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<!DOCTYPE html> <html lang="en"> <head> <title>Complexes -- development package for beta testing new version of chain complexes</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="development package for beta testing new version of chain complexes" href="index.html">Complexes</a> :: <a title="development package for beta testing new version of chain complexes" href="index.html">Complexes</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_arithmetic_spwith_spcomplex_spmaps.html">next</a> | previous | <a href="_arithmetic_spwith_spcomplex_spmaps.html">forward</a> | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Complexes -- development package for beta testing new version of chain complexes</h1> <div> <h2>Description</h2> <div> <p>This package develops new data types and routines for homological algebra. Eventually, it will replace the current facilities for homological algebra. We are making this available in order to get feedback from users before making this change. Please email the authors with any and all comments or suggestions.</p> </div> <div> <p>The overarching goal is to make all of the homological algebra routines functorial. For instance, we have <a title="gets the natural map arising from various constructions" href="_canonical__Map.html">canonical maps</a> associated to kernels, cokernels, images, coimages, cones, and cylinders.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="information about the basic constructors" href="___Making_spchain_spcomplexes.html">Making chain complexes</a> -- information about the basic constructors</span></li> <li><span><a title="information about the basic constructors" href="___Making_spmaps_spbetween_spchain_spcomplexes.html">Making maps between chain complexes</a> -- information about the basic constructors</span></li> <li><span><a title="information about accessing basic features" href="___Basic_spinvariants_spand_spproperties.html">Basic invariants and properties</a> -- information about accessing basic features</span></li> <li><span><a title="information about functorial properties" href="___Working_spwith_sp__Ext.html">Working with Ext</a> -- information about functorial properties</span></li> <li><span><a title="information about functorial properties" href="___Working_spwith_sp__Tor.html">Working with Tor</a> -- information about functorial properties</span></li> <li><span><a href="___Towards_spcomputing_spin_spthe_spderived_spcategory.html">Towards computing in the derived category</a></span></li> </ul> </div> <div> <div> <div> <h2>Authors</h2> <ul> <li><a href="http://www.mast.queensu.ca/~ggsmith">Gregory G. Smith</a><span> <<a href="mailto:ggsmith%40mast.queensu.ca">ggsmith@mast.queensu.ca</a>></span></li> <li><a href="http://www.math.cornell.edu/~mike">Mike Stillman</a><span> <<a href="mailto:mike%40math.cornell.edu">mike@math.cornell.edu</a>></span></li> </ul> </div> <div> <h2>Version</h2> <p>This documentation describes version <b>0.999995</b> of Complexes, released <b>1 May 2023</b>.</p> </div> <div> <h2>Citation</h2> <p>If you have used this package in your research, please cite it as follows:</p> <table class="examples"> <tr> <td> <pre><code class="language-bib">@misc{ComplexesSource, title = {{Complexes: beta testing new version of chain complexes. Version~0.999995}}, author = {Gregory G. Smith and Mike Stillman}, howpublished = {A \emph{Macaulay2} package available at \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}} } </code></pre> </td> </tr> </table> </div> <div> <h2>Exports</h2> <div class="exports"> <ul> <li>Types <ul> <li><span><a title="the class of all chain complexes" href="___Complex.html">Complex</a> -- the class of all chain complexes</span></li> <li><span><a title="the class of all maps between chain complexes" href="___Complex__Map.html">ComplexMap</a> -- the class of all maps between chain complexes</span></li> </ul> </li> <li>Functions and commands <ul> <li><span><a title="map from a free resolution to a module regarded as a complex" href="_augmentation__Map.html">augmentationMap</a> -- map from a free resolution to a module regarded as a complex</span></li> <li><span><a title="gets the natural map arising from various constructions" href="_canonical__Map.html">canonicalMap</a> -- gets the natural map arising from various constructions</span></li> <li><span><kbd>canonicalTruncation</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>complex</kbd> -- see <span><a title="make a chain complex" href="_complex_lp__List_rp.html">complex(List)</a> -- make a chain complex</span></span></li> <li><span><a title="indices on which a complex may be non-zero" href="_concentration.html">concentration</a> -- indices on which a complex may be non-zero</span></li> <li><span><kbd>connectingExtMap</kbd> -- see <span><a title="makes the connecting maps in Ext" href="_connecting__Ext__Map_lp__Module_cm__Matrix_cm__Matrix_rp.html">connectingExtMap(Module,Matrix,Matrix)</a> -- makes the connecting maps in Ext</span></span></li> <li><span><kbd>connectingMap</kbd> -- see <span><a title="construct the connecting homomorphism on homology" href="_connecting__Map_lp__Complex__Map_cm__Complex__Map_rp.html">connectingMap(ComplexMap,ComplexMap)</a> -- construct the connecting homomorphism on homology</span></span></li> <li><span><kbd>connectingTorMap</kbd> -- see <span><a title="makes the connecting maps in Tor" href="_connecting__Tor__Map_lp__Module_cm__Matrix_cm__Matrix_rp.html">connectingTorMap(Module,Matrix,Matrix)</a> -- makes the connecting maps in Tor</span></span></li> <li><span><span class="tt">constantStrand</span> (missing documentation)<!--tag: constantStrand--> </span></li> <li><span><a title="make the mapping cylinder of a morphism of chain complexes" href="_cylinder.html">cylinder</a> -- make the mapping cylinder of a morphism of chain complexes</span></li> <li><span><span class="tt">epicResolutionMap</span> (missing documentation)<!--tag: epicResolutionMap--> </span></li> <li><span><a title="compute a free resolution of a module or ideal" href="_free__Resolution.html">freeResolution</a> -- compute a free resolution of a module or ideal</span></li> <li><span><kbd>horseshoeResolution</kbd> -- see <span><a title="make the horseshoe resolution" href="_horseshoe__Resolution_lp__Complex_rp.html">horseshoeResolution(Complex)</a> -- make the horseshoe resolution</span></span></li> <li><span><kbd>isComplexMorphism</kbd> -- see <span><a title="whether a complex map is a morphism of complexes" href="_is__Complex__Morphism_lp__Complex__Map_rp.html">isComplexMorphism(ComplexMap)</a> -- whether a complex map is a morphism of complexes</span></span></li> <li><span><kbd>isFree</kbd> -- see <span><a title="whether a complex consists of free modules" href="_is__Free_lp__Complex_rp.html">isFree(Complex)</a> -- whether a complex consists of free modules</span></span></li> <li><span><kbd>isNullHomotopic</kbd> -- see <span><a title="whether a map of complexes is null-homotopic" href="_is__Null__Homotopic_lp__Complex__Map_rp.html">isNullHomotopic(ComplexMap)</a> -- whether a map of complexes is null-homotopic</span></span></li> <li><span><kbd>isNullHomotopyOf</kbd> -- see <span><a title="whether the first map of chain complexes is a null homotopy for the second" href="_is__Null__Homotopy__Of_lp__Complex__Map_cm__Complex__Map_rp.html">isNullHomotopyOf(ComplexMap,ComplexMap)</a> -- whether the first map of chain complexes is a null homotopy for the