Re: Create subspace from Basis : Maple

In article <1148567059.226496.293590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
matrix <iyerns@xxxxxxxxx> wrote:
Hi,
I have the Basis vectors of a subspace. How can I form the whole
subspace (all possible linear combinations) from these basis vectors in
Maple ?

I use symbolic computations mod 2.

If your field is Z_2 (i.e. the integers mod 2), and the "vectors" are
implemented as lists or Vectors, then the span of a set of vectors V
can be obtained as follows:

T:= combinat[cartprod]([seq]([0,1],i=V);
n:= nops(V);
makevec:= proc(L) add(L[i]*V[i],i=1..n); % mod 2 end;
{seq}(makevec(T[nextvalue]()), i=1..2^n);

Note: if the set is not necessarily linearly independent, it's
better using lists here rather than Maple's Vectors,
because duplicate lists are automatically removed from a set, while
duplicate Vectors are not. Of course you can easily convert from
lists to Vectors or vice versa.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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