Sebastian Pancratz wrote :
> The problem is here:
>
>     
> http://trac.sagemath.org/sage_trac/attachment/ticket/6441/trac_6441_b_df_charpoly_412rebase.patch
>     new lines 1084--1089
>
> When I wrote the code for computing characteristic polynomials in a
> division-free way in order for it to work over more general base
> rings, it turned out that the computation of determinants via the
> characteristic polynomial was a *lot* faster than the previous code.
> Unfortunately, it seemed that in order to call the polynomial code,
> one needed to supply a variable.  In most cases this isn't a problem,
> but in symbolic rings it might.  I was hoping to get around this by
> simple choosing "A0123456789" as a new variable.
>   
It's your work, I do nothing, and I'll use it !

So I admire your work and don't criticize it.
 
A variable name "inner_variable_in_minpoly" may be nicer :
 
the name A0123456789 has no human sense, but "inner_variable...." 
explains were we can find this variable if a bug occures.

It seems this variable is global and can't be a local symbolic variable. 
So the choice of its name feels important.

F.

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