## 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 .