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Update aplK.py

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calquezar 2024-08-18 13:05:23 +02:00
parent ca4194694c
commit ff67beab63
1 changed files with 24 additions and 14 deletions
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aplK.py
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@ -168,6 +168,7 @@ class AplN(DifferentialGCAlgebra_multigraded, UniqueRepresentation):
for k in self.homogeneous_parts() if list(k)[0] == degree] for k in self.homogeneous_parts() if list(k)[0] == degree]
return self.parent()(sum(parts)) return self.parent()(sum(parts))
#@cached_function
def reduce(self, relations=[]): def reduce(self, relations=[]):
"""" """"
The method reduces the polynomial by the Ideal <sum(t_i)-1, sum(y_j)> The method reduces the polynomial by the Ideal <sum(t_i)-1, sum(y_j)>
@ -350,7 +351,7 @@ class AplN(DifferentialGCAlgebra_multigraded, UniqueRepresentation):
else: else:
return w+theta.primitive() return w+theta.primitive()
@cached_function
def AlgebraPL(n): def AlgebraPL(n):
""" """
The graded commutative differential cochain algebra Apl of dimension ``n`` The graded commutative differential cochain algebra Apl of dimension ``n``
@ -435,7 +436,8 @@ class SimplicialAplN(AplN, UniqueRepresentation):
yImages.append(codomain.gens()[n+k-2]) yImages.append(codomain.gens()[n+k-2])
images = tImages+yImages images = tImages+yImages
return domain.hom(codomain=codomain, im_gens=images) return domain.hom(codomain=codomain, im_gens=images)
@cached_method
def face(self, i): def face(self, i):
"""" """"
@ -505,7 +507,8 @@ class SimplicialAplN(AplN, UniqueRepresentation):
- A polynomial that is the degeneration 'j' of self - A polynomial that is the degeneration 'j' of self
""" """
return self.degeneration_morphism(j)(self) return self.degeneration_morphism(j)(self)
#@cached_function
def propagate(self, face_list, dest_dim): def propagate(self, face_list, dest_dim):
""" """
Returns a polynomial in dimension 'dest_dim' that has 'self' as a face Returns a polynomial in dimension 'dest_dim' that has 'self' as a face
@ -648,7 +651,7 @@ class SimplicialAplN(AplN, UniqueRepresentation):
sol = Mdif.solve_right(v) sol = Mdif.solve_right(v)
return sum(map(lambda x, y: x*y, sol, primitive_basis)) return sum(map(lambda x, y: x*y, sol, primitive_basis))
@cached_function
def SimplicialAlgebraplN(n): def SimplicialAlgebraplN(n):
""" """
Returns the graded commutative differential cochain algebra (Apl)_n as part of Returns the graded commutative differential cochain algebra (Apl)_n as part of
@ -749,6 +752,7 @@ class AlgebraAplK(UniqueRepresentation, Parent):
""" """
return [tuple(e) for e in Set(simplex).subsets(length)] return [tuple(e) for e in Set(simplex).subsets(length)]
@cached_function
def zero(self): def zero(self):
""" """
Returns the zero element of the algebra Returns the zero element of the algebra
@ -828,10 +832,12 @@ class AlgebraAplK(UniqueRepresentation, Parent):
pol.propagate(face_indexes, dim) pol.propagate(face_indexes, dim)
return propagation return propagation
@cached_function
def cohomology_gens(self, degree): def cohomology_gens(self, degree):
""" """
Returns the cohomolosy generators of a given degree Returns the cohomolosy generators of a given degree
""" """
print("Cohomology_gens, degree " + str(degree), flush=True)
gens = {} gens = {}
basis = self.K.cohomology_ring(QQ).basis() basis = self.K.cohomology_ring(QQ).basis()
for k in basis.keys(): for k in basis.keys():
@ -839,7 +845,9 @@ class AlgebraAplK(UniqueRepresentation, Parent):
gens[k] = basis[k] gens[k] = basis[k]
return gens return gens
@cached_function
def cohomology_group(self, n): def cohomology_group(self, n):
print("Cohomology_group, degree " + str(n), flush=True)
chainComplex = self.K.chain_complex(base_ring=QQ) chainComplex = self.K.chain_complex(base_ring=QQ)
cochainComplex = chainComplex.dual() cochainComplex = chainComplex.dual()
Hn = cochainComplex.differential(n).right_kernel( Hn = cochainComplex.differential(n).right_kernel(
@ -890,7 +898,7 @@ class AlgebraAplK(UniqueRepresentation, Parent):
cochain_vector = self.cochain_to_vector(cochain, dim) cochain_vector = self.cochain_to_vector(cochain, dim)
cochainComplex = self.K.chain_complex(base_ring=QQ).dual() cochainComplex = self.K.chain_complex(base_ring=QQ).dual()
diff = cochainComplex.differential(dim-1) diff = cochainComplex.differential(dim-1)
show(diff.echelon_form()) #show(diff.echelon_form())
result = diff.solve_right(cochain_vector) result = diff.solve_right(cochain_vector)
return self.vector_to_cochain(result) return self.vector_to_cochain(result)
@ -908,12 +916,14 @@ class AlgebraAplK(UniqueRepresentation, Parent):
cochain[i[0].tuple()] = i[1] cochain[i[0].tuple()] = i[1]
