Opened 12 years ago

Closed 10 years ago

# Rational Point algorithm bug

Reported by: Owned by: nkaplan AlexGhitza major sage-4.8 algebraic geometry minz sage-4.8.alpha5 Moritz Minzlaff John Cremona None of the above - read trac for reasoning.

### Description (last modified by minz)

When you have a curve defined over a projective space over a finite field, it looks like sometimes the rational point list coming from the Brill-Noether package in Singular is not the full list of rational points.

```sage: S.<x,y,z> = GF(5)[]
sage: g = x*z+z^2
sage: G = Curve(g)
sage: G.rational_points('enum')
[(0 : 1 : 0), (1 : 0 : 0), (1 : 1 : 0), (2 : 1 : 0),
(3 : 1 : 0), (4 : 0 : 1), (4 : 1 : 0), (4 : 1 : 1),
(4 : 2 : 1), (4 : 3 : 1), (4 : 4 : 1)]
sage: G.rational_points('bn')
[(0 : 1 : 0), (4 : 0 : 1), (4 : 1 : 1), (4 : 2 : 1),
(4 : 3 : 1), (4 : 4 : 1)]
```

The problem was how Sage calls Singular's functions.

### comment:1 Changed 11 years ago by minz

• Cc minz added

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

• Authors set to Moritz Minzlaff
• Status changed from new to needs_work

Part of the problem was the same as in the computation of Riemann-Roch spaces #8997.

There still remains a problem: The above example works fine now if we replace z by y (which shouldn't make a difference in terms of correctness of the algorithms involved). Maybe the current singular interface makes certain assumptions about the variable names and their ordering that we still need to pay attention to here?

### Changed 11 years ago by minz

correctly wraps Singular's Brill-Noether method and adds doctest

### comment:3 Changed 11 years ago by minz

• Description modified (diff)
• Status changed from needs_work to needs_review

We were missing so far that and how Singular dehomogenizes the defining polynomial of the curve: Always with respect to the last variable. If the corresponding line is a component of the curve, the output was missing those points.

### comment:4 Changed 10 years ago by cremona

• Reviewers set to John Cremona
• Status changed from needs_review to positive_review

The patch looks good to me and applies cleanly to 4.8.alpha4. All long tests in sage/scheme pass. I am happy with this.

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

• Merged in set to sage-4.8.alpha5
• Resolution set to fixed
• Status changed from positive_review to closed
Note: See TracTickets for help on using tickets.