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

- Function: symmetricRing
- Usage:
    `R = symmetricRing S`
- Inputs:
  - S, 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:
  - R, a ring,

## Description

Given a (Schur) ring S, the function symmetricRing returns a (Symmetric) ring R that is associated to S in a natural way. Namely, if the attribute S.symmetricRing points to a ring, then the function returns that ring. If S is not a Schur ring, then the function returns S. Otherwise, if S is a Schur ring, then the function constructs a polynomial ring over the Symmetric ring R_A of the base ring A of R, having the same relative dimension over R_A as S over A.

    i1 : A = schurRing(QQ,a,6);

    i2 : B = schurRing(A,b,3);

    i3 : symmetricRing B

    o3 = QQ[e ..e , p ..p , h ..h ][e ..e , p ..p , h ..h ]
             1   6   1   6   1   6   1   3   1   3   1   3

    o3 : PolynomialRing

    i4 : symmetricRing ZZ

    o4 = ZZ

    o4 : Ring

## See also

- schurRing -- Make a SchurRing

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SchurRings.m2:1923:0.