| AddFreeWords(v,w) 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) 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. | 
| AlgebraicReduction(w) AlgebraicReduction(w,p) 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. | 
| Multiply Word(n,w) Inputs a word w and integer n. It returns the scalar multiple n⋅ w. | 
| Negate([i,j]) Inputs a pair [i,j] of integers and returns [-i,j]. | 
| NegateWord(w) Inputs a word w in a free ZG-module and returns the negated word -w. | 
| PrintZGword(w,elts) 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. | 
| TietzeReduction(S,w) 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! | 
| ResolutionBoundaryOfWord(R,n,w)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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