ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 17 Oct 2011 12:44:30 +0200Symbolic matrices and "integrity" of their inversehttps://ask.sagemath.org/question/8391/symbolic-matrices-and-integrity-of-their-inverse/I have to solve the following problem:
Does a matrix $G\in GL(n,\mathbb{Z})$ exists such that
$$
G\times A\times G^{-1}=B
$$
being $A,B$ given matrices in $\mathbb{Q}$?
Doing everything by hand, I finally find myself with a bunch of symbolic matrices. Now I have to check if they can lay inside $GL(n,\mathbb{Z})$, i.e. if there are integer values for the variables in the matrix such that the matrix is integer, invertible and with integer inverse.
E.g.:
$$\left(\begin{array}{cc}x & 0 \\\\ 0 & y\end{array}\right)$$ does the trick only for $x=y=1$.
Is there a quick method within Sage to solve that last problem?
Thanks!JesustcMon, 17 Oct 2011 12:44:30 +0200https://ask.sagemath.org/question/8391/