Basic Operations

Subsections

• Accessing Monoid Information

Accessing Monoid Information

The functions in this monoid provide access to basic information stored for a rewrite monoid M.

M . i : MonRWS, RngIntElt -> MonRWSElt

The i-th defining generator for M.

Generators(M) : MonRWS -> [ MonRWSElt]

A sequence containing the defining generators for M.

NumberOfGenerators(M) : MonRWS -> RngIntElt

Ngens(M) : MonRWS -> RngIntElt

The number of defining generators for M.

Relations(M) : MonRWS -> [MonFPRel]

A sequence containing the defining relations for M. The relations will be given between elements of the free monoid of which M is a quotient. In these relations the (image of the) left hand side (in M) will always be greater than the (image of the) right hand side (in M) in the ordering on words used to construct M.

NumberOfRelations(M) : MonRWS -> RngIntElt

Nrels(M) : MonRWS -> RngIntElt

The number of relations in M.

Ordering(M) : MonRWS -> String

The ordering of M.

Parent(w) : MonRWSElt -> MonRWS

The parent monoid M for the word w.

Example MonRWS_BasicAccess (H18E4)

> FM<a,b,B> := FreeMonoid(3);
> Q := quo< FM | a^2=1, b*B=1, B*b=1, b*b=B, B*a*B*a=a*b*a*b>;
> M<x,y,Y> := RWSMonoid(Q);
> print M;
A confluent rewrite monoid.
Generator Ordering = [ a, b, B ]
Ordering = ShortLex.
The reduction machine has 13 states.
The rewrite relations are:
    a^2 = Id(FM)
    b * B = Id(FM)
    B * b = Id(FM)
    b^2 = B
    (B * a)^2 = (a * b)^2
    B^2 = b
    (b * a)^2 = (a * B)^2
    B * a * b * a * b = b * a * B * a
    b * a * B * a * B = B * a * b * a
    b * a * B * a * b * a = a * b * a * B * a * b
    B * a * b * a * B = b * a * B * a * b
> print M.1;
x
> print M.1*M.2;
x * y
> print Generators(M);
[ x, y, Y ]
> print Ngens(M);
3
> print Relations(M);
[ a^2 = Id(FM), b * B = Id(FM), B * b = Id(FM), b^2 = B, (B * a)^2 = (a * b)^2, 
B^2 = b, (b * a)^2 = (a * B)^2, B * a * b * a * b = b * a * B * a, b * a * B * a
* B = B * a * b * a, b * a * B * a * b * a = a * b * a * B * a * b, B * a * b * 
a * B = b * a * B * a * b ]
> print Nrels(M);
11
> print Ordering(M);
ShortLex