dear forum, i try to find the most efficient way to code the following, and the manual didn't help me:
1) given a vector space given by a set R of row vectors, rewrite a family of vectors belonging to the span of R as full row vectors over another space (isomorphic to the space spanned by R). my implementation: complete R to a basis B of the full row space; use 'Coefficients(B,v)' to obtain the coefficients in that basis, then throw away the last 0's to obtain the coefficients in the basis of the subspace spanned by R. this seems extremely inefficient. 2) given a set R of row vectors, determine whether v is in the span of these vectors. my implementation: test if Rank(R)=Rank(Concatenation(R,v)). again, i suspect there should be something much better. 3) given a set R of row vectors, rewrite a family of vectors as vectors (in the full row space K^n) as full row vectors over a space isomorphic to the quotient K^n/<R>. my implementation: complete R to a basis R cup S; extract the coefficients of S 4) given a matrix K^n -> K^n, that leaves the span of R invariant, extract a matrix K^n/<R> -> K^n/<R>. again, my implementation: complete R to a basis R cup S; for each vector in S, compute its image, and rewrite it using step 3) in the basis S; use that as a row of the new matrix. thanks in advance, laurent -- Laurent Bartholdi \ laurent.bartholdi<at>gmail<dot>com EPFL SB SMA IMB MAD \ Téléphone: +41 21-6935458 Station 8 \ Secrétaire: +41 21-6935501 CH-1015 Lausanne, Switzerland \ Fax: +41 21-6930339 _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
