On Nov 25, 8:20 pm, 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?
This looks like an after-effect of ticket #6441. Sebastian Pancratz
wrote some very fast code to compute determinants over general
commutative rings, which proceeds by computing the characteristic
polynomial first. When doing this for symbolic matrices it needs to
choose a variable name that won't conflict with anything, so it uses
"A0123456789". This shouldn't leak out into the output, but it looks
like it has done here.
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