Singular Manual: matrixLog

| #### D.5.8.3 matrixLog Procedure from library `orbitparam.lib` (see orbitparam_lib). Usage: matrixLog(A); A matrix. Assume: A-E 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, log(A) Theory: We compute the power series, which terminates since A-E is nilpotent. Example:
    LIB "orbitparam.lib";
    ring R = 0,(s,t),dp;
    matrix A[3][3] = 1,s,st/2, 0,1,t, 0,0,1;
    matrixLog(A);
    ==> _[1,1]=0
    ==> _[1,2]=s
    ==> _[1,3]=0
    ==> _[2,1]=0
    ==> _[2,2]=0
    ==> _[2,3]=t
    ==> _[3,1]=0
    ==> _[3,2]=0
    ==> _[3,3]=0

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