def is_minimal(G, u, O, K):
"""
Checks if G is a minimal Groebner basis.
"""
G.sort(key=lambda g: O(sdp_LM(g, u)))
for i, g in enumerate(G):
if sdp_LC(g, K) != K.one:
return False
for h in G[:i] + G[i + 1 :]:
if monomial_divides(sdp_LM(g, u), sdp_LM(h, u)):
return False
return True
def is_minimal(G, u, O, K):
"""
Checks if G is a minimal Groebner basis.
"""
G.sort(key=lambda g: O(sdp_LM(g, u)))
for i, g in enumerate(G):
if sdp_LC(g, K) != K.one:
return False
for h in G[:i] + G[i + 1:]:
if monomial_divides(sdp_LM(g, u), sdp_LM(h, u)):
return False
return True
def test_sdp_LC():
assert sdp_LC([], QQ) == QQ(0)
assert sdp_LC([((1, 0), QQ(1, 2))], QQ) == QQ(1, 2)
assert sdp_LC([((1, 1), QQ(1, 4)), ((1, 0), QQ(1, 2))], QQ) == QQ(1, 4)