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<head><title>ChainComplexMap -- the class of all maps between chain complexes</title>
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<div><h1>ChainComplexMap -- the class of all maps between chain complexes</h1>
<div class="single"><h2>Description</h2>
<div>The usual algebraic operations are available: addition, subtraction, scalar multiplication, and composition. The identity map from a chain complex to itself can be produced with <a href="_id.html" title="identity map">id</a>. An attempt to add (subtract, or compare) a ring element to a chain complex will result in the ring element being multiplied by the appropriate identity map.</div>
</div>
<div class="waystouse"><h2>Functions and methods returning a chain complex map :</h2>
<ul><li><span>ChainComplexMap * ChainComplexMap, 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>ChainComplexMap + ChainComplexMap, 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>- ChainComplexMap, 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>ChainComplexMap - ChainComplexMap, 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><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplex ** ChainComplexMap</a> -- tensor product</span></li>
<li><span>Module ** ChainComplexMap, see <span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplex ** ChainComplexMap</a> -- tensor product</span></span></li>
<li><span>ChainComplexMap ++ ChainComplexMap, 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><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplexMap ** ChainComplex</a> -- tensor product</span></li>
<li><span>ChainComplexMap ** Module, see <span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplexMap ** ChainComplex</a> -- tensor product</span></span></li>
<li><span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplexMap ** ChainComplexMap</a> -- tensor product</span></li>
<li><span><a href="___Chain__Complex__Map_sp^_sp__Z__Z.html" title="iterated composition">ChainComplexMap ^ ZZ</a> -- iterated composition</span></li>
<li><span><a href="___Chain__Complex__Map_sp__Array.html" title="degree shift">ChainComplexMap Array</a> -- degree shift</span></li>
<li><span><a href="_dual_lp__Chain__Complex__Map_rp.html" title="dual of a chain complex">dual(ChainComplexMap)</a> -- dual of a chain complex</span></li>
<li><span><a href="_extend_lp__Chain__Complex_cm__Chain__Complex_cm__Matrix_rp.html" title="extend a module map to a chain map, if possible">extend(ChainComplex,ChainComplex,Matrix)</a> -- extend a module map to a chain map, if possible</span></li>
<li><span>Hom(ChainComplexMap,Module), see <span><a href="___Hom_lp__Matrix_cm__Module_rp.html" title="induced map on Hom modules">Hom(Matrix,Module)</a> -- induced map on Hom modules</span></span></li>
<li><span>Hom(Module,ChainComplexMap), see <span><a href="___Hom_lp__Matrix_cm__Module_rp.html" title="induced map on Hom modules">Hom(Matrix,Module)</a> -- induced map on Hom modules</span></span></li>
<li><span>inducedMap(ChainComplex,ChainComplex), see <span><a href="_induced__Map_lp__Module_cm__Module_rp.html" title="compute the map induced by the identity">inducedMap(Module,Module)</a> -- compute the map induced by the identity</span></span></li>
<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>ChainComplexMap ^ 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>ChainComplexMap _ 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(ChainComplexMap), 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(ChainComplexMap), 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>ChainComplex ^ Array, see <span><a href="___Module_sp^_sp__Array.html" title="projection onto summand">Module ^ Array</a> -- projection onto summand</span></span></li>
<li><span>ChainComplex _ Array, see <span><a href="___Module_sp_us_sp__Array.html" title="inclusion from summand">Module _ Array</a> -- inclusion from summand</span></span></li>
<li><span>nullhomotopy(ChainComplexMap), see <span><a href="_nullhomotopy.html" title="make a null homotopy">nullhomotopy</a> -- make a null homotopy</span></span></li>
<li><span><a href="_resolution_lp__Matrix_rp.html" title="given a module map represented by a matrix, produce a comparison map between resolutions of its source and target">resolution(Matrix)</a> -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target</span></li>
<li><span>tensorAssociativity(ChainComplex,ChainComplex,ChainComplex), 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 chain complex map :</h2>
<ul><li><span>RingElement * ChainComplexMap, 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>ChainComplexMap + 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>ChainComplexMap + ZZ, 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 + ChainComplexMap, 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>ZZ + ChainComplexMap, 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>ChainComplexMap - 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 - ChainComplexMap, 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>ChainComplexMap == ChainComplexMap, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ChainComplexMap == RingElement, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ChainComplexMap == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>RingElement == ChainComplexMap, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == ChainComplexMap, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z.html" title="component map">ChainComplexMap _ ZZ</a> -- component map</span></li>
<li><span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z_sp_eq_sp__Thing.html" title="install component of chain complex map">ChainComplexMap _ ZZ = Thing</a> -- install component of chain complex map</span></li>
<li><span>coimage(ChainComplexMap), see <span><a href="_coimage.html" title="coimage of a map">coimage</a> -- coimage of a map</span></span></li>
<li><span>cokernel(ChainComplexMap), 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>complete(ChainComplexMap), see <span><a href="_complete.html" title="">complete</a></span></span></li>
<li><span>components(ChainComplexMap), 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="_cone_lp__Chain__Complex__Map_rp.html" title="mapping cone of a chain map">cone(ChainComplexMap)</a> -- mapping cone of a chain map</span></li>
<li><span>degree(ChainComplexMap), see <span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></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><a href="___H__H^__Z__Z_sp__Chain__Complex__Map.html" title="cohomology of a chain complex map">HH^ZZ ChainComplexMap</a> -- cohomology of a chain complex map</span></li>
<li><span><a href="___H__H_us__Z__Z_sp__Chain__Complex__Map.html" title="homology of a chain complex map">HH_ZZ ChainComplexMap</a> -- homology of a chain complex map</span></li>
<li><span>image(ChainComplexMap), see <span><a href="_image.html" title="image of a map">image</a> -- image of a map</span></span></li>
<li><span>isHomogeneous(ChainComplexMap), see <span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></span></li>
<li><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></li>
<li><span>ring(ChainComplexMap), 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__Chain__Complex__Map_rp.html" title=" find the source of a map of chain complexes">source(ChainComplexMap)</a> -- find the source of a map of chain complexes</span></li>
<li><span><a href="_sum_lp__Chain__Complex__Map_rp.html" title="direct sum of the components of a chain map">sum(ChainComplexMap)</a> -- direct sum of the components of a chain map</span></li>
<li><span><a href="_target_lp__Chain__Complex__Map_rp.html" title=" find the target of a map of chain complexes">target(ChainComplexMap)</a> -- find the target of a map of chain complexes</span></li>
<li><span><a href="_transpose_lp__Chain__Complex__Map_rp.html" title="transpose a map of chain complexes">transpose(ChainComplexMap)</a> -- transpose a map of chain complexes</span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Chain__Complex__Map.html" title="the class of all maps between chain complexes">ChainComplexMap</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Graded__Module__Map.html" title="the class of all maps between graded modules">GradedModuleMap</a> < <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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