Re: Pari functions that support gaussian integers

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Dec 19, 2019 at 07:45:57AM +0000, Andrew Walker wrote:
> PS Then there are Eisenstein integers and beyond.... . 

Hello Andrew,
Arbitrary quadratic orders are supported with quadgen:
? w=quadgen(-3)
%1 = w
? minpoly(w)
%2 = x^2-x+1
? factor(x^4+w)
%3 = [x-w,1;x+w,1;x^2+(-1+w),1]

For the general case (arbitrary ring of integers), we have the functions
bnfinit/bnfisprincipal. Then you can do:
- factorization (idealfactor)
- gcd (idealadd)
- lcm (idealintersect)
- primality testing (idealismaximal)

Cheers,
Bill.