Opened 5 years ago

Closed 4 years ago

#22983 closed defect (fixed)

polynomial quotient rings are unique parents

Reported by: Julian Rüth Owned by:
Priority: major Milestone: sage-8.3
Component: commutative algebra Keywords: sd86.5, sd87
Cc: Merged in:
Authors: Julian Rüth Reviewers: David Roe
Report Upstream: N/A Work issues:
Branch: 966c36b (Commits, GitHub, GitLab) Commit: 966c36b92266ffbaadec4bd43e0f08f086eb5fd3
Dependencies: #23851 Stopgaps:

Status badges

Description (last modified by Xavier Caruso)

Currently quotient rings are not unique parents which sometimes causes trouble with

sage: R.<x> = QQ[]
sage: R.quo(x) is R.quo(x)
False
sage: R.quo(x) == R.quo(x)
True

The changes proposed here make the creation go through a factory which makes sure that the parents are unique.

Change History (39)

comment:1 Changed 5 years ago by Xavier Caruso

Description: modified (diff)

comment:2 Changed 5 years ago by Julian Rüth

Branch: u/saraedum/polynomial_quotient_rings_are_unique_parents

comment:3 Changed 5 years ago by Nils Bruin

Commit: 054945da4a2caea28416c684d236fce4cbe88124

Does this fully solve the problem, though? One could give different generators for the same ideal. Should we be getting identical results for those, e.g., R.quo(x-1) and R.quo(2*x-2) (provided 2 is invertible in R ...). It might be worth documenting the choice made.

I suspect that for higher rank polynomial rings, normalizing the ideal representation might be too expensive (although computing in those rings would be expensive anyway).


New commits:

054945dMake polynomial quotient rings unique parents

comment:4 Changed 5 years ago by Julian Rüth

nbruin: You are right. It should be documented. I'll fix that. I believe that your example should produce two different rings (at least for the time being.) These could be == equal but not is equal. However, getting == to work for them would require a change of the hash function which is (hard and) not the scope of this ticket.

comment:5 Changed 5 years ago by Xavier Caruso

Current R.quo(x-1) and R.quo(2*x-2) prints in the same way.

sage: R.<x>= QQ[]
sage: R.quo(x+1)
Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x + 1
sage: R.quo(2*x+2)
Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x + 1

So I would say rather that the two constructions should return the same ring; it should be easy, it suffices to make the defining polynomial monic because creating the key.

Version 0, edited 5 years ago by Xavier Caruso (next)

comment:6 in reply to:  5 Changed 5 years ago by Julian Rüth

Replying to caruso:

Currently R.quo(x-1) and R.quo(2*x-2) prints in the same way.

sage: R.<x>= QQ[]
sage: R.quo(x+1)
Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x + 1
sage: R.quo(2*x+2)
Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x + 1

So I would say rather that the two constructions should return the same ring; it should be easy, it suffices to make the defining polynomial monic because creating the key.

I agree. However, this is already happening automagically: quo creates a (principal) ideal and takes its generator as the modulus which is the same x+1 in both of your examples. At the same time, if someone insists to create a quotient with the modulus x + 1 and one with the modulus 2*x + 2 by calling PolynomialQuotientRing directly, then these should be distinct because .modulus() is going to have a different value for the two, i.e., they are distinguishable. I'll add a doctest to clarify this.

comment:7 Changed 5 years ago by git

Commit: 054945da4a2caea28416c684d236fce4cbe88124f6a1cd8a84d48f4c043b770d2f437701eb8e3089

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

f6a1cd8Document normalization of modulus

comment:8 Changed 5 years ago by Julian Rüth

Status: newneeds_review

comment:9 Changed 5 years ago by Julian Rüth

Doctests in rings/polynomial pass for me. Let's see what the patchbot thinks about everything else.

comment:10 Changed 5 years ago by Xavier Caruso

Ok. It's a bit weird and confusing that the function PolynomialQuotientRing does not have the same behaviour than the method quo (and even QuotientRing), isn't it?

    sage: R.<x> = QQ[]
    sage: QuotientRing(R, 2*x+2)
    Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus x + 1
    sage: PolynomialQuotientRing(R, 2*x+2)
    Univariate Quotient Polynomial Ring in xbar over Rational Field with modulus 2*x + 2

I would be in favour of uniformizing this... but it's definitely for another ticket.

