cobordisms Namespace Reference

Functions
	generate_permutation (n_verts, sub_verts)
	Generate a permutation of the vertices so that the subvertices are first.
	generate_permutation_AB (n_verts, sub_verts_A, sub_verts_B)
	Generate a permutation of the vertices so that AuB is first.
	dim_compare (x, y)
	Comparison to compare list of simplicies to get them in the order for oineus.
	translate_column (col, perm)
	Translate a column of indices to the new order.
	construct_pair (simplices, n_verts, sub_verts, permute)
	Construct a pair of simplices.
	convert_vertices (vertices, permute)
	Convert the vertices to the new order.
	rref_d_phi (d_phi)
	Convert the d_phi to a matrix.
	find_births (dgm_A, dgm_B, dgm_AB)
	Find the points in Cok(d_phi).
	match_points_index (sorted_ids, cok_phi, birth_ids)
	Match the points in Cok(d_phi).
	convert_index_diagram (index_dgm, kicr)
	Convert the index diagram to the original diagram.
	d_phi_generator (kicr_AB, kicr_A, kicr_B, sorted_ids_AB, sorted_ids_A, sorted_ids_B, A_verts, B_verts, perm_AB, perm_A, perm_B, inv_AB, inv_A, inv_B)
	Generate the d_phi matrix.

Function Documentation

construct_pair()

cobordisms.construct_pair	(		simplices,
			n_verts,
			sub_verts,
			permute )

Construct a pair of simplices.

Parameters

simplices	simplices
n_verts	number of vertices
sub_verts	subvertices
permute	permutation

Returns

simplices_all simplices in the new order

simplices_sub subsimplices in the new order

convert_index_diagram()

cobordisms.convert_index_diagram	(		index_dgm,
			kicr )

Convert the index diagram to the original diagram.

Parameters

index_dgm	index diagram
kicr	KICR object

convert_vertices()

cobordisms.convert_vertices	(		vertices,
			permute )

Convert the vertices to the new order.

Parameters

vertices	vertices
permute	permutation

Returns

new vertices in the new order

d_phi_generator()

cobordisms.d_phi_generator	(		kicr_AB,
			kicr_A,
			kicr_B,
			sorted_ids_AB,
			sorted_ids_A,
			sorted_ids_B,
			A_verts,
			B_verts,
			perm_AB,
			perm_A,
			perm_B,
			inv_AB,
			inv_A,
			inv_B )

Generate the d_phi matrix.

Parameters

kicr_AB	KICR object of AB
kicr_A	KICR object of A
kicr_B	KICR object of B
sorted_ids_AB	indices of the simplices in the order they appear in the cokernel
sorted_ids_A	indices of the simplices in the order they appear in the cokernel
sorted_ids_B	indices of the simplices in the order they appear in the cokernel
A_verts	vertices of A
B_verts	vertices of B
perm_AB	permutation of the vertices
perm_A	permutation of the vertices
perm_B	permutation of the vertices
inv_AB	inverse permutation of the vertices
inv_A	inverse permutation of the vertices
inv_B	inverse permutation of the vertices

Returns

d_phi matrix of the d_phi

sorted_ids indices of the simplices in the order they appear in the d_phi

dim_compare()

cobordisms.dim_compare	(		x,
			y )

Comparison to compare list of simplicies to get them in the order for oineus.

Parameters

x	simplex to compare
y	simplex to compare

Returns

-1 if x<y, 1 otherwise

find_births()

cobordisms.find_births	(		dgm_A,
			dgm_B,
			dgm_AB )

Find the points in Cok(d_phi).

Parameters

dgm_A	time and index diagram of A
dgm_B	time and index diagram of B
dgm_AB	time and index diagram of AB

Returns

birth_ids indices of the births in the order they appear in the cokernel

generate_permutation()

cobordisms.generate_permutation	(		n_verts,
			sub_verts )

Generate a permutation of the vertices so that the subvertices are first.

Parameters

n_verts	number of vertices
sub_verts	subvertices

Returns

permute_verts permutation of the vertices

inverse_perm inverse permutation of the vertices

generate_permutation_AB()

cobordisms.generate_permutation_AB	(		n_verts,
			sub_verts_A,
			sub_verts_B )

Generate a permutation of the vertices so that AuB is first.

Parameters

n_verts	number of vertices
sub_verts_A	subvertices of A
sub_verts_B	subvertices of B

Returns

permute_verts permutation of the vertices

match_points_index()

cobordisms.match_points_index	(		sorted_ids,
			cok_phi,
			birth_ids )

Match the points in Cok(d_phi).

Parameters

sorted_ids	indices of the simplices in the order they appear in the cokernel
cok_phi	cokernel of d_phi
birth_ids	indices of the births in the order they appear in the cokernel
birth_times	times of the births in the order they appear in the cokernel

rref_d_phi()

cobordisms.rref_d_phi

(

d_phi

)

Convert the d_phi to a matrix.

Parameters

d_phi

d_phi

Returns

matrix matrix of the d_phi

translate_column()

cobordisms.translate_column	(		col,
			perm )

Translate a column of indices to the new order.

Parameters

col	column of indices
perm	permutation

Returns

col column of indices in the new order