second</span></span></li> <li><span><kbd>isQuasiIsomorphism</kbd> -- see <span><a title="whether a map of complexes is a quasi-isomorphism" href="_is__Quasi__Isomorphism_lp__Complex__Map_rp.html">isQuasiIsomorphism(ComplexMap)</a> -- whether a map of complexes is a quasi-isomorphism</span></span></li> <li><span><kbd>isShortExactSequence</kbd> -- see <span><a title="whether a chain complex is a short exact sequence" href="_is__Short__Exact__Sequence_lp__Complex_rp.html">isShortExactSequence(Complex)</a> -- whether a chain complex is a short exact sequence</span></span></li> <li><span><kbd>koszulComplex</kbd> -- see <span><a title="makes the Koszul complex" href="_koszul__Complex_lp__Matrix_rp.html">koszulComplex(Matrix)</a> -- makes the Koszul complex</span></span></li> <li><span><kbd>homotopyMap</kbd> -- see <span><a title="lift a map of chain complexes along a quasi-isomorphism" href="_lift__Map__Along__Quasi__Isomorphism_lp__Complex__Map_cm__Complex__Map_rp.html">liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)</a> -- lift a map of chain complexes along a quasi-isomorphism</span></span></li> <li><span><kbd>liftMapAlongQuasiIsomorphism</kbd> -- see <span><a title="lift a map of chain complexes along a quasi-isomorphism" href="_lift__Map__Along__Quasi__Isomorphism_lp__Complex__Map_cm__Complex__Map_rp.html">liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)</a> -- lift a map of chain complexes along a quasi-isomorphism</span></span></li> <li><span><kbd>longExactSequence</kbd> -- see <span><a title="make the long exact sequence in homology" href="_long__Exact__Sequence_lp__Complex__Map_cm__Complex__Map_rp.html">longExactSequence(ComplexMap,ComplexMap)</a> -- make the long exact sequence in homology</span></span></li> <li><span><kbd>naiveTruncation</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><kbd>nullHomotopy</kbd> -- see <span><a title="a map which is a candidate for being a null homotopy" href="_null__Homotopy_lp__Complex__Map_rp.html">nullHomotopy(ComplexMap)</a> -- a map which is a candidate for being a null homotopy</span></span></li> <li><span><kbd>randomComplexMap</kbd> -- see <span><a title="a random map of chain complexes" href="_random__Complex__Map_lp__Complex_cm__Complex_rp.html">randomComplexMap(Complex,Complex)</a> -- a random map of chain complexes</span></span></li> <li><span><a title="map from a free resolution to the given complex" href="_resolution__Map.html">resolutionMap</a> -- map from a free resolution to the given complex</span></li> <li><span><kbd>tensorCommutativity</kbd> -- see <span><a title="make the canonical isomorphism arising from commutativity" href="_tensor__Commutativity_lp__Module_cm__Module_rp.html">tensorCommutativity(Module,Module)</a> -- make the canonical isomorphism arising from commutativity</span></span></li> <li><span><kbd>torSymmetry</kbd> -- see <span><a title="makes the canonical isomorphism realizing the symmetry of Tor" href="_tor__Symmetry_lp__Z__Z_cm__Module_cm__Module_rp.html">torSymmetry(ZZ,Module,Module)</a> -- makes the canonical isomorphism realizing the symmetry of Tor</span></span></li> <li><span><kbd>yonedaExtension'</kbd> -- see <span><a title="identifies the element of Ext corresponding to an extension" href="_yoneda__Extension_sq_lp__Complex_rp.html">yonedaExtension'(Complex)</a> -- identifies the element of Ext corresponding to an extension</span></span></li> <li><span><kbd>yonedaExtension</kbd> -- see <span><a title="creates a chain complex representing an extension of modules" href="_yoneda__Extension_lp__Matrix_rp.html">yonedaExtension(Matrix)</a> -- creates a chain complex representing an extension of modules</span></span></li> <li><span><kbd>yonedaMap'</kbd> -- see <span><a title="identifies the element of Ext corresponding to a map of free resolutions" href="_yoneda__Map_sq_lp__Complex__Map_rp.html">yonedaMap'(ComplexMap)</a> -- identifies the element of Ext corresponding to a map of free resolutions</span></span></li> <li><span><kbd>yonedaMap</kbd> -- see <span><a title="creates a chain complex map representing an extension of modules" href="_yoneda__Map_lp__Matrix_rp.html">yonedaMap(Matrix)</a> -- creates a chain complex map representing an extension of modules</span></span></li> <li><span><kbd>yonedaProduct</kbd> -- see <span><a title="make the product of two elements in Ext modules" href="_yoneda__Product_lp__Matrix_cm__Matrix_rp.html">yonedaProduct(Matrix,Matrix)</a> -- make the product of two elements in Ext modules</span></span></li> </ul> </li> <li>Methods <ul> <li><span><kbd>- ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap * Number</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap * RingElement</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap + ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap + Number</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap + RingElement</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap - ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap - Number</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>ComplexMap - RingElement</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>Number * ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>Number + ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>Number - ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>RingElement * ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>RingElement + ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>RingElement - ComplexMap</kbd> -- see <span><a title="perform arithmetic operations on complex maps" href="_arithmetic_spwith_spcomplex_spmaps.html">arithmetic with complex maps</a> -- perform arithmetic operations on complex maps</span></span></li> <li><span><kbd>augmentationMap(Complex)</kbd> -- see <span><a title="map from a free resolution to a module regarded as a complex" href="_augmentation__Map.html">augmentationMap</a> -- map from a free resolution to a module regarded as a complex</span></span></li> <li><span><span class="tt">basis(List,Complex)</span> (missing documentation)<!--tag: (basis,List,Complex)--> </span></li> <li><span><span class="tt">basis(List,ComplexMap)</span> (missing documentation)<!--tag: (basis,List,ComplexMap)--> </span></li> <li><span><span class="tt">basis(ZZ,Complex)</span> (missing documentation)<!--tag: (basis,ZZ,Complex)--> </span></li> <li><span><span class="tt">basis(ZZ,ComplexMap)</span> (missing documentation)<!