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<div><h1>GradedModuleMap -- the class of all maps between graded modules</h1>
<div><!--empty documentation body--></div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Graded__Module.html" title="the class of all graded modules">GradedModule</a> -- the class of all graded modules</span></li>
</ul>
</div>
<div class="waystouse"><h2>Types of graded module map :</h2>
<ul><li><span><a href="___Chain__Complex__Map.html" title="the class of all maps between chain complexes">ChainComplexMap</a> -- the class of all maps between chain complexes</span></li>
</ul>
<h2>Functions and methods returning a graded module map :</h2>
<ul><li><span>GradedModuleMap * GradedModuleMap, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>RingElement * GradedModuleMap, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>GradedModuleMap + GradedModuleMap, see <span><a href="__pl.html" title="a unary or binary operator, usually used for addition">+</a> -- a unary or binary operator, usually used for addition</span></span></li>
<li><span>GradedModuleMap + RingElement, see <span><a href="__pl.html" title="a unary or binary operator, usually used for addition">+</a> -- a unary or binary operator, usually used for addition</span></span></li>
<li><span>RingElement + GradedModuleMap, see <span><a href="__pl.html" title="a unary or binary operator, usually used for addition">+</a> -- a unary or binary operator, usually used for addition</span></span></li>
<li><span>- GradedModuleMap, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>GradedModuleMap - GradedModuleMap, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>GradedModuleMap - RingElement, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>RingElement - GradedModuleMap, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>GradedModuleMap ^ ZZ, see <span><a href="___Chain__Complex__Map_sp^_sp__Z__Z.html" title="iterated composition">ChainComplexMap ^ ZZ</a> -- iterated composition</span></span></li>
<li><span>gradedModuleMap(List), see <span><a href="_graded__Module__Map.html" title="make a map of graded modules">gradedModuleMap</a> -- make a map of graded modules</span></span></li>
<li><span>gradedModuleMap(ModuleMap), see <span><a href="_graded__Module__Map.html" title="make a map of graded modules">gradedModuleMap</a> -- make a map of graded modules</span></span></li>
<li><span>gradedModuleMap(Sequence), see <span><a href="_graded__Module__Map.html" title="make a map of graded modules">gradedModuleMap</a> -- make a map of graded modules</span></span></li>
<li><span><a href="___H__H_sp__Chain__Complex__Map.html" title="homology of a chain complex map">HH ChainComplexMap</a> -- homology of a chain complex map</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>GradedModuleMap ++ GradedModuleMap, see <span><a href="___Matrix_sp_pl_pl_sp__Matrix.html" title="direct sum of maps">Matrix ++ Matrix</a> -- direct sum of maps</span></span></li>
<li><span>GradedModuleMap ^ Array, see <span><a href="___Matrix_sp^_sp__Array.html" title="component of map corresponding to summand of target">Matrix ^ Array</a> -- component of map corresponding to summand of target</span></span></li>
<li><span>GradedModuleMap _ Array, see <span><a href="___Matrix_sp_us_sp__Array.html" title="component of map corresponding to summand of source">Matrix _ Array</a> -- component of map corresponding to summand of source</span></span></li>
<li><span>minimalPresentation(GradedModuleMap), 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(GradedModuleMap), 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>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>
<h2>Methods that use a graded module map :</h2>
<ul><li><span>GradedModuleMap == GradedModuleMap, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>GradedModuleMap == RingElement, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>GradedModuleMap == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>RingElement == GradedModuleMap, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == GradedModuleMap, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>GradedModuleMap _ ZZ, see <span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z.html" title="component map">ChainComplexMap _ ZZ</a> -- component map</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>components(GradedModuleMap), 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>degree(GradedModuleMap), see <span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></span></span></li>
<li><span><a href="___Graded__Module__Map_sp_vb_sp__Graded__Module__Map.html" title="a binary operator, often used for horizontal concatenation">GradedModuleMap | GradedModuleMap</a> -- a binary operator, often used for horizontal concatenation</span></li>
<li><span><a href="___Graded__Module__Map_sp_vb_vb_sp__Graded__Module__Map.html" title="a binary operator, often used for vertical concatenation">GradedModuleMap || GradedModuleMap</a> -- a binary operator, often used for vertical concatenation</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>ring(GradedModuleMap), 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><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><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>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Graded__Module__Map.html" title="the class of all maps between graded modules">GradedModuleMap</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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