Aurel Page on Wed, 25 Jan 2023 22:30:28 +0100

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 Re: Plane geometry in PARI

```Hi James,

```
One more remark: it is also relatively easy to implement a quadratic time algorithm for these tasks. It won't be as fast as available software, of course.
```
Best,
Aurel

On 20/01/2023 18:48, Vincent Delecroix wrote:
```
```Dear James,

Note that if your data is not generic (you have aligned
triples or coplanar quadruples) using floating point
approximation will systematically give you wrong answers
for convex hull.

One way to deal with high precision of generic points is
to convert the floating point to rationals and use something
like Normaliz that handle arbitrary precision rationals
(via GMP). An alternative to Normaliz would be PPL. I do not
think that any of these has optimized dim=2 and dim=3. You
can check CGAL for that purpose.

Best
Vincent

Le 20/01/2023 à 18:37, James Rickards a écrit :
```
```Hi all,

Thank you for the suggestions! I will check them out.

```
A brief summary of the input is I start with a quaternion algebra, generate some data, and end up with points in R^3 that are approximate real numbers. We then want to compute their convex hull and study this. The program that my collaborator is using doesn't handle precision well, and we get incorrect results for some larger inputs (i.e we can't fix it by increasing the precision of the input data). This is why I was hoping that something may have been written with PARI. However, a program that can work with large precision would also do the trick.
```
Best,
James
________________________________
From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
Sent: Friday, January 20, 2023 3:50 AM
```
To: pari-users@pari.math.u-bordeaux.fr <pari-users@pari.math.u-bordeaux.fr>
```Subject: Re: Plane geometry in PARI

On Tue, Jan 17, 2023 at 08:22:29PM +0000, James Rickards wrote:
```
Are there any libraries of methods built on top of PARI which work with plane geometry? The main things that I want to compute are:
```
*   Given a set of points (say in R^3), find their convex hull
```
*   Given a set of planes in R^3, they divide R^3 into regions. Return the connected component of the origin.
```
```
There a lot of possible software, the choice depends on the input and output you expect. Maybe give an example ? I use normaliz but it is more targetted toward discrete set.
```
Cheers,
Bill.

```
```

```