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20210323 03:04:03 +0100  edited question  matrix over symbolic ring to matrix over finite field matrix over symbolic ring to matrix over finite field I have a bunch of ideals defined symbolically, that I would like t 
20210323 03:03:18 +0100  edited question  matrix over symbolic ring to matrix over finite field matrix over symbolic ring to matrix over finite field I have a bunch of ideals defined symbolically, that I would like t 
20210323 03:00:27 +0100  commented answer  matrix over symbolic ring to matrix over finite field Thank you very much. We seem to have found a similar solution, which does not obviously involve replacing variables; nam 
20210323 02:55:37 +0100  commented answer  matrix over symbolic ring to matrix over finite field Thank you very much. We seem to have found a similar solution, which does not obviously involve replacing variables; nam 
20210323 02:49:44 +0100  commented question  matrix over symbolic ring to matrix over finite field @rburing my bad, thanks  added how the x's appear in the matrix. How would you skip the symbolic ring if your matrices 
20210323 02:47:07 +0100  edited question  matrix over symbolic ring to matrix over finite field matrix over symbolic ring to matrix over finite field I have a bunch of ideals defined symbolically, that I would like t 
20210322 02:46:20 +0100  commented question  matrix over symbolic ring to matrix over finite field Edited. No selfcontained code. But enough detail I think to render the issue intelligible. 
20210322 02:45:33 +0100  edited question  matrix over symbolic ring to matrix over finite field matrix over symbolic ring to matrix over finite field I have a bunch of ideals defined symbolically, that I would like t 
20210316 04:53:18 +0100  asked a question  matrix over symbolic ring to matrix over finite field matrix over symbolic ring to matrix over finite field I have a bunch of ideals defined symbolically, that I would like t 
20201201 05:58:13 +0100  commented answer  another factoring polynomials question A very belated thank you! 
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20200129 18:27:50 +0100  asked a question  another factoring polynomials question I have the following expression: and I would like to simplify it by gathering and factoring partial sums (I have reason to expect that the expression will look quite a bit nicer if I do this, introducing notation for the sums of course, like h_{ij} = the sum of variables i up to j) My first lame try at this was to ask sage to rational_simplify() quotients f/(u+v+x+y+z),...,f/(u+v), and so on, hoping to see more than just one big fraction. It didn't work. Any insights/suggestions/corrections would be much appreciated! Thanks, 
20190316 05:19:25 +0100  commented answer  transformation matrix for variable matrix of given jordan type Thanks very much! 
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20190308 01:57:03 +0100  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

20190303 05:38:07 +0100  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 
20190303 05:38:07 +0100  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 19:29:32 +0100  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. 