next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
SchurRings :: symmetricRing(Ring)

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

Synopsis

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 RA of the base ring A of R, having the same relative dimension over RA as S over A.

i1 : A = schurRing(QQ,a,6);
i2 : B = schurRing(A,b,3);
i3 : symmetricRing B

o3 = QQ[e , e , e , e , e , e , p , p , p , p , p , p , h , h , h , h , h , h ][e , e , e , p , p , p , h , h , h ]
         1   2   3   4   5   6   1   2   3   4   5   6   1   2   3   4   5   6   1   2   3   1   2   3   1   2   3

o3 : PolynomialRing
i4 : symmetricRing ZZ

o4 = ZZ

o4 : Ring

See also