DegreeShifts -- grading shifts for free OI-modules

Description

Used as an optional argument in makeFreeOIModule to specify shifts of grading.

Permissible values:

DegreeShifts => null for no shift of grading
DegreeShifts => List for a shift of grading indicated by a list of integers

Example 1: no shifts

The free OI-module $\mathbf{F}^{\text{OI},1}\oplus\mathbf{F}^{\text{OI},2}$ has its basis elements in degree zero.

i1 : P = makePolynomialOIAlgebra(1, 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: (1, x, QQ, RowUpColUp)
     Monomial order: Lex

o2 : FreeOIModule

i3 : apply(getBasisElements F, degree)

o3 = {0, 0}

o3 : List

Example 2: nontrivial shifts

The free OI-module $\mathbf{F}^{\text{OI},1}(-3)\oplus\mathbf{F}^{\text{OI},2}(-4)$ has its basis elements in degrees $3$ and $4$.

i4 : F = makeFreeOIModule(e, {1,2}, P, DegreeShifts => {-3,-4})

o4 = Basis symbol: e
     Basis element widths: {1, 2}
     Degree shifts: {-3, -4}
     Polynomial OI-algebra: (1, x, QQ, RowUpColUp)
     Monomial order: Lex

o4 : FreeOIModule

i5 : apply(getBasisElements F, degree)

o5 = {3, 4}

o5 : List

Functions with optional argument named DegreeShifts:

makeFreeOIModule(...,DegreeShifts=>...) -- see makeFreeOIModule -- make a FreeOIModule object

For the programmer

The object DegreeShifts is a symbol.