change_default_prec as a replacement for the deprecated set_default_prec

[ThibautVerron]

In http://trac.sagemath.org/18416, the method set_default_prec of power series rings was marked deprecated, and the warning states that the default precision should be set at construction. This was done before in #16201 for Laurent series.

The point of those changes was to ensure that power series and Laurent series rings are immutable.

I suggest to replace set_default_prec with a method change_default_prec, which would return a copy of self with the wanted precision. It would be similar to how change_ring works, for example.

For an application, see the following example:

sage: Pow.<x> = PowerSeriesRing(QQ, default_prec=5)
sage: Laur = Pow.fraction_field()
sage: f = Pow(1).add_bigoh(100); f
1 + O(x^100)
sage: f.parent()(1/(1+x))*f # forgetting about the ring Laur
1 - x + x^2 - x^3 + x^4 + O(x^5)

To get the correct precision, one would need something like

sage: R = f.parent() 
sage: S = PowerSeriesRing(R.base_ring(),R.gen(),default_prec=100)
sage: S = S.fraction_field() 
sage: S(1/(1+x))*f  
1 - x + x^2 - x^3 + x^4 + ... + x^99 + O(x^100)

The idea would be to replace that with:

sage: S = f.parent().change_default_prec(100)
sage: S(1/(1+x))*f  
1 - x + x^2 - x^3 + x^4 + ... + x^99 + O(x^100)

CC: @slel

Component: algebra

Keywords: series precision

Author: Thibaut Verron

Branch/Commit: u/gh-ThibautVerron/change_default_prec @ 94fd7c5

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32333

[ThibautVerron]

Branch: u/gh-ThibautVerron/change_default_prec

[ThibautVerron]

New commits:

3871800

Implementation of change_default_prec

[ThibautVerron]

Commit: 3871800

[slel]

Author: Thibaut Verron

[tscrim]

comment:5

I agree that we should have this feature, but I don't think we should call __copy__. Instead, we should pass the relevant information onto the constructor so that it properly creates an object normally (in particular, if it uses a cache such as UniqueRepresentation). This means that classes implementing this will likely need to implement it themselves (with a generic implementation perhaps raising a NotImplementedError).

Also, I don't think you should rely on the fraction field of a power series ring being the Laurent polynomial ring. It is not true that ZZ((x)) is the fraction field of ZZ[[x]].

[ThibautVerron]

comment:6

Thanks for the comments!

I agree that we should have this feature, but I don't think we should call __copy__

Oh, right, that didn't work.

This means that classes implementing this will likely need to implement it themselves

Okay, I made the changes and I added implementations for power series (univariate and multivariate) and Laurent series. I tried to pass all relevant parameters to the constructor, but some are just lost after the initialization (for instance implementation). change_var and change_ring do not seem to care, so I guess if it is a problem, it's a problem for another ticket?

It is not true that ZZ((x)) is the fraction field of ZZ[[x]].

Oops.

[sagetrac-git]

Changed commit from 3871800 to 94fd7c5

[sagetrac-git]

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

c15952f	Laurent series rings are not always (fraction) fields
a3863d2	Added examples
09ccf55	Generic method, implementation for univariate power series
eec8def	Implementation for multivariate power series
94fd7c5	Minor

[tscrim]

comment:8

Replying to @ThibautVerron:

Thanks for the comments!

Thank you for the changes.

Okay, I made the changes and I added implementations for power series (univariate and multivariate) and Laurent series. I tried to pass all relevant parameters to the constructor, but some are just lost after the initialization (for instance implementation). change_var and change_ring do not seem to care, so I guess if it is a problem, it's a problem for another ticket?

Yes, I agree that it should be left for another ticket. Likely some additional information is needed to be stored and passed along.

[tscrim]

Reviewer: Travis Scrimshaw