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

## Synopsis

• Function: schurRing
• Usage:
S = schurRing R
• Inputs:
• 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,

## 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