def homology(self,varient="complement",*args):
hom = {}
cc = self.chain_complex(varient,(-1,self.poly_ring.ngens()+1),*args)
#Some need wider return range
for i in range(self.poly_ring.ngens()+1):
vs_am = VectorSpace(QQ,len(cc[i]))
if len(cc[i])==0:
hom[i] = []
continue
if len(cc[i-1])!=0:
d_im = []
for b in cc[i-1]:
d_b = self.differential(b,varient,*args)
d_im.append(lift_to_basis(d_b,cc[i]))
img = vs_am.subspace(d_im)
else:
img = vs_am.subspace([vs_am.zero()])
if len(cc[i+1])!=0:
d_ker = []
for b in cc[i]:
d_b = self.differential(b,varient,*args)
d_ker.append(lift_to_basis(d_b,cc[i+1]))
ker = (matrix(QQ,d_ker)).left_kernel()
else:
ker = vs_am
quo = ker.quotient(img)
hom[i] = []
for b in quo.basis():
vec = quo.lift(b)
part_sum = LogarithmicDifferentialForm.make_zero(i,self)
for c,f in zip(vec,cc[i]):
part_sum = part_sum + c*f
hom[i].append(part_sum)
return hom
def test_interior_0_form(self): x = self.x y = self.y z = self.z logdf = LogarithmicDifferentialForm(0,[x*y-y*z+x**2-z**2+x*x-y*z],self.normal_logdf) int_product = logdf.interior_product() zero = LogarithmicDifferentialForm.make_zero(0,self.normal_logdf) self.assertTrue(int_product.equals(zero))
def test_interior_0_form(self):
x = self.x
y = self.y
z = self.z
logdf = LogarithmicDifferentialForm(
0, [x * y - y * z + x**2 - z**2 + x * x - y * z],
self.normal_logdf)
int_product = logdf.interior_product()
zero = LogarithmicDifferentialForm.make_zero(0, self.normal_logdf)
self.assertTrue(int_product.equals(zero))
def test_zero_p(self):
size = [1,3,3,1]
for s,i in zip(size,range(4)):
zero = LogarithmicDifferentialForm.make_zero(i,self.normal_logdf)
zero_vec = [self.normal_logdf.poly_ring.zero() for _ in range(s)]
self.assertEqual(zero.vec,zero_vec)
def _weighted_sum(weights,forms,diff_forms):
part = LogarithmicDifferentialForm.make_zero(forms[0].degree,diff_forms)
for w,f in zip(weights,forms):
part = part + w*f
return part
def test_zero_p(self):
size = [1, 3, 3, 1]
for s, i in zip(size, range(4)):
zero = LogarithmicDifferentialForm.make_zero(i, self.normal_logdf)
zero_vec = [self.normal_logdf.poly_ring.zero() for _ in range(s)]
self.assertEqual(zero.vec, zero_vec)