return cochain return cochain
@cached_function
def get_cohomology_aplk(self, degree): def get_cohomology_aplk(self, degree):
""" """
Returns a set of representative elements of Apl(K), one for each cohomology generator of a given degree Returns a set of representative elements of Apl(K), one for each cohomology generator of a given degree
""" """
#print("Cohomology_aplk, degree " + str(degree), flush=True)
representative_aplk_elements = {} representative_aplk_elements = {}
dic_gens = self.cohomology_gens(degree) dic_gens = self.cohomology_gens(self,degree)
for key in dic_gens.keys(): for key in dic_gens.keys():
gen = dic_gens[key] gen = dic_gens[key]
cochain = self.lift_cohomology_generator(gen) cochain = self.lift_cohomology_generator(gen)
@ -1158,11 +1168,11 @@ class AlgebraAplK(UniqueRepresentation, Parent):
dim = S.dimension() dim = S.dimension()
min_dim = self.degree() min_dim = self.degree()
for n in reversed(range(min_dim, dim+1)): for n in reversed(range(min_dim, dim+1)):
#print("Primitive Basis: Working on dimension " + str(n), flush=True) print("Primitive Basis: Working on dimension " + str(n), flush=True)
cells_sorted = S._n_cells_sorted(n) cells_sorted = S._n_cells_sorted(n)
for simplex in cells_sorted: for simplex in cells_sorted:
#print("Primitive Basis: Working on simplex " + str(simplex), flush=True) #print("Primitive Basis: Working on simplex " + str(simplex), flush=True)
print("simplex "+str(simplex)+ " is at position " +str(cells_sorted.index(simplex)) + " out of " + str(len(cells_sorted)), flush=True) #print("simplex "+str(simplex)+ " is at position " +str(cells_sorted.index(simplex)) + " out of " + str(len(cells_sorted)), flush=True)
if simplex.tuple() not in primitive_basis.keys(): if simplex.tuple() not in primitive_basis.keys():
primitive_basis[simplex.tuple()] = [] primitive_basis[simplex.tuple()] = []
# add primitive elements related to the assigned polynomial # add primitive elements related to the assigned polynomial
@ -1271,7 +1281,7 @@ class AlgebraAplK(UniqueRepresentation, Parent):
v_index = differentials.index(term) v_index = differentials.index(term)
v[offset + v_index] = dic[monomial] v[offset + v_index] = dic[monomial]
offset += len(differentials) offset += len(differentials)
print("Vector diff coordinates: offset " + str(offset), flush=True) #print("Vector diff coordinates: offset " + str(offset), flush=True)
return v return v
def _get_offsets_matrix(self, p_basis): def _get_offsets_matrix(self, p_basis):
@ -1328,10 +1338,10 @@ class AlgebraAplK(UniqueRepresentation, Parent):
dim = S.dimension() dim = S.dimension()
min_dim = self.degree() min_dim = self.degree()
for n in reversed(range(min_dim, dim+1)): for n in reversed(range(min_dim, dim+1)):
#print("Face matrix: Working on dimension " + str(n), flush=True) print("Face matrix: Working on dimension " + str(n), flush=True)
cells_sorted = S._n_cells_sorted(n) cells_sorted = S._n_cells_sorted(n)
for simplex in cells_sorted: for simplex in cells_sorted:
print("simplex "+str(simplex)+ " is at position " +str(cells_sorted.index(simplex)) + " out of " + str(len(cells_sorted)), flush=True) #print("simplex "+str(simplex)+ " is at position " +str(cells_sorted.index(simplex)) + " out of " + str(len(cells_sorted)), flush=True)
offset_simplex = offsets[simplex.tuple()] offset_simplex = offsets[simplex.tuple()]
primitives = p_basis[simplex.tuple()] primitives = p_basis[simplex.tuple()]
for f in range(n+1): for f in range(n+1):
@ -1373,9 +1383,9 @@ class AlgebraAplK(UniqueRepresentation, Parent):
def solve_primitive(self): def solve_primitive(self):
print("start _get_primitive_basis()",flush=True) print("start _get_primitive_basis()",flush=True)
p_basis = self._get_primitive_basis() p_basis = self._get_primitive_basis()
print("lenght primitive basis: ",len(p_basis),flush=True) print("length primitive basis: ",len(p_basis),flush=True)
d_basis = self._get_differential_basis(p_basis) d_basis = self._get_differential_basis(p_basis)
print("lenght differential basis: ",len(d_basis),flush=True) print("length differential basis: ",len(d_basis),flush=True)
diff_matrix = self._get_differential_matrix(p_basis, d_basis) diff_matrix = self._get_differential_matrix(p_basis, d_basis)
print("_get_vector_diff_coordinates()", flush=True) print("_get_vector_diff_coordinates()", flush=True)
v_dif = self._get_vector_diff_coordinates(d_basis) v_dif = self._get_vector_diff_coordinates(d_basis)
@ -1404,4 +1414,4 @@ class MorphismFromQQToAplK(Morphism):
for c in S._n_cells_sorted(d): for c in S._n_cells_sorted(d):
params[tuple(c)] = s(x) params[tuple(c)] = s(x)
A = AlgebraAplK(S) A = AlgebraAplK(S)
return AlgebraAplK.Element(A, params) return AlgebraAplK.Element(A, params)