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D.5.8.2 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
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