also, what should it do if the requested coefficient ring k appears in the chain this way: (k/I)[a]?

--

Date: Wed, 1 Nov 2006 15:26:21 -0600
From: Dan Grayson <dan@math.uiuc.edu>
To: Michael Stillman <mike@math.cornell.edu>
CC: dan@math.uiuc.edu
In-reply-to: <200611012122.kA1LMhLC010244@u123.math.uiuc.edu> (message from
        Dan Grayson on Wed, 1 Nov 2006 15:22:43 -0600)
Subject: Re:
Reply-to: dan@math.uiuc.edu


PS: In the interest of preserving homogeneity of ideals, flattenRing should
probably make a flat ring with the same multi-degrees for variables as before
the flattening, but it doesn't do that.

(or does it?)

Date: Wed, 1 Nov 2006 15:22:43 -0600
From: Dan Grayson <dan@math.uiuc.edu>
To: Michael Stillman <mike@math.cornell.edu>
CC: dan@math.uiuc.edu
In-reply-to: <7B4741E4-8F2D-4791-9582-DE8B90548FA3@math.cornell.edu> (message
        from Michael Stillman on Wed, 1 Nov 2006 16:08:12 -0500)
Subject: Re:
Reply-to: dan@math.uiuc.edu


Is it bad that David and Sorin have to use flattenRing to get what they want?
Doesn't that correspond to the mathematical reality that they are interested in
the Rees algebra over k rather than over A?  Perhaps it's a good thing that
they have to use flattenRing to get that.

Actually, what should flattenRing do, generally, about setting the degrees and
monomial ordering of its result?  Currently, it doesn't go out of its way to
reduce the degree length to 1, i.e., if it is given a quotient ring of a
polynomial ring, that's good enough.

