Singular Manual: hermiteNormalForm

| #### D.15.13.48 hermiteNormalForm Procedure from library `multigrading.lib` (see multigrading_lib). Usage: hermiteNormalForm( A ); Purpose: Computes the (lower triangular) Hermite Normal Form of the matrix A by column operations. Return: intmat, the Hermite Normal Form of A Example:
    LIB "multigrading.lib";
    intmat M[2][5] =
    1, 2, 3, 4, 0,
    0,10,20,30, 1;
    // Hermite Normal Form of M:
    print(hermiteNormalForm(M));
    ==>      1     0     0     0     0
    ==>      0     1     0     0     0
    intmat T[3][4] =
    3,3,3,3,
    2,1,3,0,
    1,2,0,3;
    // Hermite Normal Form of T:
    print(hermiteNormalForm(T));
    ==>      3     0     0     0
    ==>      0     1     0     0
    ==>      3    -1     0     0
    intmat A[4][5] =
    1,2,3,2,2,
    1,2,3,4,0,
    0,5,4,2,1,
    3,2,4,0,2;
    // Hermite Normal Form of A:
    print(hermiteNormalForm(A));
    ==>      1     0     0     0     0
    ==>      1     2     0     0     0
    ==>      0     0     1     0     0
    ==>      0     1     0     1     0

User manual for Singular version 4.4.1, 2025, generated by texi2html.