‣ 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.
Examples:
‣ 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.
Examples:
‣ 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.
Examples:
‣ MultiplyWord( n, w ) | ( function ) |
Inputs a word \(w\) and integer \(n\). It returns the scalar multiple \(n\cdot w\).
Examples:
‣ Negate( [i, j] ) | ( function ) |
Inputs a pair \([i,j]\) of integers and returns \([-i,j]\).
Examples:
‣ NegateWord( w ) | ( function ) |
Inputs a word \(w\) in a free \(ZG\)-module and returns the negated word \(-w\).
Examples:
‣ 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
\(r_1E_1 + \ldots + r_nE_n\)
where \(r_i\) are elements in the group ring \(ZG\), and \(E_i\) denotes the \(i\)-th free generator of the module.
Examples: 1
‣ 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!
Examples:
‣ 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.
Examples:
generated by GAPDoc2HTML