kigen.multab — kigen 19.08.05

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.

at clj macro

(at mt i j)

Convenient accessing of matrix elements by their indices.

closure clj

(closure mt exts)

(closure mt base exts)

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

elts clj

(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.

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

index-period clj

(index-period mt x)

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

min-extensions clj

(min-extensions mt elts closedsub)

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

multab clj

(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.

newelements clj

(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).

psubsgps clj

(psubsgps mt)

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

set-mul clj

(set-mul mt A B)

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

subsgps clj

(subsgps mt)

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