OIResolution -- the class of all resolutions of submodules of free OI-modules

Description

This type implements free resolutions of submodules of free OI-modules. To make an OIResolution object, use oiRes. To verify that an OI-resolution is a complex, use isComplex. To get the $n$th differential in an OI-resolution C, use C.dd_n.

i1 : P = makePolynomialOIAlgebra(2, x, QQ);

i2 : F = makeFreeOIModule(e, {1,1}, P);

i3 : installGeneratorsInWidth(F, 2);

i4 : b = x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);

i5 : time C = oiRes({b}, 1)
 -- used 0.149669s (cpu); 0.119232s (thread); 0s (gc)

o5 = 0: (e0, {2}, {-2})
     1: (e1, {4, 4}, {-4, -4})

o5 : OIResolution

i6 : C.dd_0

o6 = Source: (e0, {2}, {-2}) Target: (e, {1, 1}, {0, 0})

o6 : FreeOIModuleMap

Functions and methods returning an object of class OIResolution:

oiRes -- compute an OI-resolution

Methods that use an object of class OIResolution:

describe(OIResolution) -- describe an OI-resolution
describeFull(OIResolution) -- see describeFull -- describe an OI-resolution and the maps
isComplex(OIResolution) -- see isComplex -- verify that an OI-resolution is a complex
net(OIResolution) -- display an OI-resolution
OIResolution _ ZZ -- get a module of an OI-resolution is specified homological degree
ranks(OIResolution) -- see ranks -- display the ranks of an OI-resolution
restrictedRanks(OIResolution,ZZ) -- see restrictedRanks -- display the ranks of an OI-resolution restricted to a given width

For the programmer

The object OIResolution is a type, with ancestor classes HashTable < Thing.

The source of this document is in OIGroebnerBases.m2:2615:0.