Singular Manual: inverse_L

| #### D.3.2.3 inverse_L Procedure from library `linalg.lib` (see linalg_lib). Usage: inverse_L(A); A = square matrix Return: list Inv representing a left inverse of A, i.e - Inv[1] = matrix I and - Inv[2] = poly p such that I*A = unitmat(n)*p; Note: p=1 if 1/det(A) is computable and p=det(A) if not; the computation computes first det(A) and then uses lift Example:
    LIB "linalg.lib";
    ring r=0,(x,y),lp;
    matrix A[3][3]=x,y,1,1,x2,y,x,6,0;
    print(A);
    ==> x,y, 1,
    ==> 1,x2,y,
    ==> x,6, 0
    list Inv=inverse_L(A);
    print(Inv[1]);
    ==> -6y,  6,    -x2+y2,
    ==> xy,   -x,   -xy+1,
    ==> -x3+6,xy-6x,x3-y
    print(Inv[2]);
    ==> -x3+xy2-6xy+6
    print(Inv[1]*A);
    ==> -x3+xy2-6xy+6,0,            0,
    ==> 0,            -x3+xy2-6xy+6,0,
    ==> 0,            0,            -x3+xy2-6xy+6
See also: inverse; inverse_B.

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