Re: [Axiom-mail] A question about Axiom capabilities

[u1204]

Raoul,

If you look at the matrixcookbook that Mike mentioned, the first 10
equations are:

   (A*B)^-1      = B^-1 * A^-1
   (A*B*C...)^-1 = ...C^-1 * B^-1 * A^-1
   (A^T)^-1      = (A^-1)^T
   (A+B)^T       = A^T + B^T
   (A*B)^T       = B^T * A^T
   (A*B*C...)^T  = C^T * B^T *A^T
   (A^H)^-1      = (A^-1)^H
   (A+B)^H       = A^H + B^H
   (A*B)^H       = B^H * A^H
   (A*B*C...)^H  = ...C^H * B^H * A^H

It seems like we could create a SymbolicMatrix algebra that could
perform these manipulations with uninterpreted matrix symbols
A, B, C with a special recognized symbol 'T'.

These matrices could have actual values which, for certain operations
are ignored, so that

       (A*B)^-1      = B^-1 * A^-1

but for other operations would be evaluated as in:

       eval(B^-1 * A^-1)

giving the actual matrix result shown element by element.

An additional enhancement would be to make a SymbolicMatrixCategory
so that there could be specific domains such as 

   GeneralSymbolicMatrix,
   SymmetricSymbolicMatrix, 
   UpperTriangularSymbolicMatrix,
   DiagonalSymbolicMatrix,

etc which could exploit certain matrix-level properties at the
symbolic level.

This isn't exactly what Mike was originally asking but I think
that Axiom ought to be able to symbolically compute the equations
in the handbook.

Tim Daly