I'll try to review your ticket soon.

comment:11 Changed 5 years ago by Xavier Caruso

Why did you remove "in one variable" in the doctest.

    sage: R.<x,y> = QQ[]
    sage: PolynomialQuotientRing(R, x^2+y+1)
    ...
    TypeError: ring must be a polynomial ring

comment:12 in reply to:  11 Changed 5 years ago by Julian Rüth

Replying to caruso:

Why did you remove "in one variable" in the doctest.

    sage: R.<x,y> = QQ[]
    sage: PolynomialQuotientRing(R, x^2+y+1)
    ...
    TypeError: ring must be a polynomial ring

Because it already says "univariate" there.

comment:13 Changed 5 years ago by Julian Rüth

Keywords: sd86.5 added

comment:14 Changed 5 years ago by David Roe

Reviewers: David Roe
Status: needs_reviewpositive_review

Tests all pass for me, and it looks good.

comment:15 Changed 5 years ago by Volker Braun

Status: positive_reviewneeds_work

Merge conflict

comment:16 in reply to:  15 Changed 5 years ago by David Roe

Replying to vbraun:

Merge conflict

For me, trac is showing it as still merging cleanly. Is there a new beta against which the merge is failing, or a ticket?

comment:17 Changed 5 years ago by Julian Rüth

Status: needs_workpositive_review

We do not get a merge conflict for that one.

comment:18 Changed 5 years ago by Volker Braun

Status: positive_reviewneeds_work

Wait for the next beta

comment:19 Changed 5 years ago by git

Commit: f6a1cd8a84d48f4c043b770d2f437701eb8e308919af05916a1eb3f1fc89ba430b45afb23592dc8e

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

19af059Merge branch 'develop' into t/22983/polynomial_quotient_rings_are_unique_parents

comment:20 Changed 5 years ago by Julian Rüth

Status: needs_workpositive_review

Still no conflicts. What are we doing wrong?

comment:21 Changed 5 years ago by Volker Braun

Status: positive_reviewneeds_work

Random failures on some of the build bots:

sage -t --long src/sage/rings/polynomial/polynomial_quotient_ring.py
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1355, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
Failed example:
    L.S_units([])
Expected:
    [(1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [(-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1359, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
Failed example:
    L.S_units([K.ideal(1/2*a - 3/2)])
Expected:
    [((-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 4/3*a, +Infinity),
     (1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [((-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 4/3*a, +Infinity),
     (-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1364, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
Failed example:
    L.S_units([K.ideal(2)])
Expected:
    [((1/2*a - 1/2)*b^2 + (a + 1)*b + 3, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a + 1/2, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a - 1/2, +Infinity),
     (1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [((1/2*a - 1/2)*b^2 + (a + 1)*b + 3, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a + 1/2, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a - 1/2, +Infinity),
     (-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1445, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.units
Failed example:
    L.units()
Expected:
    [(1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [(-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
2 items had failures:
   3 of  18 in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
   1 of  23 in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.units
    [385 tests, 4 failures, 1.59 s]

comment:22 Changed 5 years ago by git

Commit: 19af05916a1eb3f1fc89ba430b45afb23592dc8eb04e7e9f5067b001f1d58ca72c0724ebfd7df715

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

b04e7e9Merge branch 'develop' into t/22983/polynomial_quotient_rings_are_unique_parents

comment:23 Changed 5 years ago by David Roe

Keywords: sd87 added

comment:24 Changed 5 years ago by git

Commit: b04e7e9f5067b001f1d58ca72c0724ebfd7df715272e7e310373cb911d9c78cef5ab622bf37d073d

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

272e7e3Merge remote-tracking branch 'origin/develop' into HEAD

comment:25 Changed 5 years ago by git

Commit: 272e7e310373cb911d9c78cef5ab622bf37d073d806d5afe806f90f2dc21e08fbee02c7640142b41

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

806d5afPickling now works

comment:26 Changed 5 years ago by Julian Rüth

Status: needs_workneeds_review

Let's see what the patchbots think now. I expect some of the S_units tests to disagree. I don't understand why they are not stable as I don't see anything happening in the implementation that would be random after my changes.

comment:27 Changed 5 years ago by Julian Rüth

Status: needs_reviewneeds_work

Some S_units fail. Let's make the tests less strict and add a _test_S_units instead.

comment:28 Changed 5 years ago by git

Commit: 806d5afe806f90f2dc21e08fbee02c7640142b41820b0a2c47f66cc5fdf6466ef378f5e18c89d6b0

