Tuukka Toivonen on Thu, 30 May 2002 21:43:13 +0300 (EEST) |
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Re: detecing non quadratic residue in sqrt/trapping errors |
On Thu, 30 May 2002, Bill Allombert wrote: >For this particular case, you can use issquare(). [...] >Yes, with the trap(,,) function, but it is an experimental feature. Thanks for these! Both were straight from the manual, I was just too blind to find them. Actually, my goal to begin with is to compute divisions and square roots of polynomial rings, modulo a polynomial, with coefficients from a finite ring, either integer modulo q or even another polynomial ring! Not to even speak yet about non-unique factorization of the polynomials... The real difficulty is that I can't find programs or much even algorithms for computing over these rings. Division of integers (i.e. solving a*x=1 mod q, q nonprime) is easy, but even square roots (solving x*x=a mod q) is over the capabilities of my programs, including Pari (or maybe I just don't know how to use them). Currently I use a C program to try all possible elements in the ring. This is slow, but possible since my modulus q is usually less than 32 bits. Any references and advice is welcome. About myself: I'm an engineer who desperately tries to learn number theory to make some applications :)