John Cremona on Sat, 24 Nov 2001 12:21:45 +0000 |
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bug in 2-adic sqrt |
This would seem to be a bug in 2-adic sqrt, in 2.1.1. I am well aware of the fact that one loses one bit of 2-adic precision doing this, but we seem to be losing two bits. Example: (12:25) gp > a=-71+O(2^5) %1 = 1 + 2^3 + 2^4 + O(2^5) (12:25) gp > b=sqrt(a) %2 = 1 + 2^2 + 2^3 + O(2^4) (12:25) gp > b^2-a %3 = 2^4 + O(2^5) Here a = -71 (mod 32) = 25 (mod 32), and b^2=a (mod 32) has general solution 5 (mod 16), so the "right" answer is surely (12:25) gp > c=5+O(2^4) %4 = 1 + 2^2 + O(2^4) (12:26) gp > c^2-a %5 = O(2^5) [What I really would like is to be able to ask for sqrt(Mod(-71,32)) and get Mod(5,16); I am only using 2-adics to simulate this.] John Cremona