def _construct_algebraic(coeffs, opt): """We know that coefficients are algebraic so construct the extension. """ from sympy.polys.numberfields import primitive_element result, exts = [], set([]) for coeff in coeffs: if coeff.is_Rational: coeff = (None, 0, QQ.from_sympy(coeff)) else: a = coeff.as_coeff_add()[0] coeff -= a b = coeff.as_coeff_mul()[0] coeff /= b exts.add(coeff) a = QQ.from_sympy(a) b = QQ.from_sympy(b) coeff = (coeff, b, a) result.append(coeff) exts = list(exts) g, span, H = primitive_element(exts, ex=True, polys=True) root = sum([s * ext for s, ext in zip(span, exts)]) domain, g = QQ.algebraic_field((g, root)), g.rep.rep for i, (coeff, a, b) in enumerate(result): if coeff is not None: coeff = a * domain.dtype.from_list(H[exts.index(coeff)], g, QQ) + b else: coeff = domain.dtype.from_list([b], g, QQ) result[i] = coeff return domain, result
def _construct_algebraic(coeffs, opt): """We know that coefficients are algebraic so construct the extension. """ from sympy.polys.numberfields import primitive_element result, exts = [], set([]) for coeff in coeffs: if coeff.is_Rational: coeff = (None, 0, QQ.from_sympy(coeff)) else: a = coeff.as_coeff_add()[0] coeff -= a b = coeff.as_coeff_mul()[0] coeff /= b exts.add(coeff) a = QQ.from_sympy(a) b = QQ.from_sympy(b) coeff = (coeff, b, a) result.append(coeff) exts = list(exts) g, span, H = primitive_element(exts, ex=True, polys=True) root = sum([ s*ext for s, ext in zip(span, exts) ]) domain, g = QQ.algebraic_field((g, root)), g.rep.rep for i, (coeff, a, b) in enumerate(result): if coeff is not None: coeff = a*domain.dtype.from_list(H[exts.index(coeff)], g, QQ) + b else: coeff = domain.dtype.from_list([b], g, QQ) result[i] = coeff return domain, result
def build_trees(args): trees = [] for a in args: if a.is_Rational: tree = ('Q', QQ.from_sympy(a)) elif a.is_Add: tree = ('+', build_trees(a.args)) elif a.is_Mul: tree = ('*', build_trees(a.args)) else: tree = ('e', a) exts.add(a) trees.append(tree) return trees