The power_mod function is redundant, since python already supports this.

sage: pow?
Type:           builtin_function_or_method
Base Class:     <type 'builtin_function_or_method'>
String Form:    <built-in function pow>
Namespace:      Python builtin
Docstring:
    pow(x, y[, z]) -> number
    
    With two arguments, equivalent to x**y.  With three arguments,
    equivalent to (x**y) % z, but may be more efficient (e.g. for longs).
Class Docstring:
    <attribute '__doc__' of 'builtin_function_or_method' objects>

This would call the __pow__ method of the function in question with the right arguments, so we can handle the modulo powering operation in the right place. Recall that the signature of the __pow__ method is actually:

__pow__(self, other[, modulus]).

So the objective of this ticket should be changed to:

• change the __pow__ methods in sage.structure.element to accept a third argument
• deprecate sage.rings.arith.power_mod
• deprecate Integer.powermod

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/5082