def test_buchberger_2(self):
"""
Example from paper
On computer algebra application to
simulation of quantum computation
p.14 lex-order
"""
a1, a2, a3, x1, x2, x3, x4, b1, b2, b3 = self.B.gens
F = [
x3 + x2 * x4 + b1,
x2 + b2,
x4 + b3,
a1 * x1 + a2 * x2 + x1 * x3 + a3 * x4 + x1 * x2 * x4,
]
G = buchberger(F, self.B)
G_assert = [
x2 + b2,
x4 + b3,
a1 * x1 + a2 * b2 + a3 * b3 + x1 * b1,
x3 + b1 + b2 * b3,
]
self.assertTrue(len(G) > 0)
self.assertTrue(len(G_assert) > 0)
def sat_groebner(P, ring):
res = gb.buchberger(P, ring)
if res == [Poly.one]:
print('UNSAT')
else:
print('SAT')
def test_buchberger_3(self):
x1, x2 = self.B.gens[:2]
F = [x1 * x2 + x1, x1 * x2 + x2]
G = buchberger(F, self.B)
G_assert = [x1 + x2]
for p in G:
self.assertTrue(p in G_assert)
def test_buchberger_6(self):
x, y, z = self.B.gens[:3]
F = [x * z + y * z + z, x * y + x * z + x + y * z + y + z]
G = buchberger(F, self.B)
G_assert = [x, y, z]
self.assertTrue(len(G) == len(G_assert))
for p in G:
self.assertTrue(p in G_assert)
def test_buchberger_5(self):
"""
Example from Sage Boolean Polynomials Documentation
"""
x0, x1, x2, x3 = self.B.gens[:4]
F = [x0 * x1 * x2 * x3 + x0 * x1 * x3 + x0 * x1 + x0 * x2 + x0]
G = buchberger(F, self.B)
G_assert = [x0 * x1 + x0 * x2 + x0, x0 * x2 * x3 + x0 * x3]
self.assertTrue(len(G) == len(G_assert))
for p in G:
self.assertTrue(p in G_assert)
def test_buchberger_7(self):
"""
Basis should be equal 1
"""
x1, x2, x3 = self.B.gens[:3]
_1 = self.B.one
F = [
x1 * x2 * x3, x1 * x2 * x3 + x1 * x2, x1 * x2 * x3 + x1 * x3,
x1 * x2 * x3 + x1 * x2 + x1 * x3 + x1, x1 * x2 * x3 + x2 * x3,
x1 * x2 * x3 + x1 * x2 + x2 * x3 + x2,
x1 * x2 * x3 + x1 * x3 + x2 * x3 + x3,
x1 * x2 * x3 + x1 * x2 + x1 * x3 + x1 + x2 * x3 + x2 + x3 + _1
]
G = buchberger(F, self.B)
self.assertTrue(len(G) == 1)
self.assertTrue(G[0].isOne())
def test_buchberger_4(self):
x1, x2, x3, x4 = self.B.gens[:4]
_1 = self.B.one
F = [
x1 * x2 * x3 + x1 * x2 + x2 * x3 + x2, x2 * x3 + x2 + x3 + _1,
x1 * x2 + x1, x1 * x4
]
G = buchberger(F, self.B)
G_assert = [
x1 * x2 + x1, x1 * x3 + x1 + x3 + _1, x1 * x4,
x2 * x3 + x2 + x3 + _1, x3 * x4 + x4
]
self.assertTrue(len(G) == len(G_assert))
for p in G:
self.assertTrue(p in G_assert)
def test_buchberger_1(self):
"""
Example from SAGE documentation
for boolean polynomials
"""
x0, x1, x2, x3 = self.B.gens[:4]
_1 = self.B.one
F = [
x0 + x1 + x2 + x3, x0 * x1 + x1 * x2 + x0 * x3 + x2 * x3,
x0 * x1 * x2 + x0 * x1 * x3 + x0 * x2 * x3 + x1 * x2 * x3,
x0 * x1 * x2 * x3 + _1
]
G = buchberger(F, self.B)
G_assert = [x0 + _1, x1 + _1, x2 + _1, x3 + _1]
for p in G:
self.assertTrue(p in G_assert)
