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.
This explains where the symbol is coming from. However, by looking at
the code (just the six lines mentioned above!), I don't quite see what
happens. Perhaps someone with a better knowledge of symbolic rings
than mine do could have a quick look at this?
Kind regards,
Sebastian
On Nov 25, 11:20 am, Michel <michel.vandenbe...@uhasselt.be> wrote:
> ----------------------------------------------------------------------
> | Sage Version 4.2, Release Date: 2009-10-24 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: var("t a b c d e f")
> (t, a, b, c, d, e, f)
> sage: M=matrix(4,4,[[1-t,-a*t,-e*t,d*t],[a,1-t,-b,-f],[e,b*t,1-t,-c],
> [-d,f*t,c*t,1-t]])
> sage: M.determinant()
> -(((t - 1)*e + c*d)*b + (c*t*e - (t - 1)*d)*f - (c^2*t + (A0123456789
> + t - 1)^2)*a)*a*t - ((t - 1)*(c*t*e - (t - 1)*d) - (b*d*t + f*t*e)*b
> + (b*c*t^2 + (t - 1)*f*t)*a)*d*t + ((t - 1)*((t - 1)*e + c*d) + (b*d*t
> + f*t*e)*f + ((t - 1)*b*t - c*f*t)*a)*t*e + (t - 1)*((t - 1)*(c^2*t +
> (A0123456789 + t - 1)^2) + ((t - 1)*b*t - c*f*t)*b + (b*c*t^2 + (t - 1)
> *f*t)*f)
> sage: expand(_)
> -a*b*c*d*t^3 + a^2*c^2*t^2 + a*b*t^3*e - 2*a*c*f*t^2*e - a*d*f*t^3 +
> b^2*d^2*t^2 + b*c*f*t^3 + 2*b*d*f*t^2*e - c*d*t^3*e +
> A0123456789^2*a^2*t + 2*A0123456789*a^2*t^2 + a^2*t^3 - a*b*c*d*t -
> 2*a*b*t^2*e + 2*a*d*f*t^2 + b^2*t^3 - 2*b*c*f*t^2 + c^2*t^3 +
> 2*c*d*t^2*e + d^2*t^3 + f^2*t^3 + f^2*t^2*e^2 + A0123456789^2*t^2 -
> 2*A0123456789*a^2*t + 2*A0123456789*t^3 - 2*a^2*t^2 + a*b*t*e -
> a*d*f*t - 2*b^2*t^2 + b*c*f*t - 2*c^2*t^2 - c*d*t*e - 2*d^2*t^2 -
> 2*f^2*t^2 + t^4 + t^3*e^2 - 2*A0123456789^2*t - 6*A0123456789*t^2 +
> a^2*t + b^2*t + c^2*t + d^2*t + f^2*t - 2*t^2*e^2 + A0123456789^2 -
> 4*t^3 + 6*A0123456789*t + 6*t^2 + t*e^2 - 2*A0123456789 - 4*t + 1
>
> Where does the symbol A0123456789 come from?
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