Singular Manual: realLLL

| #### D.8.7.17 realLLL Procedure from library `recover.lib` (see recover_lib). Usage: realLLL(M); matrix M Assume: The columns of M represent a basis of a lattice. The groundfield is the field of real number or the field of complex numbers, the elements of M are real numbers. Return: matrix: the columns representing an LLL-reduced basis of the lattice given by M Example:
    LIB "recover.lib";
    ring r=(real,50),x,dp;
    matrix M[5][4]=
    1,0,0,0,
    0,1,0,0,
    0,0,1,0,
    0,0,0,1,
    5*81726716.91827716, 817267.1691827716, poly(10)**30, 13*81726716.91827716;
    matrix L=realLLL(M);
    print(L);
    ==> 1,   0,                -3,                 -315358105194840436449,
    ==> -500,1,                0,                  -630716210389680833,
    ==> 0,   0,                0,                  1,
    ==> 0,   0,                1,                  -819931073506585134768,
    ==> 0,   817267.1691827716,-163453433.83655432,771738001439.2007536172

User manual for Singular version 4.3.2p10, 2023, generated by texi2html.