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D.3.2.17 jordan

Procedure from library linalg.lib (see linalg_lib).

Usage:
jordan(M[,opt]); M constant square matrix, opt integer

Assume:
The eigenvalues of M are in the coefficient field.

Return:
The procedure returns a list jd with 3 entries:
 
         - jd[1] ideal, eigenvalues of M,
         - jd[2] list of intvecs, jd[2][i][j] size of j-th Jordan block with
           eigenvalue jd[1][i], and
         - jd[3] a matrix, jd[3]^(-1)*M*jd[3] in Jordan normal form.
         Depending on opt, only certain entries of jd are computed.
           If opt=-1, jd[1] is computed,
           if opt= 0, jd[1] and jd[2] are computed,
           if opt= 1, jd[1], jd[2], and jd[3] are computed, and,
           if opt= 2, jd[1] and jd[3] are computed.
         By default, opt=0.

Note:
A non constant polynomial matrix M is replaced by its constant part.

Display:
The procedure displays comments if printlevel>=1.

Example:
 
LIB "linalg.lib";
ring R=0,x,dp;
matrix M[3][3]=3,2,1,0,2,1,0,0,3;
print(M);
jordan(M);


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