hilbert

[Martin Bright <M.Bright@dpmms.cam.ac.uk>]

Can somebody explain to me the behaviour of hilbert()?

? hilbert(-1+O(2^4),12+O(2^4))
%1 = -1

Correct.

? hilbert(Mod(-1,16),Mod(12,16))
%2 = 1

Why is this different?

? hilbert(-1+O(2^3),12+O(2^3))
%3 = 1

But there's not enough precision in 12+O(2^3) to be able to calculate the
Hilbert symbol. 

? hilbert(-1,12,2)
%4 = -1

Correct again.

Martin Bright

-- 
Martin Bright, Clare College, Cambridge
M.Bright@dpmms.cam.ac.uk