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

f1f2fa5Merge remote-tracking branch 'trac/u/saraedum/polynomial_quotient_rings_are_unique_parents' into trac-22983
820b0a2Fix doctests

comment:29 Changed 5 years ago by Julian Rüth

Status: needs_workneeds_review

I thought for a while that the behaviour of these doctests was random. Actually it is not. It is consistent over all patchbot runs with the same base version of Sage. Caching the polynomial rings flips some signs, I am not sure why. Anyway, the result is still correct and it is not random, so there is no need for a _test_S_units() which would be hard to write anyway.

comment:30 Changed 5 years ago by git

Commit: 820b0a2c47f66cc5fdf6466ef378f5e18c89d6b04660c1865961462098d01470773ca1ac95a96d4c

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

4660c18Fix doctests

comment:31 Changed 5 years ago by David Roe

Status: needs_reviewpositive_review

Looks good to me.

comment:32 Changed 4 years ago by Frédéric Chapoton

Milestone: sage-8.0sage-8.3

comment:33 Changed 4 years ago by Volker Braun

Status: positive_reviewneeds_work

I still get failing tests. Random failures during high load. It looks like the tests depend on whether a garbage collection is forced due to low memory.

File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1445, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
Failed example:
    L.S_units([])
Expected:
    [(1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [(-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1449, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
Failed example:
    L.S_units([K.ideal(1/2*a - 3/2)])
Expected:
    [((-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 4/3*a, +Infinity),
     (1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [((-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 4/3*a, +Infinity),
     (-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1454, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
Failed example:
    L.S_units([K.ideal(2)])
Expected:
    [((1/2*a - 1/2)*b^2 + (a + 1)*b + 3, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a + 1/2, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a - 1/2, +Infinity),
     (1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [((1/2*a - 1/2)*b^2 + (a + 1)*b + 3, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a + 1/2, +Infinity),
     ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a - 1/2, +Infinity),
     (-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1535, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.units
Failed example:
    L.units()
Expected:
    [(1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
Got:
    [(-1/2*a + 1/2, 6),
     ((-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, +Infinity),
     (2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2, +Infinity)]
**********************************************************************
File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1544, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.units
Failed example:
    L.unit_group().gens_values()
Expected:
    [-1/2*a + 1/2, (-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, 2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
Got:
    [1/2*a + 1/2, (-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2, 2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
**********************************************************************
2 items had failures:
   3 of  18 in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.S_units
   2 of  23 in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.units
    [451 tests, 5 failures, 2.92 s]
----------------------------------------------------------------------
sage -t --long src/sage/rings/polynomial/polynomial_quotient_ring.py  # 5 doctests failed
----------------------------------------------------------------------

comment:34 Changed 4 years ago by Julian Rüth

Branch: u/saraedum/polynomial_quotient_rings_are_unique_parents
Commit: 4660c1865961462098d01470773ca1ac95a96d4c

comment:35 Changed 4 years ago by Julian Rüth

Branch: u/saraedum/22983

comment:36 Changed 4 years ago by git

Commit: 966c36b92266ffbaadec4bd43e0f08f086eb5fd3

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

966c36bMerge develop and 22983

comment:37 Changed 4 years ago by Julian Rüth

Not the first time, something like this has happened: https://trac.sagemath.org/ticket/23851#comment:5


New commits:

054945dMake polynomial quotient rings unique parents
f6a1cd8Document normalization of modulus
19af059Merge branch 'develop' into t/22983/polynomial_quotient_rings_are_unique_parents
b04e7e9Merge branch 'develop' into t/22983/polynomial_quotient_rings_are_unique_parents
272e7e3Merge remote-tracking branch 'origin/develop' into HEAD
806d5afPickling now works
f1f2fa5Merge remote-tracking branch 'trac/u/saraedum/polynomial_quotient_rings_are_unique_parents' into trac-22983
4660c18Fix doctests
697d02eMerge remote-tracking branch 'trac/u/saraedum/polynomial_quotient_rings_are_unique_parents' into HEAD
966c36bMerge develop and 22983

comment:38 Changed 4 years ago by Julian Rüth

Dependencies: #23851
Status: needs_workpositive_review

The issue has been fixed in #23851. Since I did not change anything, I am setting this back to positive review.

comment:39 Changed 4 years ago by Volker Braun

Branch: u/saraedum/22983966c36b92266ffbaadec4bd43e0f08f086eb5fd3
Resolution: fixed
Status: positive_reviewclosed
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