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

(inherits from: Sequence, Callable )

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.