schurRing(Ring) -- The Schur ring corresponding to a given Symmetric ring.

Synopsis

Function: schurRing
Usage:

S = schurRing R
Inputs:
- R, a ring,
Optional inputs:
- EHPVariables => ..., default value (e,h,p), Specifies sequence of symbols representing e-, h-, and p-functions
- GroupActing => ..., default value "GL", Specifies the group that is acting
- SVariable => ..., default value s, Specifies symbol representing s-functions
Outputs:
- S, a Schur ring,

Description

Given a ring R, the function schurRing attempts to return a Schur ring S that is associated to R in a natural way. Namely, if the attribute R.Schur points to a Schur ring, then the function returns that ring. If R is already a Schur ring, then the ring R is returned. Otherwise, if the Schur level of R is at least one, then the function constructs a Schur ring over the base ring A of R, having the same relative dimension over A as R. If the Schur level of R is zero, then an error is returned.

i1 : R = schurRing(QQ,r,6);

i2 : schurRing R

o2 = R

o2 : SchurRing

i3 : Q = symmetricRing(QQ,3);

i4 : A = schurRing Q;

i5 : schurRing Q

o5 = A

o5 : SchurRing

Ways to use this method: