Re: [Caml-list] Integral solutions of rational linear equations

[Christophe Raffalli <christophe.raffalli@univ-savoie.fr>]

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Thomas Gazagnaire a écrit :
> Hello,
> 
> in my one of my Ocaml programs, I need to find all integers solutions of
> a rational equation systems. This algo uses Gauss reduction and Hermite
> normal form, and need to know if a rational is an integer or not (ie. I
> don't want to use numerical approximation : (1/3) * 3 is an integer but
> 0,333333*3 we don't know). I didn't find any integer algebra package for
> ocaml, so I tried to implement Gauss elimination (easy) and Hermite
> normal form (more difficult...). But I didn't implement optimized
> version of these algorithms...
> 
> So my question is : do you know if exists a native ocaml module or an
> interface with a C library which is able to do integer/rational matrix
> manipulation (essentialy the Hermite normal form) in an efficient way ?
> 

you did not look very hard ? OCaml is distributed with the bignum
library in standard which does both int and rationnal ...

$ ocaml nums.cma
        Objective Caml version 3.09.0

# open Num

let rec fact n = if n = 0 then Int 1 else fact (n-1) */ Int n
      ;;
val fact : int -> Num.num = <fun>
# fact 100;;
- : Num.num = Big_int <abstr>
# string_of_num (fact 100);;
- : string =
"93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000"

> Thomas
> 
> 
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