20190315 23:19:25 0500  commented answer  transformation matrix for variable matrix of given jordan type Thanks very much! 
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20190307 18:57:03 0500  commented question  transformation matrix for variable matrix of given jordan type Yes, it might. How do I do it, exactly? I would work in the ring $R/I$, where $R$ is the polynomial ring generated by matrix coefficients, and $I$ is the ideal of the Jordan form. For instance, if I have a 5 by 5 matrix $A$ of type $(3,2)$ then

20190302 22:38:07 0500  commented question  transformation matrix for variable matrix of given jordan type In general, the constraints may be more complicated than setting some entries to zero. Either way, I want Sage to figure out those constraints for me, and solve something like $g A g^{1} = J$ for a $g$, given variable $A$ and fixed $J$. If I try 
20190302 22:38:07 0500  commented question  transformation matrix for variable matrix of given jordan type Sure. Say I have an arbitrary uppertriangular matrix of Jordan type $(2,1)$. $$ A = \begin{pmatrix} 0 & A_{0} & A_{1} \\ 0 & 0 & A_{2} \\ 0 & 0 & 0 \end{pmatrix} $$ By default $$ J_d = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix} \qquad T_d = \begin{pmatrix}A_{0} A_{2} & A_{1} & 0 \\ 0 & A_{2} & 0 \\ 0 & 0 & 1\end{pmatrix} $$ However, I expect $$J = \begin{pmatrix}0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{pmatrix}$$ In this case, I know that $A_2$ must be zero for $A$ to have Jordan type $(2,1)$ so I let $A' = A\big_{A_2 = 0}$ and do $$T = \begin{pmatrix}A_{0} & 0 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & \frac{A_{0}}{A_{1}}\end{pmatrix}$$ 
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20190301 12:29:32 0500  asked a question  transformation matrix for variable matrix of given jordan type related: question/10488/whydoesjordan_formnotworkoverinexactrings/ I have, say, a nilpotent uppertriangular matrix $A$, with variable entries, and of a given Jordan type, $J$ (block type $\lambda$). I would like to know the transformation matrix $g$ such that $g A g^{1} = J$. How do I tell sage my input has a given Jordan type? My idea is to compute I would like to know if what I want is already implemented somewhere in Sage, or if there is a better way to implement it than what I propose. 