def test__get_bidegree(self):
m, n = 3, 5
mon_lst = SERing.get_mon_P1xP1(m, n)
assert SERing.get_bidegree(mon_lst) == (3, 5)
mat = SERing.random_matrix_QQ(4, len(mon_lst))
pol_lst = list(mat * sage_vector(mon_lst))
assert SERing.get_bidegree(pol_lst) == (3, 5)
))
L = ring('[2, -1/3, -5, 1/3]')
R = ring('[0, 10, -3, 0]')
mon_lst = SERing.get_mon_P1xP1(d1, d2,
vars='y0,y1,y2,y3') # basis for monomials
y = [ring('y' + str(i)) for i in range(4)]
s = {
y[0]: L[0] * y[0] + L[1] * y[1],
y[1]: L[2] * y[0] + L[3] * y[1],
y[2]: R[0] * y[2] + R[1] * y[3],
y[3]: R[2] * y[2] + R[3] * y[3]
}
f = list(matf * sage_vector(mon_lst))
g = list(matU * sage_vector([comp.subs(s) for comp in f]))
assert set(SERing.get_bidegree(f)) == set(SERing.get_bidegree(g))
SETools.p('case =', case)
SETools.p('(d1,d2,m) =', (d1, d2, m))
SETools.p('matf =', list(matf))
SETools.p('matU =', list(matU))
SETools.p('L =', L)
SETools.p('R =', R)
SETools.p('f =', f)
SETools.p('g =', g)
###############################################################################
# From here on we demonstrate how to recover L, U and matU from f and g only. #
###############################################################################
SETools.p('Recover (matU, L, R) from (f, g)...')
y = [ring('y' + str(i)) for i in range(4)]