def _construct_composite(coeffs, opt): """Handle composite domains, e.g.: ZZ[X], QQ[X], ZZ(X), QQ(X). """ numers, denoms = [], [] for coeff in coeffs: numer, denom = coeff.as_numer_denom() numers.append(numer) denoms.append(denom) try: polys, gens = parallel_dict_from_basic(numers + denoms) # XXX: sorting except GeneratorsNeeded: return None if any(gen.is_number for gen in gens): return None # generators are number-like so lets better use EX n = len(gens) k = len(polys)//2 numers = polys[:k] denoms = polys[k:] if opt.field: fractions = True else: fractions, zeros = False, (0,)*n for denom in denoms: if len(denom) > 1 or zeros not in denom: fractions = True break coeffs = set([]) if not fractions: for numer, denom in zip(numers, denoms): denom = denom[zeros] for monom, coeff in numer.iteritems(): coeff /= denom coeffs.add(coeff) numer[monom] = coeff else: for numer, denom in zip(numers, denoms): coeffs.update(numer.values()) coeffs.update(denom.values()) rationals, reals = False, False for coeff in coeffs: if coeff.is_Rational: if not coeff.is_Integer: rationals = True elif coeff.is_Float: reals = True break if reals: ground = RR elif rationals: ground = QQ else: ground = ZZ result = [] if not fractions: domain = ground.poly_ring(*gens) for numer in numers: for monom, coeff in numer.iteritems(): numer[monom] = ground.from_sympy(coeff) result.append(domain(numer)) else: domain = ground.frac_field(*gens) for numer, denom in zip(numers, denoms): for monom, coeff in numer.iteritems(): numer[monom] = ground.from_sympy(coeff) for monom, coeff in denom.iteritems(): denom[monom] = ground.from_sympy(coeff) result.append(domain((numer, denom))) return domain, result
def _construct_composite(coeffs, opt): """Handle composite domains, e.g.: ZZ[X], QQ[X], ZZ(X), QQ(X). """ numers, denoms = [], [] for coeff in coeffs: numer, denom = coeff.as_numer_denom() numers.append(numer) denoms.append(denom) polys, gens = parallel_dict_from_basic(numers + denoms) # XXX: sorting if not gens: return None if opt.composite is None: if any(gen.is_number and gen.is_algebraic for gen in gens): return None # generators are number-like so lets better use EX all_symbols = set([]) for gen in gens: symbols = gen.free_symbols if all_symbols & symbols: return None # there could be algebraic relations between generators else: all_symbols |= symbols n = len(gens) k = len(polys)//2 numers = polys[:k] denoms = polys[k:] if opt.field: fractions = True else: fractions, zeros = False, (0,)*n for denom in denoms: if len(denom) > 1 or zeros not in denom: fractions = True break coeffs = set([]) if not fractions: for numer, denom in zip(numers, denoms): denom = denom[zeros] for monom, coeff in numer.items(): coeff /= denom coeffs.add(coeff) numer[monom] = coeff else: for numer, denom in zip(numers, denoms): coeffs.update(list(numer.values())) coeffs.update(list(denom.values())) rationals, reals = False, False for coeff in coeffs: if coeff.is_Rational: if not coeff.is_Integer: rationals = True elif coeff.is_Float: reals = True break if reals: max_prec = max([c._prec for c in coeffs]) ground = RealField(prec=max_prec) elif rationals: ground = QQ else: ground = ZZ result = [] if not fractions: domain = ground.poly_ring(*gens) for numer in numers: for monom, coeff in numer.items(): numer[monom] = ground.from_sympy(coeff) result.append(domain(numer)) else: domain = ground.frac_field(*gens) for numer, denom in zip(numers, denoms): for monom, coeff in numer.items(): numer[monom] = ground.from_sympy(coeff) for monom, coeff in denom.items(): denom[monom] = ground.from_sympy(coeff) result.append(domain((numer, denom))) return domain, result
def _construct_composite(coeffs, opt): """Handle composite domains, e.g.: ZZ[X], QQ[X], ZZ(X), QQ(X). """ numers, denoms = [], [] for coeff in coeffs: numer, denom = coeff.as_numer_denom() numers.append(numer) denoms.append(denom) polys, gens = parallel_dict_from_basic(numers + denoms) # XXX: sorting if not gens: return None if opt.composite is None: if any(gen.is_number and gen.is_algebraic for gen in gens): return None # generators are number-like so lets better use EX all_symbols = set([]) for gen in gens: symbols = gen.free_symbols if all_symbols & symbols: return None # there could be algebraic relations between generators else: all_symbols |= symbols n = len(gens) k = len(polys) // 2 numers = polys[:k] denoms = polys[k:] if opt.field: fractions = True else: fractions, zeros = False, (0, ) * n for denom in denoms: if len(denom) > 1 or zeros not in denom: fractions = True break coeffs = set([]) if not fractions: for numer, denom in zip(numers, denoms): denom = denom[zeros] for monom, coeff in numer.items(): coeff /= denom coeffs.add(coeff) numer[monom] = coeff else: for numer, denom in zip(numers, denoms): coeffs.update(list(numer.values())) coeffs.update(list(denom.values())) rationals, reals = False, False for coeff in coeffs: if coeff.is_Rational: if not coeff.is_Integer: rationals = True elif coeff.is_Float: reals = True break if reals: max_prec = max([c._prec for c in coeffs]) ground = RealField(prec=max_prec) elif rationals: ground = QQ else: ground = ZZ result = [] if not fractions: domain = ground.poly_ring(*gens) for numer in numers: for monom, coeff in numer.items(): numer[monom] = ground.from_sympy(coeff) result.append(domain(numer)) else: domain = ground.frac_field(*gens) for numer, denom in zip(numers, denoms): for monom, coeff in numer.items(): numer[monom] = ground.from_sympy(coeff) for monom, coeff in denom.items(): denom[monom] = ground.from_sympy(coeff) result.append(domain((numer, denom))) return domain, result