--tag: (basis,ZZ,ComplexMap)--> </span></li> <li><span><a title="display of degrees in a complex" href="_betti_lp__Complex_rp.html">betti(Complex)</a> -- display of degrees in a complex</span></li> <li><span><kbd>canonicalMap(Complex,Complex)</kbd> -- see <span><a title="gets the natural map arising from various constructions" href="_canonical__Map.html">canonicalMap</a> -- gets the natural map arising from various constructions</span></span></li> <li><span><kbd>canonicalTruncation(Complex,InfiniteNumber,InfiniteNumber)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(Complex,InfiniteNumber,ZZ)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(Complex,Nothing,ZZ)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(Complex,Sequence)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(Complex,ZZ,InfiniteNumber)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(Complex,ZZ,Nothing)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(Complex,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></li> <li><span><kbd>canonicalTruncation(ComplexMap,InfiniteNumber,InfiniteNumber)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(ComplexMap,InfiniteNumber,ZZ)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(ComplexMap,Nothing,ZZ)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(ComplexMap,Sequence)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(ComplexMap,ZZ,InfiniteNumber)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><kbd>canonicalTruncation(ComplexMap,ZZ,Nothing)</kbd> -- see <span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></span></li> <li><span><a title="reducing the number of non-zero terms of a complex" href="_canonical__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">canonicalTruncation(ComplexMap,ZZ,ZZ)</a> -- reducing the number of non-zero terms of a complex</span></li> <li><span><a title="make the coimage of a map of complexes" href="_coimage_lp__Complex__Map_rp.html">coimage(ComplexMap)</a> -- make the coimage of a map of complexes</span></li> <li><span><a title="make the cokernel of a map of complexes" href="_cokernel_lp__Complex__Map_rp.html">cokernel(ComplexMap)</a> -- make the cokernel of a map of complexes</span></li> <li><span><span class="tt">complete(Complex)</span> (missing documentation)<!--tag: (complete,Complex)--> </span></li> <li><span><span class="tt">complete(ComplexMap)</span> (missing documentation)<!--tag: (complete,ComplexMap)--> </span></li> <li><span><a title="tensor product of complexes" href="___Complex_sp_st_st_sp__Complex.html">Complex ** Complex</a> -- tensor product of complexes</span></li> <li><span><kbd>Complex ** Module</kbd> -- see <span><a title="tensor product of complexes" href="___Complex_sp_st_st_sp__Complex.html">Complex ** Complex</a> -- tensor product of complexes</span></span></li> <li><span><kbd>Module ** Complex</kbd> -- see <span><a title="tensor product of complexes" href="___Complex_sp_st_st_sp__Complex.html">Complex ** Complex</a> -- tensor product of complexes</span></span></li> <li><span><kbd>tensor(Complex,Complex)</kbd> -- see <span><a title="tensor product of complexes" href="___Complex_sp_st_st_sp__Complex.html">Complex ** Complex</a> -- tensor product of complexes</span></span></li> <li><span><a title="create the tensor product of a complex and a map of modules" href="___Complex_sp_st_st_sp__Matrix.html">Complex ** Matrix</a> -- create the tensor product of a complex and a map of modules</span></li> <li><span><kbd>Matrix ** Complex</kbd> -- see <span><a title="create the tensor product of a complex and a map of modules" href="___Complex_sp_st_st_sp__Matrix.html">Complex ** Matrix</a> -- create the tensor product of a complex and a map of modules</span></span></li> <li><span><a title="whether two complexes are equal" href="___Complex_sp_eq_eq_sp__Complex.html">Complex == Complex</a> -- whether two complexes are equal</span></li> <li><span><kbd>Complex == ZZ</kbd> -- see <span><a title="whether two complexes are equal" href="___Complex_sp_eq_eq_sp__Complex.html">Complex == Complex</a> -- whether two complexes are equal</span></span></li> <li><span><kbd>ZZ == Complex</kbd> -- see <span><a title="whether two complexes are equal" href="___Complex_sp_eq_eq_sp__Complex.html">Complex == Complex</a> -- whether two complexes are equal</span></span></li> <li><span><kbd>Complex ^ Array</kbd> -- see <span><a title="the canonical inclusion or projection map of a direct sum" href="___Complex_sp_us_sp__Array.html">Complex _ Array</a> -- the canonical inclusion or projection map of a direct sum</span></span></li> <li><span><a title="the canonical inclusion or projection map of a direct sum" href="___Complex_sp_us_sp__Array.html">Complex _ Array</a> -- the canonical inclusion or projection map of a direct sum</span></li> <li><span><kbd>Complex ^ ZZ</kbd> -- see <span><a title="access individual object in a complex" href="___Complex_sp_us_sp__Z__Z.html">Complex _ ZZ</a> -- access individual object in a complex</span></span></li> <li><span><a title="access individual object in a complex" href="___Complex_sp_us_sp__Z__Z.html">Complex _ ZZ</a> -- access individual object in a complex</span></li> <li><span><a title="shift a complex or complex map" href="___Complex_sp__Array.html">Complex Array</a> -- shift a complex or complex map</span></li> <li><span><kbd>ComplexMap Array</kbd> -- see <span><a title="shift a complex or complex map" href="___Complex_sp__Array.html">Complex Array</a> -- shift a complex or complex map</span></span></li> <li><span><a title="make a complex by reindexing the terms of the complex" href="_complex_lp__Complex_rp.html">complex(Complex)</a> -- make a complex by reindexing the terms of the complex</span></li> <li><span><a title="make a complex by specifying the differential" href="_complex_lp__Complex__Map_rp.html">complex(ComplexMap)</a> -- make a complex by specifying the differential</span></li> <li><span><a title="make a chain complex" href="_complex_lp__Hash__Table_rp.html">complex(HashTable)</a> -- make a chain complex</span></li> <li><span><a title="make a chain complex" href="_complex_lp__List_rp.html">complex(List)</a> -- make a chain complex</span></li> <li><span><kbd>complex(Matrix)</kbd> -- see <span><a title="make a chain complex" href="_complex_lp__List_rp.html">complex(List)</a> -- make a chain complex</span></span></li> <li><span><kbd>complex(Ideal)</kbd> -- see <span><a title="make a chain complex of length zero" href="_complex_lp__Module_rp.html">complex(Module)</a> -- make a chain complex of length zero</span></span></li> <li><span><a title="make a chain complex of length zero" href="_complex_lp__Module_rp.html">complex(Module)</a> -- make a chain complex of length zero</span></li> <li><span><kbd>complex(Ring)</kbd> -- see <span><a title="make a chain complex of length zero" href="_complex_lp__Module_rp.html">complex(Module)</a> -- make a chain complex of length zero</span></span></li> <li><span><a title="composition of homomorphisms of complexes" href="___Complex__Map_sp_st_sp__Complex__Map.html">ComplexMap * ComplexMap</a> -- composition of homomorphisms of complexes</span></li> <li><span><kbd>Complex ** ComplexMap</kbd> -- see <span><a title="the map of complexes between tensor complexes" href="___Complex__Map_sp_st_st_sp__Complex__Map.html">ComplexMap ** ComplexMap</a> -- the map of complexes between tensor complexes</span></span></li> <li><span><kbd>ComplexMap ** Complex</kbd> -- see <span><a title="the map of complexes between tensor complexes" href="___Complex__Map_sp_st_st_sp__Complex__Map.html">ComplexMap ** ComplexMap</a> -- the map of complexes between tensor complexes</span></span></li> <li><span><a title="the map of complexes between tensor complexes" href="___Complex__Map_sp_st_st_sp__Complex__Map.html">ComplexMap ** ComplexMap</a> -- the map of complexes between tensor complexes</span></li> <li><span><kbd>ComplexMap ** Module</kbd> -- see <span><a title="the map of complexes between tensor complexes" href="___Complex__Map_sp_st_st_sp__Complex__Map.html">ComplexMap ** ComplexMap</a> -- the map of complexes between tensor complexes</span></span></li> <li><span><kbd>Module ** ComplexMap</kbd> -- see <span><a title="the map of complexes between tensor complexes" href="___Complex__Map_sp_st_st_sp__Complex__Map.html">ComplexMap ** ComplexMap</a> -- the map of complexes between tensor complexes</span></span></li> <li><span><kbd>tensor(ComplexMap,ComplexMap)</kbd> -- see <span><a title="the map of complexes between tensor complexes" href="___Complex__Map_sp_st_st_sp__Complex__Map.html">ComplexMap ** ComplexMap</a> -- the map of complexes between tensor