FreeOIModule -- the class of all free OI-modules over a polynomial OI-algebra

Description

This type implements free OI-modules over polynomial OI-algebras. To make a FreeOIModule object, use makeFreeOIModule. To get the basis elements and rank of a free OI-module, use getBasisElements and getRank respectively. To install the generators of a component of a free OI-module in a specified width, use installGeneratorsInWidth.

Each FreeOIModule object comes equipped with either the Lex monomial order induced by the monomial order on its underlying polynomial OI-algebra, or the Schreyer monomial order induced by another free OI-module; see makeFreeOIModule and OIMonomialOrder.

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

i2 : F = makeFreeOIModule(e, {1,2}, P)

o2 = Basis symbol: e
     Basis element widths: {1, 2}
     Degree shifts: {0, 0}
     Polynomial OI-algebra: (2, x, QQ, RowUpColUp)
     Monomial order: Lex

o2 : FreeOIModule

Functions and methods returning an object of class FreeOIModule:

getFreeOIModule -- get the free OI-module of an element
makeFreeOIModule -- make a FreeOIModule object

Methods that use an object of class FreeOIModule:

FreeOIModule _ ZZ -- get the width n component of a free OI-module
getBasisElements(FreeOIModule) -- see getBasisElements -- get the basis elements of a free OI-module
getRank(FreeOIModule) -- see getRank -- get the rank of a free OI-module
getSchreyerMap(FreeOIModule) -- see getSchreyerMap -- get the Schreyer map of a free OI-module if it exists
installGeneratorsInWidth(FreeOIModule,ZZ) -- see installGeneratorsInWidth -- install the generators for a component of a free OI-module in a specified width
isZero(FreeOIModule) -- see isZero -- check if a free OI-module is zero
net(FreeOIModule) -- display a free OI-module
toString(FreeOIModule) -- display a free OI-module in condensed form

For the programmer

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