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 |