Echelon form of a matrix over the integers using maple

Question

I need to find the (row) echolon form over the integers $\mathbb{Z}$, using maple. I know how to do this over $\mathbb{Q}$, using 'ReducedRowEchelonForm' of the package 'LinearAlgebra'.

I also know how to reduce a matrix to the echelon form, over the integers, using sage; but it would be much more comfortable to use one coding system for my needs.

Thanks in advance.

Answer 1

Use the HermitForm from the MatrixPolynomialAlgebra package.

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Example:

A:= <<0,-1,-2,1>|<-3,-3,-3,4>|<-6,-1,0,5>|<9,1,-1,-7>>;

LinearAlgebra:-ReducedRowEchelonForm(A);

$$ \begin{bmatrix} 1 & 0& 0& 1/2\\ 0&1&0&0\\ 0&0&1&-3/2\\ 0&0&0&0 \end{bmatrix} $$

MatrixPolynomialAlgebra:-HermiteForm(A);

$$\begin{bmatrix} 1&0&1&-1\\ 0&1&0&0\\ 0&0&2&-3\\ 0&0&0&0 \end{bmatrix}$$