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My real problem is that I've got a list of points in R3 and want to decide if they determine a plane, meaning they are coplanar but not colinear. Similarly, given a list of points in R2, I want to verify that they aren't colinear. Both of these can be done by converting the list of points to a matrix and finding the rank of the matrix, but I only use the rank function in the definitions of colinear and coplanar.

Maybe there's an easier way to tackle the underlying problems. Anyone got a suggestion for such?

I have written an experimental [implementation] of a Gauss-Jordan solver and matrix inverter. You might find some use for it. It does work and is reasonably fast, though not as fast as hmatrix. One advantage is that you can feed the points incrementally, and it will tell you immediately when there is no solution. It will also quickly reject redundant points, even in the presence of rounding errors.

I should note: The `solve` function isn't yet written, but it also doesn't do much. Once you have fed enough relations, the matrix will already have been reduced to the identity, so you can simply extract the solutions from the relations. Greets, Ertugrul

On Sat, Apr 25, 2015 at 10:49 AM, Jerzy Karczmarczuk < jerzy.karczmarczuk@unicaen.fr> wrote:

Many people help Mike Meyer:

And I do appreciate it.

My real problem is that I've got a list of points in R3 and want to decide if they determine a plane, meaning they are coplanar but not colinear. Similarly, given a list of points in R2, I want to verify that they aren't colinear. Both of these can be done by converting the list of points to a matrix and finding the rank of the matrix, but I only use the rank function in the definitions of colinear and coplanar.

Maybe there's an easier way to tackle the underlying problems. Anyone got a suggestion for such?

I didn't follow this discussion, so I might have missed some essential issues, I apologize then. But if THIS is the problem...

All these powerful universal libraries, with several hundreds of lines of code are important and useful, but if the problem is to find whether a list of pairs (x,y) is collinear or not, I presume that such program as below could do. I am ashamed showing something like that...

*colin ((x,y):l) = all (\(c,d)->abs(px*d-py*c)

That's not far from what I wound up with, except I generalized it to work for both 2d and 3d vectors. And yeah, I clearly got off on the wrong foot when I turned up "test the rank of the matrix" for finding collinearity and coplanarity. This pretty much solves my problem. Thanks to all who helped.