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<div=ContSect">span class="tocline< =nocss>nbsp/spanahrefchap2htmlX84F709227E5EEB55">2. ><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7F21EDDF81C27747">2.2 <span class="Heading">The applications of the <strong class="pkg">Gauss</strong> package algorithms</span></a>
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<h4>2.1 <span class="Heading">The need for extended functionality</span></h4>
<p><strong class="pkg">GAP</strong> has a lot of functionality for row echelon forms of matrices. These can be called by <code class="code">SemiEchelonForm</code> and similar commands. All of these work for the <strong class="pkg">GAP</strong> matrix type over fields. However, these algorithms are not capable of computing a reduced row echelon form (RREF) of a matrix, there is no way to "Gauss upwards". While this is not neccessary for things like Rank or Kernel computations, this was one in a number of< class="ChapSects"><a href="chap2.html#X823150E97BE77525"">2Heading">ExtendingGaussFunctionality/>
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<p>It< class"GAP/> has lot of unctionalityfor ow echelon matrices. These can be called by SemiEchelonForm and similar commands. All of these work for the GAP matrix type over fields. However, these algorithms are not capable of computing a reduced row echelon form (RREF) of a matrix, there is no way to "Gauss upwards". While
<p>I am proud to tell you that, thanks to optimizing the algorithms for matrices over GF(2), it was possible
<ppIamproud tell that,thanks optimizing algorithms matrices GF,it possibleto the()Rank of matrix above less 20minutes with usage of 3 GB/p>
<h4. <span class="Heading">The of the<trong="pkg"Gauss</strong packagealgorithms/></h4
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<p>The third procedure, <code class="code">SygygiesGeneratorsOfRows</code>, is concerned with the relations between rows of a matrix, each
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<p>and computing its
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<p>As you can see, the development of hermite algorithms was not continued for dense matrices. There are two reasons for that: <strong class="pkg">GAP</strong> already has very good algorithms for ℤ, and for small matrices the disadvantage of computing over ℤ, potentially leading to coefficient explosion, is marginal.</p>
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