GAP (AutMan) - Chapter 9: Stallings foldings

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### 9. Stallings foldings

#### 9.1 Some theory

#### 9.2 Foldings

A finitely generated subgroup of a finitely generated free group is given through a list whose first element is the number of generators of the free group and the remaining elements are the generators of the subgroup.

A generator of the subgroup may be given through a string of letters or through a list of positive integers as decribed in what follows.

When the free group has n generators, the n+j^th letter of the alphabet should be used to represent the formal inverse of the j^th generator which is represented by the j^th letter. The number of generators of the free group must not exceed 7.

For example, `[2,"abc","bbabcd"]` means the subgroup of the free group on 2 generators generated by aba^-1 and bbaba^-1b^-1. The same subgroup may be given as `[2,[1,2,3],[2,2,1,2,3,4]]`

##### 9.2-1 FlowerAutomaton

`> FlowerAutomaton`( L ) | ( function )

The argument `L` is a subgroup of the free group given through any of the representations described above.

##### 9.2-2 FoldFlowerAutomaton

`> FoldFlowerAutomaton`( A ) | ( function )

Makes identifications on the flower automaton `A`

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