| Bill Allombert on Thu, 04 Oct 2018 18:56:25 +0200 |
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| change to qfbsolve to handle arbitrary integers |
Dear PARI developers,
I have changed qfbsolve in master so that:
1) it handles non prime target value
2) it returns all the soution under the action of SO(Q,Z).
The side effect is that this breaks backward compatibility because
it used to return a single solution instead of a t_VEC of solutions.
Some example
? qfbsolve(Qfb(1,0,27),3937)
%6 = [[7,12],[47,8],[47,-8],[7,-12]]
We can check that
7^2+27*12^2 = 3937
47^2+27*8^2 = 3937
In this SO(Q,Z)={Id, -Id} so the actual number of solutions is 8.
? qfbsolve(Qfb(1,0,-32),5152)
%7 = [[-88,-9],[120,-17],[-72,1],[200,33],[-232,-39],[72,1],[120,17],[-88,9]]
There is actually an infinite number of solutions, since SO(Q,Z) is
infinite in this case.
Please test!
Cheers,
Bill