How do you construct
-adics in Sage?
A great deal of progress has been made on this
(see SageDays talks by David Harvey and David Roe).
Here only a few of the simplest examples are given.
To compute the characteristic and
residue class field of the ring Zp
of integers of Qp
,
use the syntax illustrated by the folowing examples.
sage: K = Qp(3) sage: K.residue_class_field() Finite Field of size 3 sage: K.residue_characteristic() 3 sage: a = K(1); a 1 + O(3^20) sage: 82*a 1 + 3^4 + O(3^20) sage: 12*a 3 + 3^2 + O(3^21) sage: a in K True sage: b = 82*a sage: b^4 1 + 3^4 + 3^5 + 2*3^9 + 3^12 + 3^13 + 3^16 + O(3^20)
See About this document... for information on suggesting changes.