dmp_from_to_dict(): assert dmp_from_dict({}, 1, ZZ) == [[]] assert dmp_to_dict([[]], 1) == {} f = [[3],[],[],[2],[],[],[],[],[8]] g = {(8,0): 3, (5,0): 2, (0,0): 8} assert dmp_from_dict(g, 1, ZZ) == f assert dmp_to_dict(f, 1) == g
def test_dmp_from_to_dict(): assert dmp_from_dict({}, 1, ZZ) == [[]] assert dmp_to_dict([[]], 1) == {} f = [[3], [], [], [2], [], [], [], [], [8]] g = {(8, 0): 3, (5, 0): 2, (0, 0): 8} assert dmp_from_dict(g, 1, ZZ) == f assert dmp_to_dict(f, 1) == g
def test_dmp_from_to_dict(): assert dmp_from_dict({}, 1, ZZ) == [[]] assert dmp_to_dict([[]], 1) == {} assert dmp_to_dict([], 0, ZZ, zero=True) == {(0,): ZZ(0)} assert dmp_to_dict([[]], 1, ZZ, zero=True) == {(0,0): ZZ(0)} f = [[3],[],[],[2],[],[],[],[],[8]] g = {(8,0): 3, (5,0): 2, (0,0): 8} assert dmp_from_dict(g, 1, ZZ) == f assert dmp_to_dict(f, 1) == g
def to_sympy_dict(f, zero=False): """Convert `f` to a dict representation with SymPy coefficients. """ rep = dmp_to_dict(f.rep, f.lev, f.dom, zero=zero) for k, v in rep.iteritems(): rep[k] = f.dom.to_sympy(v) return rep
def to_sympy_dict(f): """Convert ``f`` to a dict representation with SymPy coefficients. """ rep = dmp_to_dict(f.rep, 0, f.dom) for k, v in rep.iteritems(): rep[k] = f.dom.to_sympy(v) return rep
def dmp_lift(f, u, K): """ Convert algebraic coefficients to integers in ``K[X]``. Examples ======== >>> from sympy.polys import ring, QQ >>> from sympy import I >>> K = QQ.algebraic_field(I) >>> R, x = ring("x", K) >>> f = x**2 + K([QQ(1), QQ(0)])*x + K([QQ(2), QQ(0)]) >>> R.dmp_lift(f) x**8 + 2*x**6 + 9*x**4 - 8*x**2 + 16 """ if K.is_GaussianField: K1 = K.as_AlgebraicField() f = dmp_convert(f, u, K, K1) K = K1 if not K.is_Algebraic: raise DomainError( 'computation can be done only in an algebraic domain') F, monoms, polys = dmp_to_dict(f, u), [], [] for monom, coeff in F.items(): if not coeff.is_ground: monoms.append(monom) perms = variations([-1, 1], len(monoms), repetition=True) for perm in perms: G = dict(F) for sign, monom in zip(perm, monoms): if sign == -1: G[monom] = -G[monom] polys.append(dmp_from_dict(G, u, K)) return dmp_convert(dmp_expand(polys, u, K), u, K, K.dom)
def dmp_lift(f, u, K): """ Convert algebraic coefficients to integers in ``K[X]``. Examples ======== >>> from sympy.polys import ring, QQ >>> from sympy import I >>> K = QQ.algebraic_field(I) >>> R, x = ring("x", K) >>> f = x**2 + K([QQ(1), QQ(0)])*x + K([QQ(2), QQ(0)]) >>> R.dmp_lift(f) x**8 + 2*x**6 + 9*x**4 - 8*x**2 + 16 """ if not K.is_Algebraic: raise DomainError( 'computation can be done only in an algebraic domain') F, monoms, polys = dmp_to_dict(f, u), [], [] for monom, coeff in F.items(): if not coeff.is_ground: monoms.append(monom) perms = variations([-1, 1], len(monoms), repetition=True) for perm in perms: G = dict(F) for sign, monom in zip(perm, monoms): if sign == -1: G[monom] = -G[monom] polys.append(dmp_from_dict(G, u, K)) return dmp_convert(dmp_expand(polys, u, K), u, K, K.dom)
def dmp_lift(f, u, K): """ Convert algebraic coefficients to integers in ``K[X]``. Examples ======== >>> from sympy import I >>> from sympy.polys.domains import QQ >>> from sympy.polys.densetools import dmp_lift >>> K = QQ.algebraic_field(I) >>> f = [K(1), K([QQ(1), QQ(0)]), K([QQ(2), QQ(0)])] >>> dmp_lift(f, 0, K) [1/1, 0/1, 2/1, 0/1, 9/1, 0/1, -8/1, 0/1, 16/1] """ if not K.is_Algebraic: raise DomainError( 'computation can be done only in an algebraic domain') F, monoms, polys = dmp_to_dict(f, u), [], [] for monom, coeff in F.iteritems(): if not coeff.is_ground: monoms.append(monom) perms = variations([-1, 1], len(monoms), repetition=True) for perm in perms: G = dict(F) for sign, monom in zip(perm, monoms): if sign == -1: G[monom] = -G[monom] polys.append(dmp_from_dict(G, u, K)) return dmp_convert(dmp_expand(polys, u, K), u, K, K.dom)
def is_quadratic(f): """Returns `True` if `f` is quadratic in all its variables. """ return all([ sum(monom) <= 2 for monom in dmp_to_dict(f.rep, f.lev, f.dom).keys() ])
def is_linear(f): """Returns `True` if `f` is linear in all its variables. """ return all([ sum(monom) <= 1 for monom in dmp_to_dict(f.rep, f.lev, f.dom).keys() ])
def to_dict(f): """Convert `f` to a dict representation with native coefficients. """ return dmp_to_dict(f.rep, 0, f.dom)
def to_dict(f, zero=False): """Convert `f` to a dict representation with native coefficients. """ return dmp_to_dict(f.rep, f.lev, f.dom, zero=zero)