### 20 Words in free ZG-modules

#### 20.1

 ‣ AddFreeWords( v, w ) ( function )

Inputs two words v,w in a free ZG-module and returns their sum v+w. If the characteristic of Z is greater than 0 then the next function might be more efficient.

 ‣ AddFreeWordsModP( v, w, p ) ( function )

Inputs two words v,w in a free ZG-module and the characteristic p of Z. It returns the sum v+w. If p=0 the previous function might be fractionally quicker.

##### 20.1-3 AlgebraicReduction
 ‣ AlgebraicReduction( w ) ( function )
 ‣ AlgebraicReduction( w, p ) ( function )

Inputs a word w in a free ZG-module and returns a reduced version of the word in which all pairs of mutually inverse letters have been cancelled. The reduction is performed in a free abelian group unless the characteristic p of Z is entered.

##### 20.1-4 MultiplyWord
 ‣ MultiplyWord( n, w ) ( function )

Inputs a word w and integer n. It returns the scalar multiple n⋅ w.

##### 20.1-5 Negate
 ‣ Negate( [i, j] ) ( function )

Inputs a pair [i,j] of integers and returns [-i,j].

##### 20.1-6 NegateWord
 ‣ NegateWord( w ) ( function )

Inputs a word w in a free ZG-module and returns the negated word -w.

##### 20.1-7 PrintZGword
 ‣ PrintZGword( w, elts ) ( function )

Inputs a word w in a free ZG-module and a (possibly partial but sufficient) listing elts of the elements of G. The function prints the word w to the screen in the form

r_1E_1 + ... + r_nE_n

where r_i are elements in the group ring ZG, and E_i denotes the i-th free generator of the module.

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##### 20.1-8 TietzeReduction
 ‣ TietzeReduction( S, w ) ( function )

Inputs a set S of words in a free ZG-module, and a word w in the module. The function returns a word w' such that {S,w'} generates the same abelian group as {S,w}. The word w' is possibly shorter (and certainly no longer) than w. This function needs to be improved!

##### 20.1-9 ResolutionBoundaryOfWord
 ‣ ResolutionBoundaryOfWord( R, n, w ) ( function )

Inputs a resolution R, a positive integer n and a list w representing a word in the free module R_n. It returns the image of w under the n-th boundary homomorphism.

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