Bill Allombert on Sat, 15 Sep 2012 11:48:09 +0200 |
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Re: relative saturation? |
On Fri, Sep 14, 2012 at 06:46:46PM -0500, Daniel Allcock wrote: > Dear all, > > I have a basis for a saturated subgroup L of Z^n, and one extra vector V in > Z^n but not in L. I'd like to find an element of Z^n which together with L > generates the saturation of the span of L and V. I think of this as the > "saturation of <L,V> relative to L". > > I can't find any ready-made function that lends itself to an easy > implementation of this. The best I can think of right now is to find a basis > for the saturation of <L,V>, express it in terms of V and my basis for L, > look at the V-components, and follow Euclid's algorithm to find a Z-linear > comb whose V-component is smallest possible. This looks icky and I am > probably missing something more obvious. I would suggest you look first at the GP function matrixqz(). I would start by expressing V as an element W of L\otimes Q and use matrixqz(,-2) to compute the saturation of [W|Z^n]. Cheers, Bill.