$p$-adic numbers in SAGE

Question

The standard output in SAGE for $p$-adic numbers is in the series representation:

sage: x = Zp(7)(12495)
sage: x
3*7^2 + 7^3 + 5*7^4 + O(7^22)

Is there a way to change it to a "sequence" representation, like

(..., 12495, 490, 147, 0, 0)

Answer 1

You could use the .list() method to get the coefficients.

sage: x = Zp(7)(12495)
sage: x
3*7^2 + 7^3 + 5*7^4 + O(7^22)
sage: x.list()
[0, 0, 3, 1, 5]

and cook up something from there:

sage: xx = x.list()
sage: xx
[0, 0, 3, 1, 5]
sage: [sum(xx[k]*7^k for k in xrange(k+1)) for k in xrange(len(xx))]
[0, 0, 147, 490, 12495]

but you can get the residues you want directly with this command

sage: [x.residue(k+1) for k in xrange(x.precision_absolute())]
[0,
 0,
 147,
 490,
 12495,
 12495,
 ...
 12495,
 12495]

There doesn't seem to be a residue_list method which would give the whole list all at once.

Note that you can discover the methods available for the object x by typing

sage: x.

and hitting the TAB key.