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# 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 0.0810202s (cpu); 0.0810205s (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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OIGroebnerBases.m2:2615:0.