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kigen.multab

Functions for dealing with abstract multiplication tables of semigroups. The multiplicative elements are represented by their indices in a given sequence. The tables are vectors of vectors (the rows of the table), so multiplication is just a constant-time look up. Functionality for multiplying subsets of elements and computing closures and thus enumerating subsemigroups. The subsemigroups can be stored in efficient int-sets.

Functions for dealing with abstract multiplication tables of semigroups.
The multiplicative elements are represented by their indices in a
given sequence. The tables are vectors of vectors (the rows of the table),
so multiplication is just a constant-time look up.
Functionality for multiplying subsets of elements and computing closures
and thus enumerating subsemigroups. The subsemigroups can be stored in
efficient int-sets.
raw docstring

atcljmacro

(at mt i j)

Convenient accessing of matrix elements by their indices.

Convenient accessing of matrix elements by their indices.
sourceraw docstring

closureclj

(closure mt exts)
(closure mt base exts)

It calculates the closure of base with elements in the set exts.

It calculates the closure of base with elements in the set exts.
sourceraw docstring

eltsclj

(elts mt)

Returns the elements of the given multiplication table. The elements are just the set of indices from 0 to n-1 in an int-set.

Returns the elements of the given multiplication table.
The elements are just the set of indices from 0 to n-1 in an int-set.
sourceraw docstring

elts-cachedclj

source

in-closure?clj

(in-closure? mt gens x)
(in-closure? mt sgp gens x)

Returns true if an element x is in the closure of sgp by gens

Returns true if an element x is in the closure of sgp by gens
sourceraw docstring

index-periodclj

(index-period mt x)

The index-period pair of integers in a vector in a multiplication table.

The index-period pair of integers in a vector in a multiplication table.
sourceraw docstring

min-extensionsclj

(min-extensions mt elts closedsub)

Returns the minimal extensions (by new element) of closed subarray of multiplication table mt.

Returns the minimal extensions (by new element) of closed subarray of
multiplication table mt.
sourceraw docstring

multabclj

(multab xs mul)

Returns the multiplication table of the elements xs by the function mul. The order of elements in xs is preserved and used to define indices.

Returns the multiplication table of the elements xs by the function mul.
The order of elements in xs is preserved and used to define indices.
sourceraw docstring

newelementsclj

(newelements mt S X)

For a subsemigroup S and a subset X in mt this returns the elements ((S U X)X U X(S U X)) setminus (S U X).

For a subsemigroup S and a subset X in mt this returns the elements
((S U X)X U X(S U X)) setminus (S U X).
sourceraw docstring

psubsgpsclj

(psubsgps mt)

All subsemigroups of an abstract semigroup given by its multiplication table computed in parallel.

All subsemigroups of an abstract semigroup given by its multiplication
table computed in parallel.
sourceraw docstring

set-mulclj

(set-mul mt A B)

Set-wise multiplication of subsets of a multab. For A and B it returns AB.

Set-wise multiplication of subsets of a multab. For A and B it returns AB.
sourceraw docstring

subsgpsclj

(subsgps mt)

All subsemigroups of an abstract semigroup given by its multiplication table.

All subsemigroups of an abstract semigroup given by its multiplication
table.
sourceraw docstring

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