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<div><h1>GradedModule -- the class of all graded modules</h1>
<div class="single"><h2>Description</h2>
<div>A new graded module can be made with 'M = new GradedModule'. The i-th module can be installed with a statement like <tt>M#i=N</tt>, and can be retrieved with an expression like <tt>M_i</tt>. The ground ring should be installed with a statement like <tt>M.ring = R</tt>.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Graded__Module__Map.html" title="the class of all maps between graded modules">GradedModuleMap</a> -- the class of all maps between graded modules</span></li>
</ul>
</div>
<div class="waystouse"><h2>Types of graded module :</h2>
<ul><li><span><a href="___Chain__Complex.html" title="the class of all chain complexes">ChainComplex</a> -- the class of all chain complexes</span></li>
</ul>
<h2>Functions and methods returning a graded module :</h2>
<ul><li><span><a href="_ambient_lp__Graded__Module_rp.html" title="">ambient(GradedModule)</a></span></li>
<li><span>GradedModule ++ GradedModule, see <span><a href="___Chain__Complex_sp_pl_pl_sp__Chain__Complex.html" title="direct sum">ChainComplex ++ ChainComplex</a> -- direct sum</span></span></li>
<li><span>coimage(GradedModuleMap), see <span><a href="_coimage.html" title="coimage of a map">coimage</a> -- coimage of a map</span></span></li>
<li><span>cokernel(GradedModuleMap), see <span><a href="_cokernel.html" title="cokernel of a map of modules, graded modules, or chaincomplexes">cokernel</a> -- cokernel of a map of modules, graded modules, or chaincomplexes</span></span></li>
<li><span>cover(GradedModule), see <span><a href="_cover_lp__Module_rp.html" title="get the covering free module">cover(Module)</a> -- get the covering free module</span></span></li>
<li><span>directSum(GradedModule), see <span><a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></span></li>
<li><span>gradedModule(ChainComplex), see <span><a href="_graded__Module.html" title="make a graded module">gradedModule</a> -- make a graded module</span></span></li>
<li><span>gradedModule(List), see <span><a href="_graded__Module.html" title="make a graded module">gradedModule</a> -- make a graded module</span></span></li>
<li><span>gradedModule(Module), see <span><a href="_graded__Module.html" title="make a graded module">gradedModule</a> -- make a graded module</span></span></li>
<li><span>gradedModule(Sequence), see <span><a href="_graded__Module.html" title="make a graded module">gradedModule</a> -- make a graded module</span></span></li>
<li><span><a href="___Graded__Module_sp_st_st_sp__Graded__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** GradedModule</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<li><span><a href="___Graded__Module_sp_st_st_sp__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** Module</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<li><span>Module ** GradedModule, see <span><a href="___Graded__Module_sp_st_st_sp__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** Module</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><a href="___Graded__Module_sp__Array.html" title="degree shift">GradedModule Array</a> -- degree shift</span></li>
<li><span><a href="___H__H_sp__Chain__Complex.html" title="homology of a chain complex">HH ChainComplex</a> -- homology of a chain complex</span></li>
<li><span>image(GradedModuleMap), see <span><a href="_image.html" title="image of a map">image</a> -- image of a map</span></span></li>
<li><span>kernel(GradedModuleMap), see <span><a href="_kernel_lp__Chain__Complex__Map_rp.html" title="kernel of a chain complex map">kernel(ChainComplexMap)</a> -- kernel of a chain complex map</span></span></li>
<li><span>minimalPresentation(GradedModule), see <span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></span></li>
<li><span>prune(GradedModule), see <span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></span></li>
<li><span>GradedModule ++ Module, see <span><a href="___Module_sp_pl_pl_sp__Module.html" title="direct sum of modules">Module ++ Module</a> -- direct sum of modules</span></span></li>
<li><span>Module ++ GradedModule, see <span><a href="___Module_sp_pl_pl_sp__Module.html" title="direct sum of modules">Module ++ Module</a> -- direct sum of modules</span></span></li>
<li><span><a href="_source_lp__Graded__Module__Map_rp.html" title="find the source of a map of graded modules">source(GradedModuleMap)</a> -- find the source of a map of graded modules</span></li>
<li><span>super(GradedModule), see <span><a href="_super.html" title="get the ambient module">super</a> -- get the ambient module</span></span></li>
<li><span><a href="_target_lp__Graded__Module__Map_rp.html" title="find the target of a map of graded modules">target(GradedModuleMap)</a> -- find the target of a map of graded modules</span></li>
</ul>
<h2>Methods that use a graded module :</h2>
<ul><li><span>GradedModule == GradedModule, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span><a href="_betti_lp__Graded__Module_rp.html" title="display of degrees in a graded module">betti(GradedModule)</a> -- display of degrees in a graded module</span></li>
<li><span><a href="___Chain__Complex_sp_st_st_sp__Graded__Module.html" title="tensor product">ChainComplex ** GradedModule</a> -- tensor product</span></li>
<li><span>GradedModule _ ZZ, see <span><a href="___Chain__Complex_sp_us_sp__Z__Z.html" title="component">ChainComplex _ ZZ</a> -- component</span></span></li>
<li><span><a href="_chain__Complex_lp__Graded__Module_rp.html" title="make a chain complex from a graded module">chainComplex(GradedModule)</a> -- make a chain complex from a graded module</span></li>
<li><span>complete(GradedModule), see <span><a href="_complete.html" title="">complete</a></span></span></li>
<li><span>components(GradedModule), see <span><a href="_components.html" title="list the components of a direct sum">components</a> -- list the components of a direct sum</span></span></li>
<li><span><a href="___Graded__Module_sp_st_st_sp__Chain__Complex.html" title="tensor product">GradedModule ** ChainComplex</a> -- tensor product</span></li>
<li><span>heft(GradedModule), see <span><a href="_heft.html" title="heft vector of ring, module, graded module, or resolution">heft</a> -- heft vector of ring, module, graded module, or resolution</span></span></li>
<li><span>isDirectSum(GradedModule), see <span><a href="_is__Direct__Sum.html" title="whether something is a direct sum">isDirectSum</a> -- whether something is a direct sum</span></span></li>
<li><span><a href="_length_lp__Graded__Module_rp.html" title="length of a graded module">length(GradedModule)</a> -- length of a graded module</span></li>
<li><span>map(GradedModule,GradedModule,Function), see <span><a href="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Function_rp.html" title="make a map of chain complexes">map(ChainComplex,ChainComplex,Function)</a> -- make a map of chain complexes</span></span></li>
<li><span><a href="_max_lp__Graded__Module_rp.html" title="maximum of elements of a list">max(GradedModule)</a> -- maximum of elements of a list</span></li>
<li><span><a href="_min_lp__Graded__Module_rp.html" title="minimum of elements of a list">min(GradedModule)</a> -- minimum of elements of a list</span></li>
<li><span>rank(GradedModule), see <span><a href="_rank.html" title="compute the rank">rank</a> -- compute the rank</span></span></li>
<li><span>ring(GradedModule), see <span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></span></li>
<li><span>tensorAssociativity(GradedModule,GradedModule,GradedModule), see <span><a href="_tensor__Associativity.html" title="associativity isomorphisms for tensor products">tensorAssociativity</a> -- associativity isomorphisms for tensor products</span></span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Graded__Module.html" title="the class of all graded modules">GradedModule</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> < <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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