7.106 Bug in matrix of power n, expand in Maple 4 to Maple 8 and simplify in Maple 4 to Maple 6 (5.2.01)

7.106.1 HARALD PLEYM

Can anyone explain this strange behaviour, both in R4 / R5 and Maple 6.

>with(linalg): 
>A:=diag(1,2,3)^n: 
> expand(A); 
                                    n 
                                 bb
 

The same result with Maple 7 and Maple 8. Corrected with Maple 9. (U. Klein)

> simplify(A); 
                                   n 
                                  b
 

This is corrected with Maple 7. (U. Klein)

I expected only the matrix A as output.

7.106.2 Dr. TANAKA, Kazuo (13.2.01)

This is not the answer with which you are satisfied. This is my comments.

A command "expand" is a reverse of "factor". Therefore, I think that we should not apply "expand" to matrix, vector and so on.

A command "simplify" is a simplification rule for various types of expressions, which, I am afraid, do not include matrix, vector nor,....

Please try as followings;

 >with(linalg): 
 >A:=diag(1,2,3); 
 >evalm(A^4);
 

7.106.3 Colin Birch (13.2.01)

I cannot explain where bb comes from, but if A is a matrix, in R4 / R5 the expressions A^n, A*A or A+A are syntax errors, which won’t do what you want. You have to use multiply() and add(). In Maple 6 you can use the LinearAlgebra package instead:

> with(LinearAlgebra): A:=DiagonalMatrix([1,2,3])^2: expand(A); 
 
                            [1    0    0] 
                            [           ] 
                            [0    4    0] 
                            [           ] 
                            [0    0    9]
 

but I am afraid you still get:

> with(LinearAlgebra): A:=DiagonalMatrix([1,2,3])^n: expand(A); 
 
                            [1    0    0]n 
                            [           ] 
                            [0    2    0] 
                            [           ] 
                            [0    0    3]
 

My impression is that linalg is only being maintained for the sake of compatibility between releases.

7.106.4 Renato Portugal (13.2.01)

This is a bug!

Look at the following commads, which are independent on linalg or package LinearAlgebra of Maple 6:

> Z := array(1 .. 3, 1 .. 3,[(1, 1)=1,(3, 2)=0,(2, 1)=0,(2, 2)=2,(3, 3)=3, 
             (1, 2)=0,(2, 3)=0,(1, 3)=0,(3, 1)=0])^m; 
 
> simplify(%); 
 
                                   m 
                                  b 
> expand(%%); 
 
                                   m 
                                 bb
 

The bug seems to be in procedure

`simplify/commonpow` and `expand/power`

which have b and bb as local variables respectively. It seems that it is a problem of evaluation to name of these local variables.