Opened 4 years ago

Closed 4 years ago

# Normalize bound checking in points function

Reported by: Owned by: Raghukul Raman major sage-8.3 algebraic geometry algebraic scheme, gsoc2018 Ben Hutz, Raghukul Raman Raghukul Raman Ben Hutz N/A b9266c6 b9266c657e20c8832e043bddd24d1abace89dc5a

### Description

Consider this example

```sage: P.<x,y> = ProjectiveSpace(QQ, 1)
sage: print sorted(list(P.points_of_bounded_height(bound=3)))
[(-2 : 1), (-1 : 1), (-1/2 : 1), (0 : 1), (1/2 : 1), (1 : 0), (1 : 1), (2 : 1)]
```

Points of height 3 are not present.

```sage: P.<x,y,z> = ProjectiveSpace(2,QQ)
sage: list(P.points_of_bounded_height(bound=5))
```

here we have some points like `(2 : -4/3 : 1)` which have height=6, if we use enum_projective_rational_field function results are as we would expect. So the underlying definition for height of rational points need to be uniform in all these functions.

### comment:1 Changed 4 years ago by Raghukul Raman

Branch: → u/raghukul01/normalize_bound_checking_in_points_function

### comment:2 Changed 4 years ago by Raghukul Raman

Authors: → Raghukul Raman → 26c28949343ffa6dc2d1ba1e142fe4a28d312543 new → needs_review

New commits:

 ​26c2894 `25780: Corrected algorithm in points function`

### comment:3 Changed 4 years ago by Ben Hutz

Just one comment here. What do you think about using?

```self.point(c, check=False)
```

It is about twice as fast and since the function is for projective space (not a subscheme) it's not like we need to check that the point is well-defined. It will cause them not to be normalized to the last coordinate to 1 though.

I have the doctests running now, but I don't really expect a failure.

### comment:4 Changed 4 years ago by git

Commit: 26c28949343ffa6dc2d1ba1e142fe4a28d312543 → b9266c657e20c8832e043bddd24d1abace89dc5a

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

 ​b9266c6 `25780: Improved conversion to projective point`

### comment:5 Changed 4 years ago by Ben Hutz

Reviewers: → Ben Hutz needs_review → positive_review

### comment:6 Changed 4 years ago by Volker Braun

Branch: u/raghukul01/normalize_bound_checking_in_points_function → b9266c657e20c8832e043bddd24d1abace89dc5a → fixed positive_review → closed
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