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<title>GAP (HAP) - Chapter 14: Words in free ZG-modules </title>
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<div class="ChapSects"><a href="chap14.html#X8276B4377D092A80">14. <span class="Heading"> Words in free ZG-modules </span></a>
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<h3>14. <span class="Heading"> Words in free ZG-modules </span></h3>
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<td class="tdleft"><code class="code"> AddFreeWords(v,w) </code></p>
<p>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.</td>
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<td class="tdleft"><code class="code"> AddFreeWordsModP(v,w,p) </code></p>
<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.</td>
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<td class="tdleft"><code class="code"> AlgebraicReduction(w) </code> <br /> <code class="code"> AlgebraicReduction(w,p) </code></p>
<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.</td>
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<td class="tdleft"><code class="code"> Multiply Word(n,w) </code></p>
<p>Inputs a word w and integer n. It returns the scalar multiple n* w.</td>
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<td class="tdleft"><code class="code"> Negate([i,j]) </code></p>
<p>Inputs a pair [i,j] of integers and returns [-i,j].</td>
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<td class="tdleft"><code class="code"> NegateWord(w) </code></p>
<p>Inputs a word w in a free ZG-module and returns the negated word -w.</td>
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<td class="tdleft"><code class="code"> PrintZGword(w,elts) </code></p>
<p>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</p>
<p>r_1E_1 + ... + r_nE_n</p>
<p>where r_i are elements in the group ring ZG, and E_i denotes the i-th free generator of the module.</td>
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<td class="tdleft"><code class="code"> TietzeReduction(S,w) </code></p>
<p>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!</td>
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