Ideals in p-adic rings

[roed314]

Adds a new class for ideals in discrete valuation rings that improves speed and comparison.

Prerequisite for #12077, #8240.

Component: padics

Author: David Roe

Branch: u/saraedum/12053

Issue created by migration from https://trac.sagemath.org/ticket/12053

[saraedum]

comment:2

Attachment: 12053.patch.gz

Reviewing this I wondered why this is in the padics/ directory. Of course, the main application right now would be over the padics but it seems that everything would work like that for any DVR so should it probably be moved to rings/?

[sagetrac-dmharvey]

comment:3

What is reduce() supposed to do? I don't understand that function.

This is a little alarming:

sage: ~R.ideal(5) * 5
Fractional ideal (5^-1) of 5-adic Field with capped relative precision 20

But I see fractional ideals are not implemented. Perhaps there should be a NotImplementedError somewhere rather than manifestly incorrect behaviour. Is this fixed in a later patch?

I agree with saraedum's comment above, but for the moment it wouldn't hurt for it to live in padics/, especially as all that code is under heavy active development at the moment.

It wouldn't hurt to add some doctests to cover some unramified and ramified extensions of Zp (I tried a few myself and everything seems to work).

Apart from these issues the patch looks good to me.

[roed314]

comment:4

I agree that ~R.ideal(5) * 5 is a bug. I'll try to fix it soon.

[saraedum]

Branch: u/saraedum/develop

[saraedum]

Changed branch from u/saraedum/develop to none

[saraedum]

comment:13

Not sure whether you still think that this code is useful…I turned it into a branch so it is easier to see what's going on.

[saraedum]

Branch: u/saraedum/12053