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D.5.10.2 matrixExp

Procedure from library orbitparam.lib (see orbitparam_lib).

Usage:
matrixExp(A); A matrix.

Assume:
A is a nilpotent n x n matrix.
If the characteristic p of the ground field is positive, then n has to be smaller than p.

Return:
matrix, exp(A)

Theory:
We compute the power series, which terminates since A is nilpotent.

Example:
 
LIB "orbitparam.lib";
ring R = 0,(x),dp;
matrix A[4][4] = 0,0,1,0, 0,0,1,0, 0,0,0,0;
matrixExp(A);
==> _[1,1]=1
==> _[1,2]=0
==> _[1,3]=1
==> _[1,4]=0
==> _[2,1]=0
==> _[2,2]=1
==> _[2,3]=1
==> _[2,4]=0
==> _[3,1]=0
==> _[3,2]=0
==> _[3,3]=1
==> _[3,4]=0
==> _[4,1]=0
==> _[4,2]=0
==> _[4,3]=0
==> _[4,4]=1