complexes</span></span></li> <li><span><a title="direct sum of complex maps" href="___Complex__Map_sp_pl_pl_sp__Complex__Map.html">ComplexMap ++ ComplexMap</a> -- direct sum of complex maps</span></li> <li><span><kbd>directSum(ComplexMap)</kbd> -- see <span><a title="direct sum of complex maps" href="___Complex__Map_sp_pl_pl_sp__Complex__Map.html">ComplexMap ++ ComplexMap</a> -- direct sum of complex maps</span></span></li> <li><span><a title="whether two complex maps are equal" href="___Complex__Map_sp_eq_eq_sp__Complex__Map.html">ComplexMap == ComplexMap</a> -- whether two complex maps are equal</span></li> <li><span><kbd>ComplexMap == ZZ</kbd> -- see <span><a title="whether two complex maps are equal" href="___Complex__Map_sp_eq_eq_sp__Complex__Map.html">ComplexMap == ComplexMap</a> -- whether two complex maps are equal</span></span></li> <li><span><kbd>ZZ == ComplexMap</kbd> -- see <span><a title="whether two complex maps are equal" href="___Complex__Map_sp_eq_eq_sp__Complex__Map.html">ComplexMap == ComplexMap</a> -- whether two complex maps are equal</span></span></li> <li><span><a title="the composition with the canonical inclusion or projection map" href="___Complex__Map_sp%5E_sp__Array.html">ComplexMap ^ Array</a> -- the composition with the canonical inclusion or projection map</span></li> <li><span><kbd>ComplexMap _ Array</kbd> -- see <span><a title="the composition with the canonical inclusion or projection map" href="___Complex__Map_sp%5E_sp__Array.html">ComplexMap ^ Array</a> -- the composition with the canonical inclusion or projection map</span></span></li> <li><span><a title="the n-fold composition" href="___Complex__Map_sp%5E_sp__Z__Z.html">ComplexMap ^ ZZ</a> -- the n-fold composition</span></li> <li><span><a title="access individual matrices in a complex map" href="___Complex__Map_sp_us_sp__Z__Z.html">ComplexMap _ ZZ</a> -- access individual matrices in a complex map</span></li> <li><span><a title="join or concatenate maps horizontally" href="___Complex__Map_sp_vb_sp__Complex__Map.html">ComplexMap | ComplexMap</a> -- join or concatenate maps horizontally</span></li> <li><span><a title="join or concatenate maps vertically" href="___Complex__Map_sp_vb_vb_sp__Complex__Map.html">ComplexMap || ComplexMap</a> -- join or concatenate maps vertically</span></li> <li><span><a title="list the components of a direct sum" href="_components_lp__Complex_rp.html">components(Complex)</a> -- list the components of a direct sum</span></li> <li><span><a title="list the components of a direct sum" href="_components_lp__Complex__Map_rp.html">components(ComplexMap)</a> -- list the components of a direct sum</span></li> <li><span><kbd>concentration(Complex)</kbd> -- see <span><a title="indices on which a complex may be non-zero" href="_concentration.html">concentration</a> -- indices on which a complex may be non-zero</span></span></li> <li><span><kbd>max(Complex)</kbd> -- see <span><a title="indices on which a complex may be non-zero" href="_concentration.html">concentration</a> -- indices on which a complex may be non-zero</span></span></li> <li><span><kbd>min(Complex)</kbd> -- see <span><a title="indices on which a complex may be non-zero" href="_concentration.html">concentration</a> -- indices on which a complex may be non-zero</span></span></li> <li><span><a title="indices on which a complex map may be non-zero" href="_concentration_lp__Complex__Map_rp.html">concentration(ComplexMap)</a> -- indices on which a complex map may be non-zero</span></li> <li><span><a title="make the mapping cone of a morphism of chain complexes" href="_cone_lp__Complex__Map_rp.html">cone(ComplexMap)</a> -- make the mapping cone of a morphism of chain complexes</span></li> <li><span><kbd>connectingExtMap(Matrix,Matrix,Module)</kbd> -- see <span><a title="makes the connecting maps in Ext" href="_connecting__Ext__Map_lp__Module_cm__Matrix_cm__Matrix_rp.html">connectingExtMap(Module,Matrix,Matrix)</a> -- makes the connecting maps in Ext</span></span></li> <li><span><a title="makes the connecting maps in Ext" href="_connecting__Ext__Map_lp__Module_cm__Matrix_cm__Matrix_rp.html">connectingExtMap(Module,Matrix,Matrix)</a> -- makes the connecting maps in Ext</span></li> <li><span><a title="construct the connecting homomorphism on homology" href="_connecting__Map_lp__Complex__Map_cm__Complex__Map_rp.html">connectingMap(ComplexMap,ComplexMap)</a> -- construct the connecting homomorphism on homology</span></li> <li><span><kbd>connectingTorMap(Matrix,Matrix,Module)</kbd> -- see <span><a title="makes the connecting maps in Tor" href="_connecting__Tor__Map_lp__Module_cm__Matrix_cm__Matrix_rp.html">connectingTorMap(Module,Matrix,Matrix)</a> -- makes the connecting maps in Tor</span></span></li> <li><span><a title="makes the connecting maps in Tor" href="_connecting__Tor__Map_lp__Module_cm__Matrix_cm__Matrix_rp.html">connectingTorMap(Module,Matrix,Matrix)</a> -- makes the connecting maps in Tor</span></li> <li><span><span class="tt">constantStrand(Complex,List)</span> (missing documentation)<!--tag: (constantStrand,Complex,List)--> </span></li> <li><span><span class="tt">constantStrand(Complex,ZZ)</span> (missing documentation)<!--tag: (constantStrand,Complex,ZZ)--> </span></li> <li><span><kbd>cylinder(ComplexMap)</kbd> -- see <span><a title="make the mapping cylinder of a morphism of chain complexes" href="_cylinder.html">cylinder</a> -- make the mapping cylinder of a morphism of chain complexes</span></span></li> <li><span><a title="get the degree of a map of chain complexes" href="_degree_lp__Complex__Map_rp.html">degree(ComplexMap)</a> -- get the degree of a map of chain complexes</span></li> <li><span><kbd>Symbol ^ Complex</kbd> -- see <span><a title="get the maps between the terms in a complex" href="_differential_spof_spa_spchain_spcomplex.html">differential of a chain complex</a> -- get the maps between the terms in a complex</span></span></li> <li><span><kbd>Complex ++ Complex</kbd> -- see <span><a title="direct sum of complexes" href="_direct__Sum_lp__Complex_rp.html">directSum(Complex)</a> -- direct sum of complexes</span></span></li> <li><span><a title="direct sum of complexes" href="_direct__Sum_lp__Complex_rp.html">directSum(Complex)</a> -- direct sum of complexes</span></li> <li><span><a title="make the dual of a complex" href="_dual_lp__Complex_rp.html">dual(Complex)</a> -- make the dual of a complex</span></li> <li><span><a title="the dual of a map of complexes" href="_dual_lp__Complex__Map_rp.html">dual(ComplexMap)</a> -- the dual of a map of complexes</span></li> <li><span><kbd>transpose(ComplexMap)</kbd> -- see <span><a title="the dual of a map of complexes" href="_dual_lp__Complex__Map_rp.html">dual(ComplexMap)</a> -- the dual of a map of complexes</span></span></li> <li><span><span class="tt">epicResolutionMap(Complex)</span> (missing documentation)<!--tag: (epicResolutionMap,Complex)--> </span></li> <li><span><kbd>extend(Complex,Complex,Matrix)</kbd> -- see <span><a title="extend a map of modules to a map of chain complexes" href="_extend_lp__Complex_cm__Complex_cm__Matrix_cm__Sequence_rp.html">extend(Complex,Complex,Matrix,Sequence)</a> -- extend a map of modules to a map of chain complexes</span></span></li> <li><span><a title="extend a map of modules to a map of chain complexes" href="_extend_lp__Complex_cm__Complex_cm__Matrix_cm__Sequence_rp.html">extend(Complex,Complex,Matrix,Sequence)</a> -- extend a map of modules to a map of chain complexes</span></li> <li><span><span class="tt">formation(Complex)</span> (missing documentation)<!