Let the user define their own primitive element for Fq (in givaro)

[dimpase]

Sage does not allow Fq to be defined with a user-supplied polynomial together with a user-supplied primitive element. However, recent (4.0.2 or newer) givaro is able to accept such input and use it.

CC: @sagetrac-jakobkroeker @ClementPernet @malb

Component: finite rings

Issue created by migration from https://trac.sagemath.org/ticket/20670

[jdemeyer]

Replying to @dimpase:

Givaro does not allow Fq to be defined with a user-supplied polynomial.

Why do you think that?

sage: k.<a> = GF(9, modulus=x^2+1)
sage: k
Finite Field in a of size 3^2
sage: k.modulus()
x^2 + 1
sage: type(k)
<class 'sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro_with_category'>

[jdemeyer]

Reviewer: Jeroen Demeyer

[dimpase]

comment:3

Do you know how to do this on C++ level?

At least, that's what Macaulay2 people came up with, that patch in the ticket branch.
Perhaps they should have done this differently?

[jdemeyer]

comment:4

In givgfq.h, there is

template<typename Vector>
GFqDom(const UTT P, const UTT e, const Vector& modPoly);

right above the line added by Macaulay2.

Note the subtle difference: it does not take a generatorPoly argument in case that matters.

[dimpase]

comment:5

well, yes, indeed, in Macaulay2 one can specify a primitive element along with a modulus. So with this patch Sage can do the same (although I don't see how to override k.multiplicative_generator(); I thought I can just specify self.__multiplicative_generator in FiniteField_givaro, but it does not work...)

It seems that FiniteField_givaro isn't even used, and the whole class structure is a mystery to me here.

[jdemeyer]

comment:6

Are you sure that Macaulay2 really requires a custom primitive element and a custom polynomial or is that just an implementation detail?

[dimpase]

comment:7

Replying to @jdemeyer:

Are you sure that Macaulay2 really requires a custom primitive element and a custom polynomial or is that just an implementation detail?

Given a modulus (or not), it can certainly compute a primitive element, although it does have an option to supply a custom primitive element. And to do this it uses givaro backend with the patch in question.

[dimpase]

comment:8

This is one of the two patches (another one is for ffpack) needed to build and run Macaulay2 v1.9 (the current version, with an adaptation of Sage's pari/mpir workaround --- after I told them about Sage's pari/mpir workaround related to memory allocators) within Sage.

[dimpase]

Author: Dima Pasechnik

[vbraun]

comment:10

The patch should have some sort of documentation (ideally in the patch header)

[dimpase]

comment:11

Replying to @vbraun:

The patch should have some sort of documentation (ideally in the patch header)

my hope is to implement a possibility to supply a primitive element to GF(), using this patch as a backend. But I got lost trying to figure out how the current implementation uses givaro.

Could anyone point me to the right place in the code?

[dimpase]

comment:12

I am told that the patch on the branch is in givaro 4.0.2.

[dimpase]

Dependencies: #17635

[ClementPernet]

comment:15

Indeed, the patch has been merged upstream in linbox-team/givaro#18 and released in 4.0.2 that is now in #17635.

[jdemeyer]

Changed reviewer from Jeroen Demeyer to Dima Pasechnik, Jeroen Demeyer

[jdemeyer]

Changed author from Dima Pasechnik to none

[dimpase]

comment:17

the question I asked in comment:11 is still unanswered.

[embray]

comment:18

Determined to be invalid/duplicate/wontfix (closing as "wontfix" as a catch-all resolution).

[dimpase]

comment:20

Replying to @embray:

Determined to be invalid/duplicate/wontfix (closing as "wontfix" as a catch-all resolution).

I have to re-open this, but is it possible without opening a new ticket?

[embray]

comment:21

Yes, (under action). I think you have the permissions to do that but I'm not sure. I've been yelled at before for doing this but in this case I was the one who closed the ticket so I don't mind reopening it too if you think it should be.

[jdemeyer]

Changed reviewer from Dima Pasechnik, Jeroen Demeyer to none

[jdemeyer]

Changed commit from adb59c0 to none

[jdemeyer]

Changed branch from u/dimpase/givaropatch to none

[jdemeyer]

Changed dependencies from #17635 to none

[dimpase]

comment:25

Ping - I have been recently asked how to define a custom primitive element (Magma can do it, so they have to use Magma because of this, and better support for Zech transform)