ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 16 Jun 2017 10:24:41 -0500Hermite form, entries reduced over pivotshttps://ask.sagemath.org/question/37964/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
Philippphilipp7Fri, 16 Jun 2017 10:24:41 -0500https://ask.sagemath.org/question/37964/Division of polynomial matriceshttps://ask.sagemath.org/question/10439/division-of-polynomial-matrices/Is it possible to perform euclidean division between two polynomial matrices in sage?
e.g.if
$A= \begin{bmatrix}
x^2 +1 & x \newline
0&x-1
\end{bmatrix} , B=\begin{bmatrix}
x & 2 \newline
1 &x-1
\end{bmatrix}$
are given find the matrices $Q,R$ so $A=QB +R$
*in this example the answer is $Q= \begin{bmatrix}
x & -1 \newline
0& 1
\end{bmatrix} , R=\begin{bmatrix}
2 & -1 \newline
-1 & 0
\end{bmatrix}$*koukourikosThu, 15 Aug 2013 08:03:25 -0500https://ask.sagemath.org/question/10439/