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Dear Gap Forum,

Dear Marco,

Some time ago I wrote a routine that did the work for projective

subspaces of a given PG(n,q). Since this routine is build in in a package

dealing with projective geometry, the code itself is not direct usable

for affine spaces. But maybe you can use the same idea and just adapt the

code. Suppose A1 en A2 are two projective spaces, spanned by two sets of

points a1 and a2. The routine goes as follows. We first compute two sets

of hyperplanes h1 and h2 such that A1 and A2 are exactly the intersection

of all hyperplanes in respectively h1 and h2. Then the intersection of A1

and A2 is the intersection of all the hyperplanes in h1 union h2. At last

we can again compute a set of points spanning the intersection. Remark

that we never compute all the points of the spaces A1 and A2. The linear

algebra is handled by two gap functions:

NullspaceMat

this function is used to compute the hyperplanes from a set of spanning

points (and vice versa)

SemiEchelonMat

this function is used to eliminate linear dependecies.

Both functions are clearly documented in the GAP manual.

The projective case is probably a little easier than the affine case,

since you don`t have to worry about parallel spaces. The advantage in the

affine case is that you don`t need to normalize the vectors.

You can find the code and the whole package at the following address:

http://cage.rug.ac.be/~jdebeule/pg

It is a standard gap package, the documentation is included and also

available in html.

Sincerely Yours,

Jan De Beule

-- ---------------------------------------------------------------------------- Jan De Beule jdebeule@cage.rug.ac.be Vakgroep Zuivere Wiskunde Jan.DeBeule@rug.ac.be Galglaan 2, B 9000 Gent (Belgium) http://cage.rug.ac.be/~jdebeule ----------------------------------------------------------------------------

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