Kevin Acres on Sat, 26 Dec 2009 02:01:40 +0100 |
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Re: Montgomery Square Root question |
Hi Bill, At 10:32 AM 26/12/2009, you wrote:
On Fri, Dec 25, 2009 at 10:03:08PM +1100, Kevin Acres wrote: > One more question that I have is about Montgomery square roots. Can > anyone tell me if this is supported natively by Pari/GP. > > Basically I'm trying to port a Magma SNFS example to Pari/GP and this > is about my last stumbling block. > > Currently the ported code works well for Gaussian integers, but I'm > trying to get the general case working as well. I am not sure what Montgomery square roots exactly are, but you can compute square roots over any number fields by computing the roots of x^2-a with nfroots(). Cheers, Bill.
A case in point is that I need to find the square root modulo x^3 + 60*x + 64 of:
28146578841227871637467936328085117616334995672344313744414\ 83926978867652153721301870381570719744*x^2 - 409421329393317510182732406505919857074978625675148613247217512014934258219\ 10113619606396083372032*x- 4597574705568933751179654537544093443765025\ 8546148057739453165564673458691658141449930516266483712 I know that the answer is: 189133117686159822165485681043654738588680060928*x^2 + 2055476375095129701009302875309311162506447683584*x + 1945600371033366152866700970896778949964215615488But I just don't know how to get there in Pari/GP. I've tried a couple of things with nfroots, but failed to get any success as yet.
Regards, Kevin