--tag: (formation,Complex)--> </span></li> <li><span><kbd>freeResolution(Ideal)</kbd> -- see <span><a title="compute a free resolution of a module or ideal" href="_free__Resolution.html">freeResolution</a> -- compute a free resolution of a module or ideal</span></span></li> <li><span><kbd>freeResolution(Module)</kbd> -- see <span><a title="compute a free resolution of a module or ideal" href="_free__Resolution.html">freeResolution</a> -- compute a free resolution of a module or ideal</span></span></li> <li><span><kbd>freeResolution(MonomialIdeal)</kbd> -- see <span><a title="compute a free resolution of a module or ideal" href="_free__Resolution.html">freeResolution</a> -- compute a free resolution of a module or ideal</span></span></li> <li><span><a title="minimal free resolution of a complex" href="_free__Resolution_lp__Complex_rp.html">freeResolution(Complex)</a> -- minimal free resolution of a complex</span></li> <li><span><a title="compute the induced map between free resolutions" href="_free__Resolution_lp__Matrix_rp.html">freeResolution(Matrix)</a> -- compute the induced map between free resolutions</span></li> <li><span><a title="a new complex in which the differential is zero" href="_graded__Module_lp__Complex_rp.html">gradedModule(Complex)</a> -- a new complex in which the differential is zero</span></li> <li><span><a title="homology of a complex" href="___H__H_sp__Complex.html">HH Complex</a> -- homology of a complex</span></li> <li><span><a title="induced map on homology or cohomology" href="___H__H_sp__Complex__Map.html">HH ComplexMap</a> -- induced map on homology or cohomology</span></li> <li><span><kbd>HH^ZZ ComplexMap</kbd> -- see <span><a title="induced map on homology or cohomology" href="___H__H_sp__Complex__Map.html">HH ComplexMap</a> -- induced map on homology or cohomology</span></span></li> <li><span><kbd>HH_ZZ ComplexMap</kbd> -- see <span><a title="induced map on homology or cohomology" href="___H__H_sp__Complex__Map.html">HH ComplexMap</a> -- induced map on homology or cohomology</span></span></li> <li><span><kbd>HH^ZZ Complex</kbd> -- see <span><a title="homology or cohomology module of a complex" href="___H__H_us__Z__Z_sp__Complex.html">HH_ZZ Complex</a> -- homology or cohomology module of a complex</span></span></li> <li><span><a title="homology or cohomology module of a complex" href="___H__H_us__Z__Z_sp__Complex.html">HH_ZZ Complex</a> -- homology or cohomology module of a complex</span></li> <li><span><a title="the complex of homomorphisms between two complexes" href="___Hom_lp__Complex_cm__Complex_rp.html">Hom(Complex,Complex)</a> -- the complex of homomorphisms between two complexes</span></li> <li><span><kbd>Hom(Complex,Module)</kbd> -- see <span><a title="the complex of homomorphisms between two complexes" href="___Hom_lp__Complex_cm__Complex_rp.html">Hom(Complex,Complex)</a> -- the complex of homomorphisms between two complexes</span></span></li> <li><span><kbd>Hom(Complex,Ring)</kbd> -- see <span><a title="the complex of homomorphisms between two complexes" href="___Hom_lp__Complex_cm__Complex_rp.html">Hom(Complex,Complex)</a> -- the complex of homomorphisms between two complexes</span></span></li> <li><span><kbd>Hom(Module,Complex)</kbd> -- see <span><a title="the complex of homomorphisms between two complexes" href="___Hom_lp__Complex_cm__Complex_rp.html">Hom(Complex,Complex)</a> -- the complex of homomorphisms between two complexes</span></span></li> <li><span><kbd>Hom(Ring,Complex)</kbd> -- see <span><a title="the complex of homomorphisms between two complexes" href="___Hom_lp__Complex_cm__Complex_rp.html">Hom(Complex,Complex)</a> -- the complex of homomorphisms between two complexes</span></span></li> <li><span><kbd>Hom(Complex,ComplexMap)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(Complex,Matrix)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(ComplexMap,Complex)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></li> <li><span><kbd>Hom(ComplexMap,Matrix)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(ComplexMap,Module)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(ComplexMap,Ring)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(Matrix,Complex)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(Matrix,ComplexMap)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(Module,ComplexMap)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><kbd>Hom(Ring,ComplexMap)</kbd> -- see <span><a title="the map of complexes between Hom complexes" href="___Hom_lp__Complex__Map_cm__Complex__Map_rp.html">Hom(ComplexMap,ComplexMap)</a> -- the map of complexes between Hom complexes</span></span></li> <li><span><a title="get the element of Hom from a map of complexes" href="_homomorphism_sq_lp__Complex__Map_rp.html">homomorphism'(ComplexMap)</a> -- get the element of Hom from a map of complexes</span></li> <li><span><a title="get the homomorphism from an element of Hom" href="_homomorphism_lp__Complex__Map_rp.html">homomorphism(ComplexMap)</a> -- get the homomorphism from an element of Hom</span></li> <li><span><a title="get the homomorphism from an element of Hom" href="_homomorphism_lp__Z__Z_cm__Matrix_cm__Complex_rp.html">homomorphism(ZZ,Matrix,Complex)</a> -- get the homomorphism from an element of Hom</span></li> <li><span><a title="make the horseshoe resolution" href="_horseshoe__Resolution_lp__Complex_rp.html">horseshoeResolution(Complex)</a> -- make the horseshoe resolution</span></li> <li><span><kbd>horseshoeResolution(Matrix,Matrix)</kbd> -- see <span><a title="make the horseshoe resolution" href="_horseshoe__Resolution_lp__Complex_rp.html">horseshoeResolution(Complex)</a> -- make the horseshoe resolution</span></span></li> <li><span><a title="make the image of a map of complexes" href="_image_lp__Complex__Map_rp.html">image(ComplexMap)</a> -- make the image of a map of complexes</span></li> <li><span><a title="make the map of complexes induced at each term by the identity map" href="_induced__Map_lp__Complex_cm__Complex_rp.html">inducedMap(Complex,Complex)</a> -- make the map of complexes induced at each term by the identity map</span></li> <li><span><a title="whether a complex map commutes with the differentials" href="_is__Commutative_lp__Complex__Map_rp.html">isCommutative(ComplexMap)</a> -- whether a complex map commutes with the differentials</span></li> <li><span><a title="whether a complex map is a morphism of complexes" href="_is__Complex__Morphism_lp__Complex__Map_rp.html">isComplexMorphism(ComplexMap)</a> -- whether a complex map is a morphism of complexes</span></li> <li><span><kbd>isExact(Complex)</kbd> -- see <span><a title="whether a complex is exact" href="_is__Exact_lp__Complex_cm__Number_cm__Number_rp.html">isExact(Complex,Number,Number)</a> -- whether a complex is exact</span></span></li> <li><span><kbd>isExact(Complex,InfiniteNumber,InfiniteNumber)</kbd> -- see <span><a title="whether a complex is exact" href="_is__Exact_lp__Complex_cm__Number_cm__Number_rp.html">isExact(Complex,Number,Number)</a> -- whether a complex is exact</span></span></li> <li><span><kbd>isExact(Complex,InfiniteNumber,Number)</kbd> -- see <span><a title="whether a complex is exact" href="_is__Exact_lp__Complex_cm__Number_cm__Number_rp.html">isExact(Complex,Number,Number)</a> -- whether a complex is exact</span></span></li> <li><span><kbd>isExact(Complex,Number,InfiniteNumber)</kbd> -- see <span><a title="whether a complex is exact" href="_is__Exact_lp__Complex_cm__Number_cm__Number_rp.html">isExact(Complex,Number,Number)</a> -- whether