Software specification¶
Below is an automatically generated software specification.
Public classes¶
HomLCA (A[, target, source]) |
A homomorphism between elementary LCAs. |
LCA (orders[, discrete]) |
An elementary locally compact abelian group (LCA). |
LCAFunc (representation, domain) |
A function from an LCA to a complex number. |
Public functions¶
hermite_normal_form (A) |
Compute U and H such that A*U = H. |
smith_normal_form (A[, compute_unimod]) |
Compute U,S,V such that U*A*V = S. |
solve (A, b[, p]) |
Solve eqn Ax = b mod p over Z. |
voronoi (epimorphism[, norm_p]) |
Return the Voronoi transversal function. |
Public classes (detailed)¶
LCAFunc
¶
(inherits from:Callable
)
LCAFunc (representation, domain) |
A function from an LCA to a complex number. |
__call__ (list_arg, *args, **kwargs) |
Override function calls, see evaluate() . |
__init__ (representation, domain) |
Initialize a function G -> C. |
__repr__ () |
Override the repr() function. |
copy () |
Return a copy of the instance. |
dft ([func_type]) |
If the domain allows it, compute DFT. |
evaluate (list_arg, *args, **kwargs) |
Evaluate function on a group element. |
idft ([func_type]) |
If the domain allows it, compute inv DFT. |
pointwise (other, operator) |
Apply pointwise binary operator. |
pullback (morphism) |
Return the pullback along morphism. |
pushforward (morphism[, terms_in_sum]) |
Return the pushforward along morphism. |
sample (list_of_elements, *args, **kwargs) |
Sample on a list of group elements. |
shift (list_shift) |
Shift the function. |
to_latex () |
Return as a \(\LaTeX\) string. |
to_table (*args, **kwargs) |
Return a n-dimensional table. |
transversal (epimorphism[, transversal_rule, …]) |
Pushforward using transversal rule. |
LCA
¶
LCA (orders[, discrete]) |
An elementary locally compact abelian group (LCA). |
__add__ (other) |
Override the addition (+) operator, see sum() . |
__call__ (element) |
Override function calls, see project_element() . |
__contains__ (other) |
Override the ‘in’ operator, see contained_in() . |
__eq__ (other) |
Override the equality (==) operator, see equal() . |
__getitem__ (key) |
Override the slice operator, see slice() . |
__init__ (orders[, discrete]) |
Initialize a new LCA. |
__iter__ () |
Override the iteration protocol, see iterate() . |
__len__ () |
Override the len() function, see length() . |
__pow__ (power[, modulo]) |
Override the pow (**) operator, see compose_self() . |
__repr__ () |
Override the repr() function. |
canonical () |
Return the LCA in canonical form using SNF. |
compose_self (power) |
Repeated direct summation. |
contained_in (other) |
Whether the LCA is contained in other. |
copy () |
Return a copy of the LCA. |
dual () |
Return the Pontryagin dual of the LCA. |
elements_by_maxnorm ([norm_values]) |
Yield elements corresponding to max norm value. |
equal (other) |
Whether or not two LCAs are equal. |
getitem (key) |
Return a slice of the LCA. |
is_FGA () |
Whether or not the LCA is a FGA. |
isomorphic (other) |
Whether or not two LCAs are isomorphic. |
iterate () |
Yields the groups in the direct sum one by one. |
length () |
The number of groups in the direct sum. |
project_element (element) |
Project an element onto the group. |
rank () |
Return the rank of the LCA. |
remove_indices (indices) |
Return a LCA with some groups removed. |
remove_trivial () |
Remove trivial groups from the object. |
sum (other) |
Return the direct sum of two LCAs. |
to_latex () |
Return the LCA as a \(\LaTeX\) string. |
trivial () |
Return a trivial LCA. |
HomLCA
¶
(inherits from:Callable
)
HomLCA (A[, target, source]) |
A homomorphism between elementary LCAs. |
__add__ (other) |
Override the addition (+) operator, see add() . |
__call__ (source_element) |
Override function calls, see evaluate() . |
__eq__ (other) |
Override the equality (==) operator, see equal() . |
__getitem__ (args) |
Override the slice operator, see getitem() . |
__init__ (A[, target, source]) |
Initialize a homomorphism. |
__mul__ (other) |
Override the * operator, see compose() . |
__pow__ (power[, modulo]) |
Override the pow (**) operator, see compose_self() . |
__radd__ (other) |
Override the addition (+) operator, see add() . |
__repr__ () |
Override the repr() function. |
__rmul__ (other) |
Override the * operator, see compose() . |
add (other) |
Elementwise addition. |
annihilator () |
Compute the annihilator monomorphism. |
coimage () |
Compute the coimage epimorphism. |
cokernel () |
Compute the cokernel epimorphism. |
compose (other) |
Compose two homomorphisms. |
compose_self (power) |
Repeated composition of an endomorphism. |
copy () |
Return a copy of the homomorphism. |
det () |
Determinant of the matrix representing the HomLCA. |
dual () |
Compute the dual homomorphism. |
equal (other) |
Whether or not two homomorphisms are equal. |
evaluate (source_element) |
Apply the homomorphism to an element. |
getitem (args) |
Return a slice of the homomorphism. |
identity (group) |
Return the identity morphism. |
image () |
Compute the image monomorphism. |
kernel () |
Compute the kernel monomorphism. |
project_to_source () |
Project columns to source group (orders). |
project_to_target () |
Project columns to target group. |
remove_trivial_groups () |
Remove trivial groups. |
stack_diag (other) |
Stack diagonally. |
stack_horiz (other) |
Stack horizontally (column wise). |
stack_vert (other) |
Stack vertically (row wise). |
to_latex () |
Return the homomorphism as a \(\LaTeX\) string. |
update ([new_A, new_target, new_source]) |
Return a new homomorphism with updated properties. |
zero (target, source) |
Initialize the zero morphism. |