The companion matrix of a polynomial.

[Hongyi Zhao <hongyi.zhao@gmail.com>]

Hi here,

In GAP, the following command can be used to compute a companion
matrix of the polynomial:

gap> A:=[ [ 1, -4, 0 ], [ 1, 0, -2 ], [ 3, 1, 0 ] ];;
gap> CompanionMat(A);
[ [ [ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ], [ -1, 4, 0 ] ], [ [ [
1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ -1, 0, 2 ] ] ]

When I try the similar operation in GP, the corresponding error will
be triggered:

? A=[ 1, -4, 0; 1, 0, -2; 3, 1, 0 ]
%1 =
[1 -4  0]

[1  0 -2]

[3  1  0]

? matcompanion(A)
  ***   at top-level: matcompanion(A)
  ***                 ^---------------
  *** matcompanion: incorrect type in matcompanion (t_MAT).
  ***   Break loop: type 'break' to go back to GP prompt
break>

Any tips for doing this in GP?

Regards,
Zhao
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao@gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province