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### Hermite form, entries reduced over pivots

Hello!

I have a question concerning the function hermite_form. This function unfortunately does not reduce the entries above the pivots of the hermite normal form if I use the function on a matrix with polynomial entries. Is there another function or option which enables me to do that? Following short example hopefully illustrates what I mean:

R.<x> = QQ[];
M = matrix(2,2, [x,x, 0,x]);
M.hermite_form()


This will give the exact same matrix M and not the matrix [x,0, 0,x] which I would expect or hope to get.

Especially if somebody wants to apply another algorithm to such a matrix in hermite form it can be difficult to work with non-reduced matrices.

Kind regards

Philipp

 2 retagged FrédéricC 2339 ●3 ●27 ●47

### Hermite form, entries reduced over pivots

Hello!

I have a question concerning the function hermite_form. This function unfortunately does not reduce the entries above the pivots of the hermite normal form if I use the function on a matrix with polynomial entries. Is there another function or option which enables me to do that? Following short example hopefully illustrates what I mean:

R.<x> = QQ[];
M = matrix(2,2, [x,x, 0,x]);
M.hermite_form()


This will give the exact same matrix M and not the matrix [x,0, 0,x] which I would expect or hope to get.

Especially if somebody wants to apply another algorithm to such a matrix in hermite form it can be difficult to work with non-reduced matrices.

Kind regards

Philipp