fixed max_depth error at injectivity_step and other changes
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parent
95c017f3ce
commit
c9885a03b7
17
aplK.py
17
aplK.py
@ -904,7 +904,7 @@ class AlgebraAplK(UniqueRepresentation, Parent):
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def __init__(self, parent, values):
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Element.__init__(self, parent)
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self.elements = self._reduce(values)
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# self.check()
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#self.check()
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def _repr_(self):
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"""
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@ -1123,20 +1123,16 @@ class AlgebraAplK(UniqueRepresentation, Parent):
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primitive_basis[simplex.tuple()] = []
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# add primitive elements related to the assigned polynomial
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pol = self.elements[simplex.tuple()]
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primitive_basis[simplex.tuple(
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)] += pol._get_primitive_basis()
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primitive_basis[simplex.tuple()] = list(
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set(primitive_basis[simplex.tuple()]))
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primitive_basis[simplex.tuple()] += pol._get_primitive_basis()
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primitive_basis[simplex.tuple()] = list(set(primitive_basis[simplex.tuple()]))
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primitive_basis[simplex.tuple()].sort(reverse=False)
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# propagate the primitive basis through its faces
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for f in range(n+1):
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simplex_face = S.face(simplex, f).tuple()
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if simplex_face not in primitive_basis.keys():
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primitive_basis[simplex_face] = []
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primitive_basis[simplex_face] += self._face_basis(
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primitive_basis[simplex.tuple()], f)
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primitive_basis[simplex_face] = list(
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set(primitive_basis[simplex_face]))
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primitive_basis[simplex_face] += self._face_basis(primitive_basis[simplex.tuple()], f)
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primitive_basis[simplex_face] = list(set(primitive_basis[simplex_face]))
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primitive_basis[simplex_face].sort(reverse=False)
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return primitive_basis
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@ -1162,8 +1158,7 @@ class AlgebraAplK(UniqueRepresentation, Parent):
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for n in reversed(range(min_dim, dim+1)):
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for simplex in S._n_cells_sorted(n):
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prim_diff_basis = primitive_basis[simplex.tuple()]
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differential_basis[simplex.tuple()] = self._diff_basis(
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prim_diff_basis)
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differential_basis[simplex.tuple()] = self._diff_basis(prim_diff_basis)
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return differential_basis
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def _get_differential_matrix(self, p_basis, d_basis):
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@ -221,7 +221,7 @@ def minimal_model(S, max_depth=5, max_dim=5):
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# Now we have an isomorphism in the first non-null cohomology group
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# we check if phi is a monomorphism
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[M, phi, names, degrees, differentials, limit] = injectivity_step(M, phi, first_dim+1, names,
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degrees, differentials, A, index=0, depth=0, max_depth=5)
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degrees, differentials, A, index=0, depth=0, max_depth=max_depth)
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if limit:
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print(
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"The algorithm has reach the injectivity depth-limit at dimension ", first_dim)
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@ -234,10 +234,10 @@ def minimal_model(S, max_depth=5, max_dim=5):
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[M, phi, names, degrees, cohomology_correspondence] = surjective_step(A, M, phi, i, names, degrees,
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differentials, cohomology_correspondence)
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[M, phi, names, degrees, differentials, limit] = injectivity_step(M, phi, i+1, names,
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degrees, differentials, A, index=0, depth=0, max_depth=5)
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degrees, differentials, A, index=0, depth=0, max_depth=max_depth)
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if limit:
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print(
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"The algorithm has reach the injectivity depth-limit at dimension", dim)
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"The algorithm has reach the injectivity depth-limit at dimension", i+1)
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break
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return [M, phi, cohomology_correspondence]
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@ -55,7 +55,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -135,7 +135,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -159,7 +159,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -189,7 +189,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -235,7 +235,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -253,7 +253,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -281,7 +281,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -309,7 +309,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -353,7 +353,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -392,7 +392,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -410,7 +410,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -445,7 +445,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -508,7 +508,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -526,7 +526,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -562,7 +562,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -586,7 +586,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -604,7 +604,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -625,7 +625,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -669,7 +669,7 @@
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"- $p^i \\in \\mathbb{Q}[t_1, \\dots, t_n]$\n",
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"- $(k_{1}^{i}, \\dots , k_{n}^{i}) \\neq (k_{1}^{j}, \\dots, k_{n}^{j})$ if $i \\neq j$\n",
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"\n",
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"It is easy to see that $p$ will have as much as $2^n-1$ non-null terms in the variables $y_j$.\n",
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"It is easy to see that $p$ will have at most $2^n-1$ non-null terms in the variables $y_j$.\n",
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"\n",
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"As we have set the lexicographic monomial ordering, for every two consecutive non-null terms in a polynomial $p$\n",
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"\n",
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@ -796,7 +796,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -945,7 +945,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -963,7 +963,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -984,7 +984,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -1065,7 +1065,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1214,7 +1214,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -1232,7 +1232,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -1253,7 +1253,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -1332,7 +1332,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1388,7 +1388,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"execution_count": 43,
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"metadata": {},
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"outputs": [
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{
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@ -1406,7 +1406,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 29,
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"execution_count": 51,
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"metadata": {},
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"outputs": [
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{
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@ -1427,7 +1427,14 @@
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -1446,7 +1453,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 31,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -1485,7 +1492,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 32,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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@ -5487,7 +5494,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5.beta2",
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"display_name": "SageMath 9.2",
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"language": "sage",
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"name": "sagemath"
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},
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@ -5501,7 +5508,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.10"
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"version": "3.8.5"
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},
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"toc-autonumbering": false,
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"toc-showmarkdowntxt": false
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@ -16,5 +16,5 @@ print(S.facets())
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#######################################################
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# S = simplicial_complexes.ProjectivePlane().wedge(simplicial_complexes.Sphere(2), is_mutable=False)
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#######################################################
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[sullivan_model, model_morphism, cohomology_correspondence] = minimal_model(S, max_depth=5, max_dim=8)
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[sullivan_model, model_morphism, cohomology_correspondence] = minimal_model(S, max_depth=10, max_dim=12)
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print(sullivan_model)
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