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
