ChainComplex -- the class of all chain complexes

ChainComplex -- the class of all chain complexes

The type ChainComplex is a member of the class Type. Each object of class ChainComplex is called a chain complex. Each chain complex is also a member of class GradedModule.

More general types (whose methods may also apply) :

GradedModule -- the class of all graded modules

MutableHashTable -- the class of all mutable hash tables

HashTable -- the class of all hash tables

See also:

chain complexes

Functions and methods returning a a chain complex :

chainComplex (...) -- make a chain complex

ChainComplex ** ChainComplex -- tensor product

ChainComplex ** GradedModule -- tensor product

ChainComplex ** Module

ChainComplex ++ ChainComplex -- direct sum

ChainComplex [...] -- degree shift

chainComplex List

chainComplex GradedModule -- make a chain complex from a graded module

coimage ChainComplexMap

cokernel ChainComplexMap

complete ChainComplex -- complete the internal parts

cone ChainComplexMap

dual ChainComplex -- dual

GradedModule ** ChainComplex -- tensor product

Hom(ChainComplex,Module) -- Hom

Hom(Module,ChainComplex)

image ChainComplexMap

kernel ChainComplexMap

Module ** ChainComplex

Module [...] -- make a chain complex from a module

new ChainComplex -- make a new chain complex from scratch

prune ChainComplex

resolution Ideal -- make a projective resolution

resolution Module -- make a projective resolution

resolution MonomialIdeal

RingMap ChainComplex

Methods for using a chain complex :

betti ChainComplex -- display of degrees in a chain complex

ChainComplex ** ChainComplexMap -- tensor product

ChainComplex == ChainComplex

ChainComplex _ ZZ -- get component

ChainComplexMap ** ChainComplex -- tensor product

components ChainComplex -- list the components of a direct sum

extend(ChainComplex,ChainComplex,Matrix)

gradedModule ChainComplex

HH ChainComplex -- homology of a chain complex

HH^ZZ ChainComplex -- cohomology of a chain complex

HH_ZZ ChainComplex -- homology of a chain complex

homology(Nothing,ChainComplex)

isDirectSum ChainComplex

isHomogeneous ChainComplex

length ChainComplex -- length of a chain complex or graded module

map(ChainComplex,ChainComplex)

map(ChainComplex,ChainComplex,ChainComplexMap)

map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes

max ChainComplex -- maximum index in a chain complex

min ChainComplex -- minimum index in a chain complex

net ChainComplex

poincare ChainComplex

poincareN ChainComplex

rank ChainComplex

regularity ChainComplex

status ChainComplex

sum ChainComplex -- direct sum of the components of a chain complex

summary ChainComplex

tensorAssociativity(ChainComplex,ChainComplex,ChainComplex)

tex ChainComplex

texMath ChainComplex

ZZ == ChainComplex