def _parse_poly(f):
from sage.all import SR, QQ, HyperplaneArrangements, Matrix
if type(f) == str:
f = SR(f)
if f.base_ring() == SR:
L = f.factor_list()
K = QQ
else:
L = list(f.factor())
K = f.base_ring()
L = filter(lambda T: not T[0] in K, L) # Remove constant factors
F, M = list(zip(*L))
# Verify that each polynomial factor is linear
is_lin = lambda g: all(map(lambda x: g.degree(x) <= 1, g.variables()))
if not all(map(is_lin, F)):
raise ValueError("Expected product of linear factors.")
varbs = f.variables()
varbs_str = tuple(map(lambda x: str(x), varbs))
HH = HyperplaneArrangements(K, varbs_str)
def poly_vec(g):
c = K(g.subs({x: 0 for x in g.variables()}))
return tuple([c] + [K(g.coefficient(x)) for x in varbs])
F_vec = tuple(map(poly_vec, F))
A = HH(Matrix(K, F_vec))
# This scrambles the hyperplanes, so we need to scramble M in the same way.
A_vec = tuple(map(lambda H: tuple(H.coefficients()), A.hyperplanes()))
perm = tuple([F_vec.index(v) for v in A_vec])
M_new = tuple([M[i] for i in perm])
return A, M_new
