p-Adic Extension Element.

A common superclass for all elements of extension rings and field of Zp and Qp.

AUTHORS:

• David Roe

class sage.rings.padics.padic_ext_element.pAdicExtElement

Bases: sage.rings.padics.padic_generic_element.pAdicGenericElement

abs(prec=None)

Returns the p-adic absolute value of self.

This is normalized so that the absolute value of p is 1/p.

INPUT – prec - Integer. The precision of the real field in which the answer is returned. If None, returns a rational for absolutely unramified fields, or a real with 53 bits of precision if ramified.

EXAMPLES: sage: R = Zp(5,5) sage: S.<x> = ZZ[] sage: f = x^5 + 75*x^3 - 15*x^2 +125*x - 5 sage: W.<w> = R.ext(f) sage: w.abs() 0.724779663677696