three-argument pow() on integers returns IntegerMod

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Example:

sage: pow(5,7,13).parent()
Ring of integers modulo 13

This contradicts the docstring ("Return (left ^ right) % modulus."), and it doesn't happen for other parents:

sage: R.<x> = GF(59)[]
sage: pow(x,123,x^5-x+1).parent()
Univariate Polynomial Ring in x over Finite Field of size 59

Component: basic arithmetic

Author: Lorenz Panny

Branch/Commit: 299f265

Reviewer: Dave Morris

Issue created by migration from https://trac.sagemath.org/ticket/34143

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Commit: 50a8539

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Author: Lorenz Panny

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Branch: public/fix_return_type_of_pow_with_modulus

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New commits:

eae7a9a	make pow(x,e,m) return an element with the same parent as x
50a8539	update doctests that were relying on the incorrect behaviour

[sagetrac-git]

Changed commit from 50a8539 to 299f265

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

299f265

add doctest for #34143

[DaveWitteMorris]

Reviewer: Dave Morris

[DaveWitteMorris]

comment:3

Thanks for fixing this. The documentation for lift just says "Lift an integer modulo n to the integers", but doesn't guarantee that the lift is the canonical one. However, looking at some of the code seems to show that the lift (i.e., the ivalue) is always in the correct range, so it seems to be ok.

I do think the docstring of lift should be revised to clarify this (unless I missed something), but that's not for this ticket.