On 12 sept. 2015, at 11:12, Jerzy Karczmarczuk
Le 12/09/2015 10:15, Alexey Muranov a écrit :
the difference of two points in an affine space is a vector, the sum of a point of an affine space and a vector is another point.
We can give several similar examples, but it might not be so useful for the implementation of whatever. In the affine space we can interpolate between points: p0 + 1/2*(p1-p0) is the middle point. Writing it just as 1/2*(p0+p1) might be considered as an abomination, since you should not add points... Who should allow the first and forbid the second?
I agree, it gets complicated. A more general type of "weighted sums of points" would probably be needed, but impractical...
If you have an additive group, you have automatically a module over integers. Sorry, *positive* integers.
Well, over all integers as well.
Please read the *easy* article of John Baez (2009) : http://math.ucr.edu/home/baez/torsors.html And then look upon torsors in general, and recognize that is is simply horrible.
I didn't get this (i do not know much about torsors). Alexey.