fix toy_d_basis.py

[93749b3a-c0a4-47a7-b178-004ba08b0b97]

As discussed at #6051. Line 91 of sage/rings/polynomial/toy_d_basis.py needs to be unrandomed when this is fixed.

However, when we compute the Groebner basis of I (defined over `\ZZ`), we note that there is a certain integer in the ideal which is not 1.::

    sage: d_basis(I) # random -- waiting on upstream singular fixes at #6051
    [x + 170269749119, y + 2149906854, z + ..., 282687803443]                                

CC: @malb @tscrim @kedlaya @simon-king-jena

Component: commutative algebra

Author: Frédéric Chapoton

Branch/Commit: 39616a7

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/6265

[fchapoton]

Commit: 24ad1fe

[fchapoton]

Branch: u/chapoton/6265

[fchapoton]

Author: Frédéric Chapoton

[fchapoton]

New commits:

24ad1fe

trac 6265 remove an old # random marker

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 24ad1fe to 716ac65

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

716ac65

trac 6265 fixing doctest

[tscrim]

comment:9

It doesn't seem like the problem is fixed if you have to use ... in the doctest. So I'm not sure we should remove the comment, but I haven't looked to deep into this.

[fchapoton]

comment:10

Indeed, I also have some doubts. Let us check "needs_info"

The ... are there to replace huge numbers. Maybe we should keep the top few digits ?

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 716ac65 to 140579b

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

828443d	Merge branch 'u/chapoton/6265' in 8.0.b0
140579b	trac 6265 another tentative

[fchapoton]

comment:12

Here is another try, with green bot. I changed the term order so that the Groebner basis has much smaller coefficients. Maybe this should be tested on diverse machines.

[fchapoton]

comment:14

maybe this is good enough, I don't know..

[tscrim]

comment:15

Hmm...I'm now not so sure what the point of the doctest is. From the description above it looks more like the minimal integer that is in the ideal is the important point rather than the integers that are part of the binomial generators. I'm cc-ing Simon to see if he has a thought on this. Yet, this was last touched in 2009, so maybe we can just ... the binomial term integers and be done with it.

[simon-king-jena]

comment:16

Replying to @tscrim:

Hmm...I'm now not so sure what the point of the doctest is. From the description above it looks more like the minimal integer that is in the ideal is the important point rather than the integers that are part of the binomial generators. I'm cc-ing Simon to see if he has a thought on this.

I don't know anything about the theory of d-Gröbner bases. However, from the explanation in the doctest, it seems to me that the integers in the binomial generators do not matter (at least not for the test). It seems to me that the point of the example is to show that

• there is an integer in the d_basis, and
• the prime factors of that integer have the property that the original system has solutions modulo that prime.

[tscrim]

comment:17

Thanks Simon.

So shall we revert back to 716ac65?

[fchapoton]

comment:18

IMHO, the current branch should be just as good. I would rather try to let this in and see if the buildbots of Volker report any failure on apples and oranges.

[tscrim]

comment:19

Okay, then if you break the long line into each of the generators, you can set a positive review on my behalf.

[tscrim]

Reviewer: Travis Scrimshaw

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

39616a7

trac 6265 break lines

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 140579b to 39616a7

[fchapoton]

comment:21

ok, done. Thanks. Setting to positive

[vbraun]

Changed branch from u/chapoton/6265 to 39616a7