Singular Manual: busadj

  | #### D.3.2.7 busadj Procedure from library `linalg.lib` (see linalg_lib). Usage: busadj(A); A = square matrix (of size nxn) Return: list L:
               L[1] contains the (n+1) coefficients of the characteristic
                    polynomial X of A, i.e.
                    X = L[1][1]+..+L[1][k]*t^(k-1)+..+(L[1][n+1])*t^n
               L[2] contains the n (nxn)-matrices Hk which are the coefficients of
                    the busadjoint bA = adjoint(E*t-A) of A, i.e.
                    bA = (Hn-1)*t^(n-1)+...+Hk*t^k+...+H0,  ( Hk=L[2][k+1] )
Example:
    LIB "linalg.lib";
    ring r = 0,(t,x),lp;
    matrix A[2][2] = 1,x2,x,x2+3x;
    print(A);
    ==> 1,x2,
    ==> x,x2+3x
    list L = busadj(A);
    poly X = L[1][1]+L[1][2]*t+L[1][3]*t2; X;
    ==> t2-tx2-3tx-t-x3+x2+3x
    matrix bA[2][2] = L[2][1]+L[2][2]*t;
    print(bA);               //the busadjoint of A;
    ==> t-x2-3x,x2,
    ==> x,      t-1
    print(bA*(t*unitmat(2)-A));
    ==> t2-tx2-3tx-t-x3+x2+3x,0,
    ==> 0,                    t2-tx2-3tx-t-x3+x2+3x

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