Solving polynomial equations over p-adic fields
Hi - as usual I fear my naiv-IT is coming to the fore here, but I have been going around in circles on this for 3 days and I need help please!!
There are 2 basic questions arising from the same thing:
(1) Is "solve" supposed to be implemented for p-adic numbers at all? I can get solutions to things in finite fields but when I try to "lift" them using O(p^n) etc it all goes wrong.
(2) Quite apart from that, why can I not use "solve" using the "variables" (for which I want solutions) as the indeterminates in a polynomial ring over which the equations are already defined? For example, if I define my polynomial ring via:
sage: R.<X> = Zq(3^4,2); sage: RAB.< a,b> = R;
and if I then try
it tells me that "a is not a valid variable".