>> Martin, >> >> I've been studying Pfaffian systems (related to robotics, a field I >> know a bit about). It seems that your algorithm does not work for >> embedded matrices as in: >> >> z:SQMATRIX(2,INT):=[[0,0],[0,0]] >> m:SQMATRIX(2,INT):=[[0,1],[-1,0]] >> m2:SQMATRIX(4,SQMATRIX(2,INT)):=[[m,z,z,z],[z,m,z,z],[z,z,m,z],[z,z,z,m]] >> which should be 1*1*1*1 = 1 >> >> Am I doing something wrong? > >The matrix m2 is not skew-symmetric: it should be zero along the diagonal, but >it contains m along the diagonal. Try the following instead: > >(19) -> z:SQMATRIX(2,INT):=[[0,0],[0,0]]; m:SQMATRIX(2,INT):=[[0,1],[-1,0]]; > m2:= matrix [[z,m,m,m],[-m,z,z,z],[-m,z,z,m],[-m,z,-m,z]] > > + +0 0+ + 0 1+ + 0 1+ + 0 1++ > | | | | | | | | || > | +0 0+ +- 1 0+ +- 1 0+ +- 1 0+| > | | > |+0 - 1+ +0 0+ +0 0+ +0 0+ | > || | | | | | | | | > |+1 0 + +0 0+ +0 0+ +0 0+ | > (19) | | > |+0 - 1+ +0 0+ +0 0+ + 0 1+| > || | | | | | | || > |+1 0 + +0 0+ +0 0+ +- 1 0+| > | | > |+0 - 1+ +0 0+ +0 - 1+ +0 0+ | > || | | | | | | | | > ++1 0 + +0 0+ +1 0 + +0 0+ + > Type: Matrix SquareMatrix(2,Integer) >(20) -> PfChar(l, m2) > > 4 + 0 2+ 2 +- 1 0 + > (20) l + | |l + | | > +- 2 0+ + 0 - 1+ > Type: Polynomial SquareMatrix(2,Integer) > >So, the Pfaffian is > >+- 1 0 + >| | >+ 0 - 1+ > >In particular, look at its type: the Pfaffiam is an element of the groung ring.
You're quite correct. It seems that the documentation on wikipedia is wrong, at least as I read it. Do you agree? Tim _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
