Integer matrix

hsnf.column_style_hermite_normal_form(M: ndarray[tuple[Any, ...], dtype[int64]]) → tuple[ndarray[tuple[Any, ...], dtype[int64]], ndarray[tuple[Any, ...], dtype[int64]]]

Calculate column-style Hermite normal form of M Returned matrices (H, R) satisfy H = np.dot(M, R)

Parameters:

M (array, (m, n)) – Integer matrix

Returns:

• H (array, (m, n)) – Hermite normal form of M, lower-triangular integer matrix

• R (array, (n, n)) – Unimodular matrix

hsnf.row_style_hermite_normal_form(M: ndarray[tuple[Any, ...], dtype[int64]]) → tuple[ndarray[tuple[Any, ...], dtype[int64]], ndarray[tuple[Any, ...], dtype[int64]]]

Calculate row-style Hermite normal form of M. Returned matrices (H, L) satisfy H = np.dot(L, M).

Parameters:

M (array, (m, n)) – Integer matrix

Returns:

• H (array, (m, n)) – Hermite normal form of M, upper-triangular integer matrix

• L (array, (m, m)) – Unimodular matrix

hsnf.smith_normal_form(M: ndarray[tuple[Any, ...], dtype[int64]]) → tuple[ndarray[tuple[Any, ...], dtype[int64]], ndarray[tuple[Any, ...], dtype[int64]], ndarray[tuple[Any, ...], dtype[int64]]]

Calculate Smith normal form of integer matrix M. Returned matrices (D, L, R) satisfy D = np.dot(L, np.dot(M, R)).

Parameters:

M (array, (m, n)) – Integer matrix

Returns:

• D (array, (m, n)) – Smith normal form of M

• L (array, (m, m)) – Unimodular matrix

• R (array, (n, n)) – Unimodular matrix