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<div><h1>FinitelyGeneratedAbelianGroup -- Class of finitely generated abelian groups.</h1> <div class="single"><h2>Description</h2> <div><p>The class of finitely generated abelian groups (finitely generated ZZ-modules).</p> <p>This is used to store the result of <a href="_m__Homology.html" title="Compute the homology.">mHomology</a> in a nice way.</p> <div/> <table class="examples"><tr><td><pre>i1 : C= {{{}}, {{{-1, -1, -1, -1, -1}}, {{1, 0, 0, 0, 0}}, {{0, 1, 0, 0, 0}}, {{0, 0, 1, 0, 0}}, {{0, 0, 0, 1, 0}}, {{0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1,-1}, {1, 0, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 1, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {}, {}, {}} o1 = {{{}}, {{{-1, -1, -1, -1, -1}}, {{1, 0, 0, 0, 0}}, {{0, 1, 0, 0, 0}}, ------------------------------------------------------------------------ {{0, 0, 1, 0, 0}}, {{0, 0, 0, 1, 0}}, {{0, 0, 0, 0, 1}}}, {{{-1, -1, -1, ------------------------------------------------------------------------ -1, -1}, {1, 0, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}}, {{1, ------------------------------------------------------------------------ 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}}, ------------------------------------------------------------------------ {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, ------------------------------------------------------------------------ {{-1, -1, -1, -1, -1}, {0, 0, 0, 1, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, ------------------------------------------------------------------------ 0}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 1, ------------------------------------------------------------------------ 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, ------------------------------------------------------------------------ 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 1, 0, 0}, {0, 0, ------------------------------------------------------------------------ 0, 0, 1}}, {{0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1, -1}, ------------------------------------------------------------------------ {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, ------------------------------------------------------------------------ {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 0, 0, 1, ------------------------------------------------------------------------ 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, ------------------------------------------------------------------------ 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, ------------------------------------------------------------------------ 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, ------------------------------------------------------------------------ {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, ------------------------------------------------------------------------ {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, ------------------------------------------------------------------------ {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {}, {}, {}} o1 : List</pre> </td></tr> <tr><td><pre>i2 : H=mHomology(C) o2 = {ZZ, ZZ/2, 0, 0, 0, 0} o2 : List</pre> </td></tr> <tr><td><pre>i3 : H#0 o3 = ZZ o3 : finitely generated abelian group</pre> </td></tr> <tr><td><pre>i4 : H#1 o4 = ZZ/2 o4 : finitely generated abelian group</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Methods that use a finitely generated abelian group :</h2> <ul><li>net(FinitelyGeneratedAbelianGroup)</li> </ul> </div> <div class="waystouse"><h2>For the programmer</h2> <p>The object <a href="___Finitely__Generated__Abelian__Group.html" title="Class of finitely generated abelian groups.">FinitelyGeneratedAbelianGroup</a> is <span>a <a href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a href="../../Macaulay2Doc/html/___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="../../Macaulay2Doc/html/___Thing.html" title="the class of all things">Thing</a>.</p> </div> </div> </body> </html>