a complex is exact</span></span></li> <li><span><a title="whether a complex is exact" href="_is__Exact_lp__Complex_cm__Number_cm__Number_rp.html">isExact(Complex,Number,Number)</a> -- whether a complex is exact</span></li> <li><span><a title="whether a complex consists of free modules" href="_is__Free_lp__Complex_rp.html">isFree(Complex)</a> -- whether a complex consists of free modules</span></li> <li><span><a title="whether a complex is homogeneous" href="_is__Homogeneous_lp__Complex_rp.html">isHomogeneous(Complex)</a> -- whether a complex is homogeneous</span></li> <li><span><a title="whether a map of complexes is homogeneous" href="_is__Homogeneous_lp__Complex__Map_rp.html">isHomogeneous(ComplexMap)</a> -- whether a map of complexes is homogeneous</span></li> <li><span><a title="whether a map of complexes is null-homotopic" href="_is__Null__Homotopic_lp__Complex__Map_rp.html">isNullHomotopic(ComplexMap)</a> -- whether a map of complexes is null-homotopic</span></li> <li><span><a title="whether the first map of chain complexes is a null homotopy for the second" href="_is__Null__Homotopy__Of_lp__Complex__Map_cm__Complex__Map_rp.html">isNullHomotopyOf(ComplexMap,ComplexMap)</a> -- whether the first map of chain complexes is a null homotopy for the second</span></li> <li><span><a title="whether a map of complexes is a quasi-isomorphism" href="_is__Quasi__Isomorphism_lp__Complex__Map_rp.html">isQuasiIsomorphism(ComplexMap)</a> -- whether a map of complexes is a quasi-isomorphism</span></li> <li><span><a title="whether a chain complex is a short exact sequence" href="_is__Short__Exact__Sequence_lp__Complex_rp.html">isShortExactSequence(Complex)</a> -- whether a chain complex is a short exact sequence</span></li> <li><span><a title="whether a pair of complex maps forms a short exact sequence" href="_is__Short__Exact__Sequence_lp__Complex__Map_cm__Complex__Map_rp.html">isShortExactSequence(ComplexMap,ComplexMap)</a> -- whether a pair of complex maps forms a short exact sequence</span></li> <li><span><a title="whether a pair of matrices forms a short exact sequence" href="_is__Short__Exact__Sequence_lp__Matrix_cm__Matrix_rp.html">isShortExactSequence(Matrix,Matrix)</a> -- whether a pair of matrices forms a short exact sequence</span></li> <li><span><a title="whether a complex is well-defined" href="_is__Well__Defined_lp__Complex_rp.html">isWellDefined(Complex)</a> -- whether a complex is well-defined</span></li> <li><span><a title="whether a map of chain complexes is well-defined" href="_is__Well__Defined_lp__Complex__Map_rp.html">isWellDefined(ComplexMap)</a> -- whether a map of chain complexes is well-defined</span></li> <li><span><a title="make the kernel of a map of complexes" href="_kernel_lp__Complex__Map_rp.html">kernel(ComplexMap)</a> -- make the kernel of a map of complexes</span></li> <li><span><kbd>koszulComplex(List)</kbd> -- see <span><a title="makes the Koszul complex" href="_koszul__Complex_lp__Matrix_rp.html">koszulComplex(Matrix)</a> -- makes the Koszul complex</span></span></li> <li><span><a title="makes the Koszul complex" href="_koszul__Complex_lp__Matrix_rp.html">koszulComplex(Matrix)</a> -- makes the Koszul complex</span></li> <li><span><a title="length of a complex" href="_length_lp__Complex_rp.html">length(Complex)</a> -- length of a complex</span></li> <li><span><kbd>ComplexMap // ComplexMap</kbd> -- see <span><a title="lift a map of chain complexes along a quasi-isomorphism" href="_lift__Map__Along__Quasi__Isomorphism_lp__Complex__Map_cm__Complex__Map_rp.html">liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)</a> -- lift a map of chain complexes along a quasi-isomorphism</span></span></li> <li><span><kbd>homotopyMap(ComplexMap)</kbd> -- see <span><a title="lift a map of chain complexes along a quasi-isomorphism" href="_lift__Map__Along__Quasi__Isomorphism_lp__Complex__Map_cm__Complex__Map_rp.html">liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)</a> -- lift a map of chain complexes along a quasi-isomorphism</span></span></li> <li><span><a title="lift a map of chain complexes along a quasi-isomorphism" href="_lift__Map__Along__Quasi__Isomorphism_lp__Complex__Map_cm__Complex__Map_rp.html">liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)</a> -- lift a map of chain complexes along a quasi-isomorphism</span></li> <li><span><kbd>quotient(ComplexMap,ComplexMap)</kbd> -- see <span><a title="lift a map of chain complexes along a quasi-isomorphism" href="_lift__Map__Along__Quasi__Isomorphism_lp__Complex__Map_cm__Complex__Map_rp.html">liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)</a> -- lift a map of chain complexes along a quasi-isomorphism</span></span></li> <li><span><a title="make the long exact sequence in homology" href="_long__Exact__Sequence_lp__Complex__Map_cm__Complex__Map_rp.html">longExactSequence(ComplexMap,ComplexMap)</a> -- make the long exact sequence in homology</span></li> <li><span><a title="make a new map of chain complexes from an existing one" href="_map_lp__Complex_cm__Complex_cm__Complex__Map_rp.html">map(Complex,Complex,ComplexMap)</a> -- make a new map of chain complexes from an existing one</span></li> <li><span><a title="make a map of chain complexes" href="_map_lp__Complex_cm__Complex_cm__Function_rp.html">map(Complex,Complex,Function)</a> -- make a map of chain complexes</span></li> <li><span><a title="make a map of chain complexes" href="_map_lp__Complex_cm__Complex_cm__Hash__Table_rp.html">map(Complex,Complex,HashTable)</a> -- make a map of chain complexes</span></li> <li><span><a title="make a map of chain complexes" href="_map_lp__Complex_cm__Complex_cm__List_rp.html">map(Complex,Complex,List)</a> -- make a map of chain complexes</span></li> <li><span><a title="make the zero map or identity between chain complexes" href="_map_lp__Complex_cm__Complex_cm__Z__Z_rp.html">map(Complex,Complex,ZZ)</a> -- make the zero map or identity between chain complexes</span></li> <li><span><span class="tt">mathML(Complex)</span> (missing documentation)<!--tag: (mathML,Complex)--> </span></li> <li><span><span class="tt">mathML(ComplexMap)</span> (missing documentation)<!--tag: (mathML,ComplexMap)--> </span></li> <li><span><a title="minimal presentation of all terms in a complex" href="_minimal__Presentation_lp__Complex_rp.html">minimalPresentation(Complex)</a> -- minimal presentation of all terms in a complex</span></li> <li><span><kbd>minimalPresentation(ComplexMap)</kbd> -- see <span><a title="minimal presentation of all terms in a complex" href="_minimal__Presentation_lp__Complex_rp.html">minimalPresentation(Complex)</a> -- minimal presentation of all terms in a complex</span></span></li> <li><span><kbd>prune(Complex)</kbd> -- see <span><a title="minimal presentation of all terms in a complex" href="_minimal__Presentation_lp__Complex_rp.html">minimalPresentation(Complex)</a> -- minimal presentation of all terms in a complex</span></span></li> <li><span><kbd>prune(ComplexMap)</kbd> -- see <span><a title="minimal presentation of all terms in a complex" href="_minimal__Presentation_lp__Complex_rp.html">minimalPresentation(Complex)</a> -- minimal presentation of all terms in a complex</span></span></li> <li><span><a title="a quasi-isomorphic complex whose terms have minimal rank" href="_minimize_lp__Complex_rp.html">minimize(Complex)</a> -- a quasi-isomorphic complex whose terms have minimal