Daniel Allcock on Sat, 15 Sep 2012 01:48:34 +0200 |
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relative saturation? |
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'd appreciate any tips. (I'm using library mode, so hacks using it are welcome too). Thanks, Daniel