Thanks to both Vincent and Nils!
Sage seems to include lots of ways to do things... Let me see if I
understand. Vincent suggested
R = PolynomialRing(Qp(7), 'x')
x = R.gen()
p = x^2 - 2
pari.padicappr(p, 4 + O(7^10))
Which works, but relies on using the built-in pari support; on the cell
server, one might as well switch to GP mode.
Nils suggested (essentially)
K=pAdicField(7)
g=K[x](x^2-2)
g.hensel_lift(4)
And that also works, returning (line break added)
4 + 5*7 + 4*7^2 + 5*7^4 + 4*7^5 + 5*7^6 + 4*7^7 + 2*7^8 + 4*7^11 + 5*7^12 +
5*7^13 + 6*7^14 + 4*7^15 + 5*7^16 + 5*7^17 + 2*7^18 + O(7^20)
Meaning 20 is the default precision.
I guess hensel_lift is the function I was looking for. And writing
K[x](x^2-2) tells Sage that the polynomial is to be considered as having
coefficients in Qp
Questions:
Do Qp(7) and pAdicField(7) do the same thing?
K[x] and K['x'] seem to do the same thing as well. Is that right? But if
I use y or 'y' it doesn't work unless I define y in advance. (Which I'll
have to figure out how to do... )
Thanks,
Fernando
--
=============================================================
Fernando Q. Gouvea http://www.colby.edu/~fqgouvea
Carter Professor of Mathematics
Dept. of Mathematics and Statistics
Colby College
5836 Mayflower Hill
Waterville, ME 04901
[Nuclear war] ... may not be desirable.
-- Edwin Meese III
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