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<div><h1>map -- make a map</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>map(Y,X,d) or map(Y,X)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>Y</tt>, an object, such as a ring, module, or chain complex</span></li>
<li><span><tt>X</tt>, another object of the same type</span></li>
<li><span><tt>d</tt>, a specification, such as a function, list, or matrix, or if omitted, understood to specify the identity map</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span>a map to <tt>Y</tt> from <tt>X</tt> defined by data <tt>d</tt>.</span></li>
</ul>
</div>
</li>
<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html">Degree => ...</a>, -- set the degree of a map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeLift => ...</a>, -- make a ring map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html">DegreeMap => ...</a>, -- make a ring map</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>The function <tt>map</tt> provides a general mechanism for constructing a map (homomorphism) between rings (<span>a <a href="___Ring__Map.html">ring map</a></span>), modules (<span>a <a href="___Matrix.html">matrix</a></span>), chain complexes (<span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>), or between objects in other categories.<p/>
See also the function <a href="_matrix.html" title="make a matrix">matrix</a>, which focuses on creating new matrices from rectangular arrays of ring elements or matrices.</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>map</tt> :</h2>
<ul><li><span><a href="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Chain__Complex__Map_rp.html" title="">map(ChainComplex,ChainComplex,ChainComplexMap)</a></span></li>
<li><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></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><tt>map(GaloisField,GaloisField)</tt> (missing documentation<!-- tag: (map,GaloisField,GaloisField) -->)</span></li>
<li><span><a href="_map_lp__Matrix_rp.html" title="make a matrix with a different degree">map(Matrix)</a> -- make a matrix with a different degree</span></li>
<li><span><a href="_map_lp__Module_rp.html" title="identity map">map(Module)</a> -- identity map</span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Function_rp.html" title="create a matrix by specifying a function that gives each entry">map(Module,Module,Function)</a> -- create a matrix by specifying a function that gives each entry</span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,Module,List)</a> -- create a matrix by giving a sparse or dense list of entries</span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Matrix_rp.html" title="create the matrix induced on generators by a given matrix">map(Module,Module,Matrix)</a> -- create the matrix induced on generators by a given matrix</span></li>
<li><span>map(Module,Module,Number), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a> -- construct the map induced by multiplication by a ring element on the generators</span></span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a> -- construct the map induced by multiplication by a ring element on the generators</span></li>
<li><span>map(Module,Module,ZZ), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a> -- construct the map induced by multiplication by a ring element on the generators</span></span></li>
<li><span>map(Module,ZZ,ZZ), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a> -- construct the map induced by multiplication by a ring element on the generators</span></span></li>
<li><span>map(Module,Module,RingMap,List), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></li>
<li><span>map(Module,Nothing,RingMap,List), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></span></li>
<li><span>map(Module,Nothing,RingMap,Matrix), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></span></li>
<li><span>map(Module,RingMap), see <span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></span></li>
<li><span><a href="_map_lp__Module_cm__Nothing_cm__List_rp.html" title="create a matrix by giving a doubly nested list of ring elements">map(Module,Nothing,List)</a> -- create a matrix by giving a doubly nested list of ring elements</span></li>
<li><span><a href="_map_lp__Module_cm__Nothing_cm__Matrix_rp.html" title="recast a matrix to have a new target, and a free module as source">map(Module,Nothing,Matrix)</a> -- recast a matrix to have a new target, and a free module as source</span></li>
<li><span><a href="_map_lp__Module_cm__Z__Z_cm__Function_rp.html" title="create a matrix from a free module by specifying a function that gives each entry">map(Module,ZZ,Function)</a> -- create a matrix from a free module by specifying a function that gives each entry</span></li>
<li><span><a href="_map_lp__Module_cm__Z__Z_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,ZZ,List)</a> -- create a matrix by giving a sparse or dense list of entries</span></li>
<li><span><a href="_map_lp__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Matrix)</a> -- make a ring map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_rp.html" title="make a ring map, using the names of the variables">map(Ring,Ring)</a> -- make a ring map, using the names of the variables</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__List_rp.html" title="make a ring map">map(Ring,Ring,List)</a> -- make a ring map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Ring,Matrix)</a> -- make a ring map</span></li>
<li><span>map(Ring,Ring,RingMap), see <span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Ring,Matrix)</a> -- make a ring map</span></span></li>
</ul>
</div>
<div><h3>Menu</h3>
<h4>Creating a map (matrix) between modules</h4>
<ul><li><span><a href="_map_lp__Module_cm__Module_cm__Function_rp.html" title="create a matrix by specifying a function that gives each entry">map(Module,Module,Function)</a> -- create a matrix by specifying a function that gives each entry</span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,Module,List)</a> -- create a matrix by giving a sparse or dense list of entries</span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a> -- construct the map induced by multiplication by a ring element on the generators</span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Matrix_rp.html" title="create the matrix induced on generators by a given matrix">map(Module,Module,Matrix)</a> -- create the matrix induced on generators by a given matrix</span></li>
</ul>
<h4>Creating a map between modules, where the source module is computed</h4>
<ul><li><span><a href="_map_lp__Module_cm__Z__Z_cm__Function_rp.html" title="create a matrix from a free module by specifying a function that gives each entry">map(Module,ZZ,Function)</a> -- create a matrix from a free module by specifying a function that gives each entry</span></li>
<li><span><a href="_map_lp__Module_cm__Nothing_cm__List_rp.html" title="create a matrix by giving a doubly nested list of ring elements">map(Module,Nothing,List)</a> -- create a matrix by giving a doubly nested list of ring elements</span></li>
<li><span><a href="_map_lp__Module_cm__Z__Z_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,ZZ,List)</a> -- create a matrix by giving a sparse or dense list of entries</span></li>
<li><span><a href="_map_lp__Module_cm__Nothing_cm__Matrix_rp.html" title="recast a matrix to have a new target, and a free module as source">map(Module,Nothing,Matrix)</a> -- recast a matrix to have a new target, and a free module as source</span></li>
</ul>
<h4>Creating a map with a different degree</h4>
<ul><li><span><a href="_map_lp__Matrix_rp.html" title="make a matrix with a different degree">map(Matrix)</a> -- make a matrix with a different degree</span></li>
</ul>
<h4>Creating a map between modules over different rings</h4>
<ul><li><span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></li>
</ul>
<h4>Creating a map between rings</h4>
<ul><li><span><a href="_map_lp__Ring_cm__Ring_rp.html" title="make a ring map, using the names of the variables">map(Ring,Ring)</a> -- make a ring map, using the names of the variables</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__List_rp.html" title="make a ring map">map(Ring,Ring,List)</a> -- make a ring map</span></li>
<li><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Ring,Matrix)</a> -- make a ring map</span></li>
</ul>
<h4>Creating a map between chain complexes</h4>
<ul><li><span><a href="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Chain__Complex__Map_rp.html" title="">map(ChainComplex,ChainComplex,ChainComplexMap)</a></span></li>
<li><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></li>
</ul>
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