Singular Manual: inverse

  | #### D.3.2.1 inverse Procedure from library `linalg.lib` (see linalg_lib). Usage: inverse(A [,opt]); A a square matrix, opt integer Return:
                a matrix:
                - the inverse matrix of A, if A is invertible;
                - the 1x1 0-matrix if A is not invertible (in the polynomial ring!).
                There are the following options:
                - opt=0 or not given: heuristically best option from below
                - opt=1 : apply std to (transpose(E,A)), ordering (C,dp).
                - opt=2 : apply interred (transpose(E,A)), ordering (C,dp).
                - opt=3 : apply lift(A,E), ordering (C,dp).
Note: parameters and minpoly are allowed; opt=2 is only correct for matrices with entries in a field Example:
    LIB "linalg.lib";
    ring r=0,(x,y,z),lp;
    matrix A[3][3]=
    1,4,3,
    1,5,7,
    0,4,17;
    print(inverse(A));"";
    ==> 57, -56,13,
    ==> -17,17, -4,
    ==> 4,  -4, 1
    ==>
    matrix B[3][3]=
    y+1,  x+y,    y,
    z,    z+1,    z,
    y+z+2,x+y+z+2,y+z+1;
    print(inverse(B));
    ==> -xz+y+1, -xz-x+y,   xz-y,
    ==> z,       z+1,       -z,
    ==> xz-y-z-2,xz+x-y-z-2,-xz+y+z+1
    print(B*inverse(B));
    ==> 1,0,0,
    ==> 0,1,0,
    ==> 0,0,1
See also: inverse_B; inverse_L.

User manual for Singular version 4.4.0, 2024, generated by texi2html.