rank</span></li> <li><span><kbd>naiveTruncation(Complex,InfiniteNumber,InfiniteNumber)</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(Complex,InfiniteNumber,ZZ)</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(Complex,Nothing,ZZ)</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(Complex,Sequence)</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(Complex,ZZ,InfiniteNumber)</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(Complex,ZZ,Nothing)</kbd> -- see <span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></span></li> <li><span><a title="drops all terms of a complex outside a given interval" href="_naive__Truncation_lp__Complex_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(Complex,ZZ,ZZ)</a> -- drops all terms of a complex outside a given interval</span></li> <li><span><kbd>naiveTruncation(ComplexMap,InfiniteNumber,InfiniteNumber)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(ComplexMap,InfiniteNumber,ZZ)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(ComplexMap,Nothing,ZZ)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(ComplexMap,Sequence)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(ComplexMap,Sequence,Sequence)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(ComplexMap,ZZ,InfiniteNumber)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><kbd>naiveTruncation(ComplexMap,ZZ,Nothing)</kbd> -- see <span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></span></li> <li><span><a title="drops all terms in the source of a complex outside a given interval" href="_naive__Truncation_lp__Complex__Map_cm__Z__Z_cm__Z__Z_rp.html">naiveTruncation(ComplexMap,ZZ,ZZ)</a> -- drops all terms in the source of a complex outside a given interval</span></li> <li><span><a title="a map which is a candidate for being a null homotopy" href="_null__Homotopy_lp__Complex__Map_rp.html">nullHomotopy(ComplexMap)</a> -- a map which is a candidate for being a null homotopy</span></li> <li><span><span class="tt">nullhomotopy(ComplexMap)</span> (missing documentation)<!--tag: (nullhomotopy,ComplexMap)--> </span></li> <li><span><a title="extract a graded component of a complex" href="_part_lp__List_cm__Complex_rp.html">part(List,Complex)</a> -- extract a graded component of a complex</span></li> <li><span><kbd>part(ZZ,Complex)</kbd> -- see <span><a title="extract a graded component of a complex" href="_part_lp__List_cm__Complex_rp.html">part(List,Complex)</a> -- extract a graded component of a complex</span></span></li> <li><span><a title="extract a graded component of a map of complexes" href="_part_lp__List_cm__Complex__Map_rp.html">part(List,ComplexMap)</a> -- extract a graded component of a map of complexes</span></li> <li><span><kbd>part(ZZ,ComplexMap)</kbd> -- see <span><a title="extract a graded component of a map of complexes" href="_part_lp__List_cm__Complex__Map_rp.html">part(List,ComplexMap)</a> -- extract a graded component of a map of complexes</span></span></li> <li><span><a title="assemble degrees of a chain complex into a polynomial" href="_poincare_lp__Complex_rp.html">poincare(Complex)</a> -- assemble degrees of a chain complex into a polynomial</span></li> <li><span><a title="assemble degrees of a chain complex into a polynomial" href="_poincare__N_lp__Complex_rp.html">poincareN(Complex)</a> -- assemble degrees of a chain complex into a polynomial</span></li> <li><span><a title="a random map of chain complexes" href="_random__Complex__Map_lp__Complex_cm__Complex_rp.html">randomComplexMap(Complex,Complex)</a> -- a random map of chain complexes</span></li> <li><span><span class="tt">rank(Complex)</span> (missing documentation)<!--tag: (rank,Complex)--> </span></li> <li><span><a title="compute the Castelnuovo-Mumford regularity" href="_regularity_lp__Complex_rp.html">regularity(Complex)</a> -- compute the Castelnuovo-Mumford regularity</span></li> <li><span><kbd>resolutionMap(Complex)</kbd> -- see <span><a title="map from a free resolution to the given complex" href="_resolution__Map.html">resolutionMap</a> -- map from a free resolution to the given complex</span></span></li> <li><span><a title="access the ring of a complex or a complex map" href="_ring_lp__Complex_rp.html">ring(Complex)</a> -- access the ring of a complex or a complex map</span></li> <li><span><kbd>ring(ComplexMap)</kbd> -- see <span><a title="access the ring of a complex or a complex map" href="_ring_lp__Complex_rp.html">ring(Complex)</a> -- access the ring of a complex or a complex map</span></span></li> <li><span><kbd>Complex ** Ring</kbd> -- see <span><a title="tensor a complex along a ring map" href="___Ring__Map_sp_st_st_sp__Complex.html">RingMap ** Complex</a> -- tensor a complex along a ring map</span></span></li> <li><span><kbd>Complex ** RingMap</kbd> -- see <span><a title="tensor a complex along a ring map" href="___Ring__Map_sp_st_st_sp__Complex.html">RingMap ** Complex</a> -- tensor a complex along a ring map</span></span></li> <li><span><kbd>Ring ** Complex</kbd> -- see <span><a title="tensor a complex along a ring map" href="___Ring__Map_sp_st_st_sp__Complex.html">RingMap ** Complex</a> -- tensor a complex along a ring map</span></span></li> <li><span><a title="tensor a complex along a ring map" href="___Ring__Map_sp_st_st_sp__Complex.html">RingMap ** Complex</a> -- tensor a complex along a ring map</span></li> <li><span><kbd>tensor(Complex,RingMap)</kbd> -- see <span><a title="tensor a complex along a ring map" href="___Ring__Map_sp_st_st_sp__Complex.html">RingMap ** Complex</a> -- tensor a complex along a ring map</span></span></li> <li><span><kbd>tensor(RingMap,Complex)</kbd> -- see <span><a title="tensor a complex along a ring map" href="___Ring__Map_sp_st_st_sp__Complex.html">RingMap ** Complex</a> -- tensor a complex along a ring map</span></span></li> <li><span><kbd>ComplexMap ** Ring</kbd> -- see <span><a title="tensor a map of complexes along a ring map" href="___Ring__Map_sp_st_st_sp__Complex__Map.html">RingMap ** ComplexMap</a> -- tensor a map of complexes along a ring map</span></span></li> <li><span><kbd>ComplexMap ** RingMap</kbd> -- see <span><a title="tensor a map of complexes along a ring map" href="___Ring__Map_sp_st_st_sp__Complex__Map.html">RingMap ** ComplexMap</a> -- tensor a map of complexes along a ring map</span></span></li> <li><span><kbd>Ring ** ComplexMap</kbd> -- see <span><a title="tensor a map of complexes along a ring map" href="___Ring__Map_sp_st_st_sp__Complex__Map.html">RingMap ** ComplexMap</a> -- tensor a map of complexes along a ring map</span></span></li> <li><span><a title="tensor a map of complexes along a ring map" href="___Ring__Map_sp_st_st_sp__Complex__Map.html">RingMap ** ComplexMap</a> -- tensor a map of complexes along a ring map</span></li> <li><span><kbd>tensor(ComplexMap,RingMap)</kbd> -- see <span><a title="tensor a map of complexes along a ring map" href="___Ring__Map_sp_st_st_sp__Complex__Map.html">RingMap ** ComplexMap</a> -- tensor a map of complexes along a ring map</span></span></li> <li><span><kbd>tensor(RingMap,ComplexMap)</kbd> -- see <span><a title="tensor a map of complexes along a ring map" href="___Ring__Map_sp_st_st_sp__Complex__Map.html">RingMap ** ComplexMap</a> -- tensor a map of complexes along a ring map</span></span></li> <li><span><a title="apply a ring map" href="___Ring__Map_sp__Complex.html">RingMap Complex</a> -- apply a ring map</span></li> <li><span><a title="apply a ring map to a map of complexes" href="___Ring__Map_sp__Complex__Map.html">RingMap ComplexMap</a> -- apply a ring map to a map of complexes</span></li> <li><span><a title="get the source of a map of chain complexes" href="_source_lp__Complex__Map_rp.html">source(ComplexMap)</a> -- get the source of a map of chain complexes</span></li> <li><span><span class="tt">status(Complex)</span> (missing documentation)<!