def test_contained_in_ambient(self):
x = self.x
y = self.y
z = self.z
smA = SingularModule([[x, y**3, z + x], [z, x, x**2]])
am = smA.ambient_free_module()
self.assertTrue(am.contains(smA))
def test_contains_combination(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Assert we contain a combination of the generorators
self.assertTrue(sm.contains([2 * x, 2 * y + z, z**3 - 2 * y + z]))
def test_contains_fail_multiple(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x**2, x * y, x * z]])
#Detect that this is not contianed even though a multiple is
self.assertFalse(sm.contains([x, y, z]))
def test_lift_linear(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
vec = sm1.lift([3 * x, 3 * y + z, z**3 - 2 * y + 2 * z], True)
self.assertEqual(vec, [1, 2])
def test_is_free(self):
x = self.x
y = self.y
zero = self.poly_ring.zero()
free = SingularModule([[x, zero, zero], [zero, y, zero],
[zero, zero, x**2]])
self.assertTrue(free.is_free())
def test_create_module_str(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, 2 * y**2, 3 * z**3]])
self.assertEqual(
sm.create_module_str("MT"),
"module MT=[1*x(1)^1,2*x(2)^2,3*x(3)^3];\n groebner(MT);\n")
def test_create_singular_free(self):
free_matrix = "MM[1,1]=1\nMM[1,2]=0\nMM[1,3]=0\n"
free_matrix = free_matrix + "MM[2,1]=0\nMM[2,2]=1\nMM[2,3]=0\n"
free_matrix = free_matrix + "MM[3,1]=0\nMM[3,2]=0\nMM[3,3]=1\n"
free_c = SingularModule.create_from_singular_matrix(
self.poly_ring, free_matrix)
free = SingularModule.create_free_module(3, self.poly_ring)
self.assertTrue(free.equals(free_c))
def test_contains_zero(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
zero = self.poly_ring.zero()
#Assert we always contain zero
self.assertTrue(sm.contains([zero, zero, zero]))
def test_contains_gen(self):
x = self.x
y = self.y
z = self.z
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Assert we contain our generators
self.assertTrue(sm.contains([x, y + z, z**3 - 2 * y]))
self.assertTrue(sm.contains([x, y, z]))
def test_2_modules_crossing_ngens(self): x = self.x y = self.y z = self.z zero = self.poly_ring.zero() crossing = self.x*self.y*self.z logdf = LogarithmicDifferentialForms(crossing) crossing_2_module = SingularModule([[z,zero,zero],[zero,y,zero],[zero,zero,x]]) self.assertTrue(crossing_2_module.equals(logdf.p_module(2)))
def test_contains_module(self):
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
smA = SingularModule([[x**2, x * y, y * z], [x, y, z]])
smB = SingularModule([[x**2 + x, x * y + y, y * z + z],
[zero, zero, y * z - x * z]])
self.assertTrue(smA.contains(smB))
def test_1_modules_crossing_ngens(self): x = self.x y = self.y z = self.z zero = self.poly_ring.zero() crossing = x*y*z logdf = LogarithmicDifferentialForms(crossing) crossing_1_module = SingularModule([[y*z,zero,zero],[zero,x*z,zero],[zero,zero,x*y]]) self.assertTrue(crossing_1_module.equals(logdf.p_module(1)))
def test_equals_not(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y, z]])
#Assert these are not equal
self.assertFalse(sm1.equals(sm2))
def test_standard_basis_irredundent(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
std_gens = sm1.standard_basis()
std_mod = SingularModule(std_gens)
self.assertTrue(sm1.equals(std_mod))
def test_equals_B(self):
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
#Assert these are equal - from crossing divisor
sm1 = SingularModule([[x, zero, zero], [zero, y, zero],
[zero, zero, z]])
sm2 = SingularModule([[zero, y, z], [zero, zero, z], [x, zero, zero]])
self.assertTrue(sm1.equals(sm2))
def test_lift_zero(self):
x = self.x
y = self.y
z = self.z
one = self.poly_ring.one()
zero = self.poly_ring.zero()
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2], [one, x, y]])
vec = sm1.lift([zero, zero, zero])
self.assertEqual(vec, [zero for _ in range(4)])
def test_equals_A(self):
