Karim Belabas on Mon, 06 Jun 2005 09:58:13 +0200 |
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Re: Lattice intersection |
* Mak Trifkovic [2005-06-06 03:16]: > I have a number field F and I want to intersect an ideal I of O_F with an > order O. The manual claims that I can use idealintersect to get an > intersection of any two Z-modules, As I understand it, it does not claim that: idealintersect(nf,x,y): intersection of the two ideals x and y in the number field nf. When x and y are given by Z-bases, this does not depend on nf and can be used to compute the intersection of any two Z-modules. If your order is not an ideal (most orders aren't:-), then the above does not apply. How would you reword the above text to make it more explicit ? > but the command seems to convert a lattice to the ideal it generates. This is the documented behaviour. > E.g., if F=Q(y) is a quadratic NF, idealintersect(F,[1,0;0,3],[1,0;0,3]) > yields [1,0;0,1], which means that takes [1,0;0,3] to be the ideal > generated by 1 and 3y, and not the order Z[3y]? > > Am I using this the wrong way? Is there another way to intersect > lattices in number fields? If you have Z-bases, then you are just intersecting Z-modules. Unless speed is a major concern use K = matkerint(concat(A,B)); \\ extract first rows in 2.2.* idiom. Replace by Str(1".."length(A)) in 2.1.* K = vecextract(K, Str(1, "..", #A), ".."); mathnf(K * A) \\ just to get a canonical answer Hope this helps, Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dep. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Universite Paris-Sud http://www.math.u-psud.fr/~belabas/ F-91405 Orsay (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]