-Adic Base Generic Element
A common superclass for features shared among all elements of and
(regardless of implementation).
AUTHORS:
Bases: sage.rings.padics.padic_generic_element.pAdicGenericElement
Initialization
EXAMPLES:
sage: R = Zp(5); a = R(1287) #indirect doctest
Applies a Frobenius automorphism to this element. This is the identity
map, since this element lies in ; it exists for compatibility
with the
frobenius()
method of elements of extensions of
.
INPUT:
OUTPUT:
EXAMPLES:
sage: Qp(7)(2).frobenius()
2 + O(7^20)
Returns a minimal polynomial of this -adic element, i.e., x - self
INPUT:
OUTPUT:
EXAMPLES:
sage: Zp(5,5)(1/3).minimal_polynomial('x')
(1 + O(5^5))*x + (3 + 5 + 3*5^2 + 5^3 + 3*5^4 + O(5^5))
Returns the norm of this -adic element over the ground ring.
NOTE! This is not the -adic absolute value. This is a field
theoretic norm down to a ground ring. If you want the
-adic
absolute value, use the abs() function instead.
INPUT:
OUTPUT:
EXAMPLES:
sage: Zp(5)(5).norm()
5 + O(5^21)
Returns the trace of this -adic element over the ground ring
INPUT:
OUTPUT:
EXAMPLES:
sage: Zp(5,5)(5).trace()
5 + O(5^6)