7.100 bug in LinearAlgebra,GramSchmidt, Maple 6 to Maple 8 (13.9.02)

7.100.1 Jack-Michel CORNIL

When working on an exercise for my students in order to reduce a symmetric matrix with an orthogonal transition matrix, I fell on the following error :

> with(LinearAlgebra): 
 
> A:=Matrix(3,3,[[2,-2,-2],[2,-2],[2]],scan=triangular,shape=symmetric); 
 
> T:=Eigenvectors(A); 
 
> T2:=T[2]; 
> B:=[Column(T2,1..3)]; 
 
> U:=GramSchmidt(B,'normalized'); 
Error, (in LinearAlgebra:-LA_Main:-Normalize) datatype of in-place Vector 
(algebraic) and datatype of result (anything) do not agree
 

It is the option ’normalized’ which causes the trouble.

I think that the problem comes from the "datatype" of the elements of the resulting matrix T2 as we can see below but it is impossible to modify this option.

> VectorOptions(B[1]); 
 
  shape = [], datatype = algebraic, orientation = column, 
 
        storage = rectangular, order = Fortran_order 
 
> MatrixOptions(T2); 
 
  shape = [], datatype = algebraic, storage = rectangular, 
 
        order = Fortran_order