x = self.x
y = self.y
z = self.z
#Assert these are equal
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y, z], [x, y + z, z**3 - 2 * y],
[x, y, z**2]])
self.assertTrue(sm1.equals(sm2))
def test_contains_fail(self):
x = self.x
y = self.y
z = self.z
one = self.poly_ring.one()
sm = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Detect that certain vectors are not contained
self.assertFalse(sm.contains([one, x, z]))
self.assertFalse(sm.contains([y, y, y]))
self.assertFalse(sm.contains([z, y, x]))
def test_ambient_free_module(self):
x = self.x
y = self.y
z = self.z
one = self.poly_ring.one()
zero = self.poly_ring.zero()
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
self.assertEqual(
sm1.ambient_free_module().gens,
[[one, zero, zero], [zero, one, zero], [zero, zero, one]])
def test_create_relationB(self):
#From an error uncovered in log derivations
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
relation = [y * z, x * z, x * y]
ideal = Ideal(self.poly_ring, [x * y * z])
mod = SingularModule.create_from_relation(relation, ideal)
true_mod = SingularModule([[x, zero, zero], [zero, y, zero],
[zero, zero, z]])
self.assertTrue(mod.equals(true_mod))
def test_create_relationA(self):
x = self.x
y = self.y
z = self.z
one = self.poly_ring.one()
zero = self.poly_ring.zero()
relation = [x**2, one + z**2, y]
ideal = Ideal(self.poly_ring, [x**2 * y - z**2])
mod = SingularModule.create_from_relation(relation, ideal)
true_mod = SingularModule([[one, -x**2, x**4], [zero, y, -z**2 - 1],
[zero, z**2, -x**2 * z**2 - x**2],
[zero, zero, x**2 * y - z**2]])
self.assertTrue(mod.equals(true_mod))
def test_intersect(self):
x = self.x
y = self.y
z = self.z
smA = SingularModule([[x, y**3, z + x], [z, x, x**2]])
smB = SingularModule([[z, y, x], [-z, x**2, 4 * y + z]])
smI = smA.intersection(smB)
gen_1_1 = x**5 * z + x * y**3 * z**2 + 4 * y**4 * z**2 + y**3 * z**3 + x**3 * y * z - x**3 * z**2 - x**2 * z**3 - x**3 * z - 4 * x**2 * y * z - x**2 * z**2 - x * y * z**2 - y * z**3
gen_2_1 = x**4 * y**3 * z - x**3 * y**3 * z + x**2 * y**4 * z + 4 * y**5 * z + y**4 * z**2 + x**5 - x**4 * z - x**3 * z**2 - 4 * x**2 * y**2 - 2 * x**2 * y * z - x * y * z**2
gen_3_1 = x**3 * y**3 * z - x**3 * y * z + 4 * x**2 * y**4 * z + x**2 * y**3 * z**2 + x**6 - 4 * x**3 * y**2 - x**4 * z - x**3 * z**2 - x**3 * z - 4 * x**2 * y * z + 4 * x * y**2 * z - 2 * x**2 * z**2 - 3 * x * y * z**2 + 4 * y**2 * z**2 - x * z**3 + y * z**3
gens = [[gen_1_1, gen_2_1, gen_3_1]]
#Test this example
self.assertEqual(gens, smI.gens)
def __init__(self, divisor):
self.divisor = divisor
poly_ring = divisor.parent()
#Compute gen set
rel = [poly_ring.zero() for _ in range(poly_ring.ngens())]
for _, mon in divisor:
exp = mon.exponents()[0]
for i in range(poly_ring.ngens()):
rel[i] = rel[i] + exp[i] * mon // poly_ring.gens()[i]
ideal = Ideal(poly_ring, [divisor])
base_mod = SingularModule.create_from_relation(rel, ideal)
SingularModule.__init__(self, base_mod.gens)
self.relation = rel
def __init__(self,divisor):
self.divisor = divisor
poly_ring = divisor.parent()
#Compute gen set
rel = [poly_ring.zero() for _ in range(poly_ring.ngens())]
for _,mon in divisor:
exp = mon.exponents()[0]
for i in range(poly_ring.ngens()):
rel[i] = rel[i] + exp[i]*mon//poly_ring.gens()[i]
ideal = Ideal(poly_ring,[divisor])
base_mod = SingularModule.create_from_relation(rel,ideal)
SingularModule.__init__(self,base_mod.gens)
self.relation = rel
def test_lift_satisfy(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
vec = sm1.lift([
x**2 + x * z + x, x * y + x * z + y * z + y,
z**3 * x - 2 * y * x + z**2 + z
])
self.assertEqual(vec[0] * x + vec[1] * x, x**2 + x * z + x)
self.assertEqual(vec[0] * (y + z) + vec[1] * y,
x * y + x * z + y * z + y)
self.assertEqual(vec[0] * (z**3 - 2 * y) + vec[1] * z,
z**3 * x - 2 * y * x + z**2 + z)
