Opened 6 years ago

Closed 6 months ago

# reduce method of polynomial ideals gives incorrect results

Reported by: Owned by: lftabera major sage-duplicate/invalid/wontfix algebra days94 dimpase Dima Pasechnik N/A

Define the following polynomial ring, polynomial, and ideal:

```sage: term_order = TermOrder('degrevlex', 2) + TermOrder('degrevlex', 2)
sage: K = PolynomialRing(QQ, 'x,y,a0,a1', order=term_order)
sage: x, y, a0, a1 = K.gens()
sage: f = x**3 + x**2*y
sage: m = Ideal(x**4, x**2*y, y**2)
```

Before #27508, we get an incorrect reduction:

```sage: m.reduce(f) == f.reduce(m.groebner_basis())
False
sage: m.reduce(f)
x^3 + x^2*y
sage: f.reduce(m.groebner_basis())
x^3
```

Singular computes correctly the reduction as `x^3`.

The problem is we call singular via libsingular without asking for tail reduction.

This was fixed in #27508, after which we get correct results:

```sage: m.reduce(f) == f.reduce(m.groebner_basis())
True
sage: m.reduce(f)
x^3
sage: f.reduce(m.groebner_basis())
x^3
```

### comment:1 Changed 3 years ago by lftabera

• Milestone changed from sage-6.8 to sage-8.3

### comment:2 Changed 3 years ago by lftabera

I am not able to debug this. For me, it seems that this is an error in libsingular and, probably, a duplicate of #12529

### comment:3 Changed 3 years ago by vdelecroix

• Milestone changed from sage-8.3 to sage-8.4

update milestone 8.3 -> 8.4

### comment:4 Changed 8 months ago by gh-mwageringel

• Milestone changed from sage-8.4 to sage-duplicate/invalid/wontfix
• Status changed from new to needs_review

This works correctly in 9.2.beta10, possibly since #27508.

### comment:5 Changed 8 months ago by dimpase

• Reviewers set to Dima Pasechnik
• Status changed from needs_review to positive_review

indeed

### comment:6 Changed 6 months ago by slelievre

• Resolution set to worksforme
• Status changed from positive_review to closed

### comment:7 Changed 6 months ago by slelievre

• Description modified (diff)
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