def linearly_indep_tuples(self):
bd = PrecisionDeg2(self.strum_bound())
dim = self.dimension()
tpls = sorted(bd.group_by_reduced_forms().keys(),
key=lambda x: (x[0] + x[2], max(x[0], x[2])))
ml = [[f[t] for f in self.basis()] for t in tpls]
idcs = linearly_indep_rows_index_list(ml, dim)
return [tpls[i] for i in idcs]
def _linearly_indep_tuples_of_given_bd(self, bd):
basis = self.basis()
dim = self.dimension()
if is_number(bd):
bd = list(PrecisionDeg2(bd))
tpls = sorted(list(bd), key=lambda x: (x[0] + x[2], max(x[0], x[2])))
tpls_w_idx = reduce(operator.add,
[[(t, i) for i in range(self.sym_wt + 1)]
for t in tpls], [])
ml = [[f.forms[i][t] for f in basis] for t, i in tpls_w_idx]
index_list = linearly_indep_rows_index_list(ml, dim)
res = [tpls_w_idx[i] for i in index_list]
return res
def test_lin_indep(self):
A = [[1, 0, 0], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1]]
self.assertEqual(linearly_indep_rows_index_list(A, 3), [0, 3, 5])
A = [[1, 0], [0, 0], [1, 0], [0, 1]]
self.assertEqual(linearly_indep_rows_index_list(A, 2), [0, 3])
