next | previous | forward | backward | up | top | index | toc | Macaulay2 website
SchurRings :: schurRing(Ring)

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



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