Opened 12 years ago

Closed 3 years ago

## #6472 closed defect (worksforme)

Reported by: Owned by: broune tbd major sage-duplicate/invalid/wontfix commutative algebra Reported upstream. Developers acknowledge bug. todo

This is wrong:

```sage: R.<a,b,c,d>=PolynomialRing(QQ,order="lex")
sage: ideal(a-b^16,b-c^16,c-d^1024).groebner_basis()
[a - d^4096, b - d^16384, c - d^1024]
```

The correct answer as given by Macaulay 2:

```i30 : R=QQ[a,b,c,d, MonomialOrder=>Lex];
i31 : I=ideal(a-b^16,b-c^16,c-d^1024);
i32 : gens gb I
o32 = | c-d1024 b-d16384 a-d262144 |
```

In particular the binomial involving a should raise d to the power 262144=218, not 4096=212 as Sage reports.

I suspect that the reason is that by default Sage uses Singular to implement groebner_basis, and Singular has limitations on the size of exponents. See https://www.singular.uni-kl.de/Manual/4-0-2/sing_455.htm which in particular says

```the maximal allowed exponent of a ring variable depends on the ordering of the ring
and is at least 32767.
```

(I suppose "least" is a typo, should be "most"...)

### comment:1 Changed 12 years ago by rlm

• Milestone changed from sage-4.1 to sage-4.1.1

### comment:2 Changed 11 years ago by AlexGhitza

• Component changed from algebra to commutative algebra

### comment:3 Changed 8 years ago by jdemeyer

• Milestone changed from sage-5.11 to sage-5.12

### comment:4 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.1 to sage-6.2

### comment:5 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.2 to sage-6.3

### comment:6 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:7 Changed 6 years ago by jakobkroeker

• Report Upstream set to N/A
• Stopgaps set to todo

### comment:8 Changed 5 years ago by jakobkroeker

• Report Upstream changed from N/A to Reported upstream. No feedback yet.

reported upstream:

### comment:9 Changed 5 years ago by jakobkroeker

another funny example :

```R.<b,c,d>=PolynomialRing(QQ,order="lex")
sage: ideal(b-c^64,c-d^1024).groebner_basis()
```

(wrong result and zero not shown)

```[b - , c - d^1024]
```

### comment:10 Changed 5 years ago by dimpase

• Description modified (diff)

Does Singular simply return incorrect results, or it's rather a Sage interface bug?

### comment:11 Changed 5 years ago by jakobkroeker

• Report Upstream changed from Reported upstream. No feedback yet. to Reported upstream. Developers acknowledge bug.

### comment:12 Changed 3 years ago by sbrandhorst

• Status changed from new to needs_review
```sage: R.<a,b,c,d>=PolynomialRing(QQ,order="lex")
....:
sage: I = ideal(a-b^16,b-c^16,c-d^1024)
sage: I.groebner_basis()
skipping text from `)` error at token `)`
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
RuntimeError: Error raised calling singular function
...
RuntimeError: error in Singular function call 'groebner':
exponent bound is 65535
error occurred in or before standard.lib::stdhilb line 381: `    i=interred(i);`
leaving standard.lib::stdhilb
leaving standard.lib::groebner
```

Looks good to me.

Last edited 3 years ago by sbrandhorst (previous) (diff)

### comment:13 Changed 3 years ago by dimpase

• Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix

This

```  skipping text from `)` error at token `)`
```

looks ugly, but otherwise there seems nothing to fix here---unless nowadays Singular offers an option to have bigger exponents.

### comment:14 Changed 3 years ago by embray

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