Date: Thu, 6 Jul 2006 23:18:20 -0500
From: Dan Grayson <dan@math.uiuc.edu>
To: mike@math.cornell.edu
CC: dan@math.uiuc.edu
Subject: Smith n.f.
Reply-to: dan@math.uiuc.edu


I wonder whether the following procedure always leads to a diagonal matrix:

    R = QQ[x,y, MonomialOrder => Position => Up]
    f = substitute (random(R^5, R^{5:-1}),y=>1)
    gens gb transpose oo
    gens gb transpose oo
    gens gb transpose oo
    .
    .
    .

If so, it's an easy way to code Smith normal form!

--

A related issue : what if, for all cases where you accumulate a change of basis
matrix, you were to accumulate the inverse, too?  (Won't someone need it some
day?)

