Re: [Mathlib-develop] Re: Symbolic calculations

[mark <msp...@ya...>]

On Saturday 15 Feb 2003 10:04 pm, Alejandro Torras wrote:
> Hi Mark and Stefan!!
>
> > > Actually I meant finding factors of polynomials
> > > i.e. x^2 + 2*x + 1 =3D> (x+1)^2
> > >
> > > Though I'll check the link out since the the current implementation=
 of
> > > numerical factorization is pretty slow.
> >
> > Sorry, I've no clue at all. I've never done anything with symbolic
> > stuff.
>
> Me too, but I think we can give us hints to a proper sollution, as we h=
ave
> done before ;-)
>
> Finding the roots of polynomials, I have read something about the
> Tartaglia's triangle, Pascal's or Newton's one, but I don't remeber now=
=2E
>
> You can see a plenty tutorial about it at
> http://www.krysstal.com/binomial.html
>
> But this works only for binomial power of expressions like (x + y)^z wh=
ere
> x,y are integers and z is a natural number.
>
> If we want general root finding, including complex roots, we should sea=
rch
> a bit more.
>
> Regards,
> Alejandro.
>

Well I'm not sure that we need to worry about complex roots to begin with=
 but=20
it does need to be more general than just binomial expansions. Things lik=
e

x^3 + 6x^2 + 11x + 6 =3D (x+1)(x+2)(x+3)

I wasn't able to find anything on google but there is a section on it in=20
volume 2 of The Art Of  Computer Programming. I'll read through that toda=
y.

Best Regards

Mark