On Friday 17 April 2009, Stavros Macrakis wrote:
> I am not aware of a function called poly_discriminant in Maxima or for
> that matter a function by some other name that calculates polynomial
> discriminants? That said, the formulae are straightforward and you
> can easily write it yourself, something like
I can clearly see this function at the beginning of the file
/opt/maxima/share/maxima/5.15.0/src/result.lisp
simply use grep ;-)
Andre
>
> disc3(p,var) := /* cubic case only -- no input validation */
> block( [a,b,c,d],
> p: rat(p,var),
> a: ratcoef(p,var,3),
> b: ratcoef(p,var,2),
> c: ratcoef(p,var,1),
> d: ratcoef(p,var,0),
> b^2*c^2 -4*a*c^3 -4*b^3*d -27*a^2*d^2 +18*a*b*c*d )$
>
> -s
>
> On Fri, Apr 17, 2009 at 11:25 AM, andre maute <andre.maute at gmx.de> wrote:
> > On Friday 17 April 2009, Stavros Macrakis wrote:
> >> In this cubic, all three roots are real, but cannot be expressed with
> >> real radicals, even in principle. See
> >> http://en.wikipedia.org/wiki/Casus_irreducibilis . ?They *can* be
> >> expressed as real expressions involving trigonometric functions, which
> >> is what rectform does for you.
> >>
> >> That said, I wonder why you want the roots expressed as symbolic
> >> expressions. ?I suppose there must be some application where
> >> (8*cos(atan(sqrt(2101)/(69*sqrt(3)))/3)-sqrt(3))/sqrt(3) is more
> >> useful than 3.584428340330492, but usually the latter is what you
> >> really want, in which case why not calculate it directly using
> >> realroots or allroots (which, unlike solve, work for *all*
> >> polynomials, not just those which reduce to the quartic case or
> >> simpler by factorization or polynomial decomposition).
> >
> > I still use Maxima 5.15.0,
> > and I cannot find poly_discriminant in the html documentation
> > poly_discriminant is nice to detect the casus irreducibilis
> >
> > Andre
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