def _compute_1_form_generators(self):
rels = _log_1_form_rels(self.divisor)
ideals = [[self.divisor]*self.poly_ring for _ in range(len(rels))]
self._p_modules[1] = SingularModule.create_from_relations(rels,ideals);
self._p_gens[1] = []
for g in self._p_modules[1].gens:
self._p_gens[1].append(LogarithmicDifferentialForm(1,g,self))
def test_creation(self):
x = self.x
y = self.y
z = self.z
SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z]])
#Check this did cause an error
self.assertTrue(True)
def lift_to_basis(form,basis,make_linear=False):
graded_basis = {}
poly_ring = basis[0].diff_forms.poly_ring
lift = [poly_ring.zero() for _ in basis]
for i,b in enumerate(basis):
if b.degree in graded_basis.keys():
graded_basis[b.degree].append((i,b))
else:
graded_basis[b.degree] = [(i,b)]
for f in form:
if f.degree in graded_basis.keys():
g_part = graded_basis[f.degree]
b_mod = SingularModule([b.vec for _,b in g_part])
res = b_mod.lift(f.vec,make_linear)
for i,c in enumerate(res):
lift[g_part[i][0]] = c
return lift
def test_reduce_lossless(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2.reduce_generators()
self.assertTrue(sm1.equals(sm2))
def test_create_relation_satisfy_A(self):
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
relation = [x + x**4 - y, (y + z)**3, -2 * y + self.poly_ring.one()]
ideal = Ideal(self.poly_ring, [x**2 * y - z**2])
mod = SingularModule.create_from_relation(relation, ideal)
for gen in mod.gens:
sum = zero
for g, rel in zip(gen, relation):
sum = sum + g * rel
self.assertTrue(sum in ideal)
def test_intersect_contains(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y**2, z**3]])
#Assert the intersection is contained in both modules
gens = (sm1.intersection(sm2)).gens
for gen in gens:
self.assertTrue(sm1.contains(gen))
for gen in gens:
self.assertTrue(sm2.contains(gen))
def test_intersection_symetry(self):
x = self.x
y = self.y
z = self.z
sm1 = SingularModule([[x, y + z, z**3 - 2 * y], [x, y, z],
[x, y, z**2]])
sm2 = SingularModule([[x, y**2, z**3]])
sm_1_2 = sm1.intersection(sm2)
sm_2_1 = sm2.intersection(sm1)
#Assert that equals is symetric
self.assertTrue(sm_1_2.equals(sm_2_1))
def test_create_relations_satisfy(self):
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
relations = [[x**2, z * y], [y**2, -x]]
ideals = [
Ideal(self.poly_ring, [x**2 * y - z**2]),
Ideal(self.poly_ring, [x * y - z])
]
mod = SingularModule.create_from_relations(relations, ideals)
for relation, ideal in zip(relations, ideals):
for gen in mod.gens:
sum = zero
for g, rel in zip(gen, relation):
sum = sum + g * rel
self.assertTrue(sum in ideal)
def test_create_singular(self):
out = "mat_inter[1,1]=0\n"
out = out + "mat_inter[1,2]=0\n"
out = out + "mat_inter[1,3]=x(1)*x(2)*x(3)\n"
out = out + "mat_inter[2,1]=x(2)\n"
out = out + "mat_inter[2,2]=0\n"
out = out + "mat_inter[2,3]=0\n"
out = out + "mat_inter[3,1]=-x(3)\n"
out = out + "mat_inter[3,2]=x(3)\n"
out = out + "mat_inter[3,3]=0\n"
mod = SingularModule.create_from_singular_matrix(
self.poly_ring, out, "mat_inter")
x = self.x
y = self.y
z = self.z
zero = self.poly_ring.zero()
mod_true = [[zero, y, -z], [zero, zero, z], [x * y * z, zero, zero]]
self.assertEqual(mod.gens, mod_true)
def __init__(self,gens,column_wieghts,var_wieghts): SingularModule.__init__(self,gens) self.column_wieghts = column_wieghts self.var_wieghts = var_wieghts
def test_3_modules_crossing_ngens(self): crossing = self.x*self.y*self.z logdf = LogarithmicDifferentialForms(crossing) crossing_3_module = SingularModule([[self.poly_ring.one()]]) self.assertTrue(crossing_3_module.equals(logdf.p_module(3)))
def test_0_modules_crossing_ngens(self): crossing = self.x*self.y*self.z logdf = LogarithmicDifferentialForms(crossing) crossing_0_module = SingularModule([[crossing]]) self.assertTrue(crossing_0_module.equals(logdf.p_module(0)))
