def test_dmp_from_to_dict(): assert dmp_from_dict({}, 0, ZZ) == [] assert dmp_to_dict([], 0) == {} f = [3, 0, 0, 2, 0, 0, 0, 0, 8] h = {(8, ): 3, (5, ): 2, (0, ): 8} assert dmp_from_dict(h, 0, ZZ) == f assert dmp_to_dict(f, 0) == h R, x, y = ring("x,y", ZZ) f = [R(3), R(0), R(2), R(0), R(0), R(8)] h = {(5, ): R(3), (3, ): R(2), (0, ): R(8)} assert dmp_from_dict(h, 0, R) == f assert dmp_to_dict(f, 0) == h assert dmp_to_dict([1, 0, 5, 0, 7], 0) == {(0, ): 7, (2, ): 5, (4, ): 1} 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 dmp_lift(f, u, K): """ Convert algebraic coefficients to integers in ``K[X]``. Examples ======== >>> from diofant.polys import ring, QQ >>> from diofant 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.domain)
def dmp_factor_list(f, u, K0): """Factor polynomials into irreducibles in `K[X]`. """ if not u: return dup_factor_list(f, K0) J, f = dmp_terms_gcd(f, u, K0) cont, f = dmp_ground_primitive(f, u, K0) if K0.is_FiniteField: # pragma: no cover coeff, factors = dmp_gf_factor(f, u, K0) elif K0.is_Algebraic: coeff, factors = dmp_ext_factor(f, u, K0) else: if not K0.is_Exact: K0_inexact, K0 = K0, K0.get_exact() f = dmp_convert(f, u, K0_inexact, K0) else: K0_inexact = None if K0.has_Field: K = K0.get_ring() denom, f = dmp_clear_denoms(f, u, K0, K) f = dmp_convert(f, u, K0, K) else: K = K0 if K.is_ZZ: levels, f, v = dmp_exclude(f, u, K) coeff, factors = dmp_zz_factor(f, v, K) for i, (f, k) in enumerate(factors): factors[i] = (dmp_include(f, levels, v, K), k) elif K.is_Poly: f, v = dmp_inject(f, u, K) coeff, factors = dmp_factor_list(f, v, K.domain) for i, (f, k) in enumerate(factors): factors[i] = (dmp_eject(f, v, K), k) coeff = K.convert(coeff, K.domain) else: # pragma: no cover raise DomainError('factorization not supported over %s' % K0) if K0.has_Field: for i, (f, k) in enumerate(factors): factors[i] = (dmp_convert(f, u, K, K0), k) coeff = K0.convert(coeff, K) if K0_inexact is None: coeff = coeff / denom else: for i, (f, k) in enumerate(factors): f = dmp_quo_ground(f, denom, u, K0) f = dmp_convert(f, u, K0, K0_inexact) factors[i] = (f, k) coeff = K0_inexact.convert(coeff * denom**i, K0) K0 = K0_inexact for i, j in enumerate(reversed(J)): if not j: continue term = {(0, ) * (u - i) + (1, ) + (0, ) * i: K0.one} factors.insert(0, (dmp_from_dict(term, u, K0), j)) return coeff * cont, _sort_factors(factors)