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

- 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

## See also

- symmetricRing -- Make a Symmetric ring

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SchurRings.m2:1892:0.