VectorInWidth -- the class of all elements of a free OI-module

Description

An element of a free OI-module $\mathbf{F}$ is defined to be an element of $\mathbf{F}_n$ for some integer $n\geq0$. Such an element is implemented as a VectorInWidth object. One typically makes VectorInWidth objects by defining a FreeOIModule object, calling installGeneratorsInWidth, and then manipulating the generators; see below for an example.

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

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

i3 : installGeneratorsInWidth(F, 2);

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

o4 = x   e        + x   e
      1,1 2,{1},1    2,1 2,{1},2

                                 4
o4 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

i5 : instance(b, VectorInWidth)

o5 = true

Methods that use an object of class VectorInWidth :

- VectorInWidth -- multiply an element of a free OI-module by -1
degree(VectorInWidth) -- get the degree of an element of a free OI-module
FreeOIModuleMap VectorInWidth -- apply a free OI-module map to an element
getFreeOIModule(VectorInWidth) -- see getFreeOIModule -- get the free OI-module of an element
getWidth(VectorInWidth) -- see getWidth -- get the width of an element of a free OI-module
isHomogeneous(VectorInWidth) -- check if an element of a free OI-module is homogeneous
isZero(VectorInWidth) -- check if an element of a free OI-module is zero
leadCoefficient(VectorInWidth) -- get the lead coefficient of an element of a free OI-module
leadMonomial(VectorInWidth) -- get the lead monomial of an element of a free OI-module
leadTerm(VectorInWidth) -- get the lead term of an element of a free OI-module
net(VectorInWidth) -- display an element of a free OI-module
Number * VectorInWidth -- multiply an element of a free OI-module by a number
RingElement * VectorInWidth -- multiply an element of a free OI-module by a ring element
terms(VectorInWidth) -- get the terms of an element of a free OI-module
VectorInWidth + VectorInWidth -- add two elements of a free OI-module
VectorInWidth - VectorInWidth -- subtract an element of a free OI-module from another

For the programmer

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