Opened 7 years ago

Closed 7 years ago

# Fix conversion from PARI to multivariate polynomial rings

Reported by: Owned by: pbruin major sage-6.6 algebra multivariate polynomials pari Peter Bruin Vincent Delecroix N/A 7a7e1cd 7a7e1cd5fe3d77da4ed242ebab9f0cb03c52aaa9

### Description

Conversion of multivariate polynomials from PARI does not always work:

```sage: A.<a> = PolynomialRing(QQ)
sage: B.<d,e> = PolynomialRing(A)
sage: f = pari(a*d)
sage: B(f)
Traceback (most recent call last):
...
TypeError: Unable to coerce PARI d to an Integer
```

A similar example:

```sage: A.<a,b> = PolynomialRing(QQ)
sage: B.<d,e> = PolynomialRing(A)
sage: f = pari(a*d)
sage: B(f)
Traceback (most recent call last):
...
TypeError: Could not find a mapping of the passed element to this ring.
```

### comment:1 Changed 7 years ago by pbruin

• Authors set to Peter Bruin
• Branch set to u/pbruin/17974-multivariate_polynomials_pari
• Commit set to 8be3fe6225d04415b144c8d36e87ec0e2595921e
• Status changed from new to needs_review

### comment:2 follow-up: ↓ 3 Changed 7 years ago by vdelecroix

• Status changed from needs_review to needs_info

Hello,

Do you know how pari chooses the order of the variables

```sage: A.<a> = PolynomialRing(QQ)
sage: B.<d,e> = PolynomialRing(A)
sage: f = pari(a*d)
sage: f
d*a
sage: B(f)
a*d
```

On the other hand, what do you think of

```sage: f.sage()
Traceback (most recent call last):
...
NameError: name 'd' is not defined
```

Vincent

### comment:3 in reply to: ↑ 2 ; follow-up: ↓ 4 Changed 7 years ago by pbruin

Hello Vincent,

Do you know how pari chooses the order of the variables

```sage: A.<a> = PolynomialRing(QQ)
sage: B.<d,e> = PolynomialRing(A)
sage: f = pari(a*d)
sage: f
d*a
sage: B(f)
a*d
```

In PARI, the variables `x` and `y` are predefined (with `x` of higher priority) and subsequent variables get a successively lower priority in the order in which they are encountered. Polynomials are printed with the variable of highest priority on the right. In this example PARI sees `a` first, therefore it has higher priority than `d`. Compare

```sage: gp('a*d')
d*a
```

On the other hand, what do you think of

```sage: f.sage()
Traceback (most recent call last):
...
NameError: name 'd' is not defined
```

This is because user-defined names are not part of the default context in which the evaluation is done. You have to do

```sage: f.sage({'a': a, 'd': d})
a*d
```

or

```sage: f.sage(globals())
a*d
```

### comment:4 in reply to: ↑ 3 ; follow-up: ↓ 5 Changed 7 years ago by vdelecroix

On the other hand, what do you think of

```sage: f.sage()
Traceback (most recent call last):
...
NameError: name 'd' is not defined
```

This is because user-defined names are not part of the default context in which the evaluation is done. You have to do

```sage: f.sage({'a': a, 'd': d})
a*d
```

or

```sage: f.sage(globals())
a*d
```

Ha nice! Could you add it to the documentation where you check pari conversion?

### comment:5 in reply to: ↑ 4 Changed 7 years ago by pbruin

• Status changed from needs_info to needs_work
• Work issues set to expand documentation

You have to do

```sage: f.sage({'a': a, 'd': d})
a*d
```

or

```sage: f.sage(globals())
a*d
```

Ha nice! Could you add it to the documentation where you check pari conversion?

OK, I can add it for completeness (there are somewhat similar examples in the documentation of `f.sage()`).

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

• Commit changed from 8be3fe6225d04415b144c8d36e87ec0e2595921e to 7a7e1cd5fe3d77da4ed242ebab9f0cb03c52aaa9

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

 ​7a7e1cd `Trac 17974: add example for f.sage()`

### comment:7 Changed 7 years ago by pbruin

• Status changed from needs_work to needs_review
• Work issues expand documentation deleted

### comment:8 Changed 7 years ago by vdelecroix

• Reviewers set to Vincent Delecroix
• Status changed from needs_review to positive_review

### comment:9 Changed 7 years ago by vbraun

• Branch changed from u/pbruin/17974-multivariate_polynomials_pari to 7a7e1cd5fe3d77da4ed242ebab9f0cb03c52aaa9
• Resolution set to fixed
• Status changed from positive_review to closed
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