# Ticket #13976(closed defect: fixed)

Opened 5 months ago

## Problem in the return type of BooleanIdeal.variety()

Reported by: Owned by: Bouillaguet malb major sage-5.7 commutative algebra malb, AlexanderDreyer N/A Martin Albrecht Charles Bouillaguet sage-5.7.beta1

### Description

One can do:

```sage= R.<x,y,z> = GF(2)[]
sage: I = ideal( [ x*y*z + x*z + y + 1, x+y+z+1] )
sage: sols = (I+sage.rings.ideal.FieldIdeal(R)).variety()
sage: sols
[{y: 1, z: 0, x: 0}, {y: 1, z: 1, x: 1}]

sage: sols[0][y]
1
```

Now the same thing fails in BooleanRing's:

```sage: R.<x,y,z> = BooleanPolynomialRing()
sage: I = ideal( [ x*y*z + x*z + y + 1, x+y+z+1] )
sage: sols = I.variety()
sage: sols
[{y: 1, z: 0, x: 0}, {y: 1, z: 1, x: 1}]

sage: sols[0][y]
Traceback (most recent call last):
...
KeyError: y
```

This is caused by an ugly hack (I authored...) in #13103 to make the variety() function work on BooleanIdeal's.

## Change History

### comment:1 Changed 5 months ago by Bouillaguet

• Status changed from new to needs_review
• Authors set to Charles Bouillaguet

### comment:2 Changed 5 months ago by malb

• Status changed from needs_review to positive_review
• Reviewers set to Martin Albrecht

Looks okay.

### comment:3 Changed 5 months ago by AlexanderDreyer

Nice patch, and Thank you for your great supporting work, Charles!

### comment:4 Changed 5 months ago by jdemeyer

• Status changed from positive_review to closed
• Resolution set to fixed
• Merged in set to sage-5.7.beta1
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