Please help with these additional questions. (1) The covariant components of a second order tensor with respect to the basis e[1]=i[1]+i[2], e[2]=i[2]+i[3],e[3]=i[1]+i[3] are given by (a[ij]) = array([[2,0,1],[-1,2,0],[0,2,-1]]) Find the components a^ij, a[i]^k, a[k]^i

Can Maple be used to test infinite series for convergence ? Are the many tests for convergence already built-in Maple ? Thanks, v/r,

Please Help, Show that Sum(1/((2*n-1)*(2*n+1)), n = 1..infinity) = 1/2) Hint. (Show by mathematical induction that s[m] = m/(2*m+1) Thanks, v/r,

Can the commutator command in the tensors package be used with tensors of rank greater than 1 ? I recently tried to prove the jacobi identity using the 2 x 2 Pauli Matrices, that I created as arrays, but kept getting an error message saying something about the improper rank, of the arguments of the commutator command. I noticed in the help pages that the arguments of commutator must be of rank 1. I also tried all combinations of covariance and contravariance of the pauli matrices, but nothing worked. Can anyone help with this ? Is there any way to get around this ? thanks, v/r,

The special linear group SL(2)consists of all 2 x 2 matrices (with complex elements) having a determinant of +1. Show that such matrices form a group. Note. The SL(2) group can be related to the full Lorentz group in Section 4.4, much as the SU(2) group is related to SO(3). Arfken, and Weber. v/r, thanks,