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From: Michael Walter (michael.walter_at_[hidden])
Date: 2007-03-15 10:04:51


On 3/15/07, Andreas Harnack <ah.boost.04_at_[hidden]> wrote:
> Hi Ben, interesting stuff, it just leaves one question to me:
> How can you represent an affine point in a computer program? My
> guess is: you can't.

You can, as you describe yourself in the following sentence:

> But you can implement vector spaces and you
> can map an affine space to a vector space by choosing a basis,
> i.e. an origin and a set of orthogonal unit vectors.

...except that this is a (Cartesian) _coordinate system_, not a basis.
A basis is a minimal set spanning a vector space.

> I'm not sure if the following is correct, but may be we can
> define affinity as the whole of all possible representations

Just as you could define a vector space as the whole of all its bases
(although one is certainly sufficient ;-).

> Affine spaces and vector spaces are two different things that
> live without each other, [...]

Not quite; you need a vector space to define an affine space, for the
difference between two points lives in that vector space.


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