--tag: (status,Complex)--> </span></li> <li><span><a title="make the direct sum of all terms" href="_sum_lp__Complex_rp.html">sum(Complex)</a> -- make the direct sum of all terms</span></li> <li><span><kbd>sum(ComplexMap)</kbd> -- see <span><a title="make the direct sum of all terms" href="_sum_lp__Complex_rp.html">sum(Complex)</a> -- make the direct sum of all terms</span></span></li> <li><span><a title="get the target of a map of chain complexes" href="_target_lp__Complex__Map_rp.html">target(ComplexMap)</a> -- get the target of a map of chain complexes</span></li> <li><span><a title="make the canonical isomorphism arising from associativity" href="_tensor__Associativity_lp__Complex_cm__Complex_cm__Complex_rp.html">tensorAssociativity(Complex,Complex,Complex)</a> -- make the canonical isomorphism arising from associativity</span></li> <li><span><a title="make the canonical isomorphism arising from commutativity" href="_tensor__Commutativity_lp__Complex_cm__Complex_rp.html">tensorCommutativity(Complex,Complex)</a> -- make the canonical isomorphism arising from commutativity</span></li> <li><span><a title="make the canonical isomorphism arising from commutativity" href="_tensor__Commutativity_lp__Module_cm__Module_rp.html">tensorCommutativity(Module,Module)</a> -- make the canonical isomorphism arising from commutativity</span></li> <li><span><a title="makes the canonical isomorphism realizing the symmetry of Tor" href="_tor__Symmetry_lp__Z__Z_cm__Module_cm__Module_rp.html">torSymmetry(ZZ,Module,Module)</a> -- makes the canonical isomorphism realizing the symmetry of Tor</span></li> <li><span><a title="truncation of a complex at a specified degree or set of degrees" href="_truncate_lp__List_cm__Complex_rp.html">truncate(List,Complex)</a> -- truncation of a complex at a specified degree or set of degrees</span></li> <li><span><kbd>truncate(ZZ,Complex)</kbd> -- see <span><a title="truncation of a complex at a specified degree or set of degrees" href="_truncate_lp__List_cm__Complex_rp.html">truncate(List,Complex)</a> -- truncation of a complex at a specified degree or set of degrees</span></span></li> <li><span><a title="truncation of a complex map at a specified degree or set of degrees" href="_truncate_lp__List_cm__Complex__Map_rp.html">truncate(List,ComplexMap)</a> -- truncation of a complex map at a specified degree or set of degrees</span></li> <li><span><kbd>truncate(ZZ,ComplexMap)</kbd> -- see <span><a title="truncation of a complex map at a specified degree or set of degrees" href="_truncate_lp__List_cm__Complex__Map_rp.html">truncate(List,ComplexMap)</a> -- truncation of a complex map at a specified degree or set of degrees</span></span></li> <li><span><a title="identifies the element of Ext corresponding to an extension" href="_yoneda__Extension_sq_lp__Complex_rp.html">yonedaExtension'(Complex)</a> -- identifies the element of Ext corresponding to an extension</span></li> <li><span><a title="creates a chain complex representing an extension of modules" href="_yoneda__Extension_lp__Matrix_rp.html">yonedaExtension(Matrix)</a> -- creates a chain complex representing an extension of modules</span></li> <li><span><a title="identifies the element of Ext corresponding to a map of free resolutions" href="_yoneda__Map_sq_lp__Complex__Map_rp.html">yonedaMap'(ComplexMap)</a> -- identifies the element of Ext corresponding to a map of free resolutions</span></li> <li><span><a title="creates a chain complex map representing an extension of modules" href="_yoneda__Map_lp__Matrix_rp.html">yonedaMap(Matrix)</a> -- creates a chain complex map representing an extension of modules</span></li> <li><span><a title="make the product of two elements in Ext modules" href="_yoneda__Product_lp__Matrix_cm__Matrix_rp.html">yonedaProduct(Matrix,Matrix)</a> -- make the product of two elements in Ext modules</span></li> <li><span><a title="make the product map between Ext modules" href="_yoneda__Product_lp__Module_cm__Module_rp.html">yonedaProduct(Module,Module)</a> -- make the product map between Ext modules</span></li> </ul> </li> <li>Symbols <ul> <li><span><kbd>UseTarget</kbd> -- see <span><a title="gets the natural map arising from various constructions" href="_canonical__Map.html">canonicalMap</a> -- gets the natural map arising from various constructions</span></span></li> <li><span><a title="optional argument used to specify the concentration" href="___Concentration.html">Concentration</a> -- optional argument used to specify the concentration</span></li> <li><span><span class="tt">FreeToExact</span> (missing documentation)<!--tag: FreeToExact--> </span></li> <li><span><kbd>minimizingMap</kbd> -- see <span><a title="a quasi-isomorphic complex whose terms have minimal rank" href="_minimize_lp__Complex_rp.html">minimize(Complex)</a> -- a quasi-isomorphic complex whose terms have minimal rank</span></span></li> <li><span><kbd>Boundary</kbd> -- see <span><a title="a random map of chain complexes" href="_random__Complex__Map_lp__Complex_cm__Complex_rp.html">randomComplexMap(Complex,Complex)</a> -- a random map of chain complexes</span></span></li> <li><span><kbd>Cycle</kbd> -- see <span><a title="a random map of chain complexes" href="_random__Complex__Map_lp__Complex_cm__Complex_rp.html">randomComplexMap(Complex,Complex)</a> -- a random map of chain complexes</span></span></li> <li><span><kbd>InternalDegree</kbd> -- see <span><a title="a random map of chain complexes" href="_random__Complex__Map_lp__Complex_cm__Complex_rp.html">randomComplexMap(Complex,Complex)</a> -- a random map of chain complexes</span></span></li> <li><span><kbd>OverField</kbd> -- see <span><a title="algorithm for computing free resolutions over a field" href="___Strategy_spfor_spfree_spresolutions_spover_spa_spfield.html">Strategy for free resolutions over a field</a> -- algorithm for computing free resolutions over a field</span></span></li> <li><span><kbd>OverZZ</kbd> -- see <span><a title="algorithm for computing free resolutions of ZZ-modules" href="___Strategy_spfor_spfree_spresolutions_spover_spthe_spintegers.html">Strategy for free resolutions over the integers</a> -- algorithm for computing free resolutions of ZZ-modules</span></span></li> <li><span><kbd>Homogenization</kbd> -- see <span><a title="algorithm for computing free resolutions by first homogenizing" href="___Strategy_spfor_spfree_spresolutions_spvia_sphomogenization.html">Strategy for free resolutions via homogenization</a> -- algorithm for computing free resolutions by first homogenizing</span></span></li> <li><span><kbd>Nonminimal</kbd> -- see <span><a title="algorithm for computing nonminimal free resolutions" href="___Strategy_spfor_spnonminimal_spfree_spresolutions.html">Strategy for nonminimal free resolutions</a> -- algorithm for computing nonminimal free resolutions</span></span></li> </ul> </li> </ul> </div> </div> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="development package for beta testing new version of chain complexes" href="index.html">Complexes</a> is <span>a <a title="the class of all packages" href="../../Macaulay2Doc/html/___Package.html">package</a></span>, defined in <span class="tt">Complexes.m2</span>, with auxiliary files in <span class="tt">Complexes/</span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Complexes/ChainComplexDoc.m2:38:0</span>.</p> </div> </div> </div> </body> </html>