next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Seminormalization :: ringProduct

ringProduct -- compute the product of a list of rings

Synopsis

Description

Given a list of rings, of finite type over the same coefficient ring, this computes a ring isomorphic to a product of the rings. It returns a list with three entries. First is the ring. Second is the list of orthogonal idempotents. Finally, it lists where the variables of each of the rings in the list go in the new ring.

i1 : R = QQ[a];
i2 : S = QQ[b];
i3 : T = QQ[c];
i4 : ringProduct({R,S})

                     QQ[aRE0RE0, e0, bRE1RE1, e1]
o4 = {---------------------------------------------------------, {- e1 + 1,
                      2
      (e0 + e1 - 1, e1  - e1, bRE1RE1*e1 - bRE1RE1, aRE0RE0*e1)
     ------------------------------------------------------------------------
     e1}, {{aRE0RE0}, {bRE1RE1}}}

o4 : List
i5 : ringProduct({R,S,T})

                                           QQ[aRE0RE0, e0, bRE1RE1, e1, cRE2R
o5 = {-----------------------------------------------------------------------
                           2                                      2
      (e0 + e1 + e2 - 1, e2  - e2, cRE2RE2*e2 - cRE2RE2, e1*e2, e1  - e1, bRE
     ------------------------------------------------------------------------
     E2, e2]
     -------------------------------------------, {- e1 - e2 + 1, e1, e2},

     1RE1*e1 - bRE1RE1, aRE0RE0*e1 + aRE0RE0*e2)
     ------------------------------------------------------------------------
     {{aRE0RE0}, {bRE1RE1}, {cRE2RE2}}}

o5 : List

Ways to use ringProduct :