[GiNaC-list] normal() bug-or-feature

[Sheplyakov Alexei]

Hello!

On Thu, Nov 18, 2004 at 01:51:03PM +0100, Christian Bauer wrote:

> > 	symbol m1("m1");
> > 	symbol m2("m2");
> > 	symbol x("x");
> > 	ex e1 = pow(x,2)*pow(m1,2) - pow(x,2)*pow(m2,2);
> > 	ex e2 = pow(pow(x,2)*pow(m1,2)-pow(x,2)*pow(m2,2),100);
> > 	ex ca, cb, gc;
> > 	gc = gcd(e1, e2, &ca, &cb, false);
> > 	cout << c2 << endl;
> > 	// this won't be just x^198*(m1^2-m2^2)^99.
> > 	// (m1^2-m2^2)^99 gets expanded.
> > 	cout << (e1/e2).normal() << endl;
> > 	// won't print just x^(-198)*(m1^2-m2^2)^(-99), 
> > 	// (m1^2-m2^2)^99 gets expanded 

I'm sorry, there is a small error in my previous post, e1 should be

ex e1 = pow(x,2)*pow(m2,2) - pow(x,2)*pow(m1,2);

> I'm getting ca = 1,
> cb = (-m2^2*x^2+m1^2*x^2)^99,

I'm getting the same with e1 = x^2*m1^2 - x^2*m2^2.
But with e1 = x^2*m2^2 - x^2*m1^2 

ca = -1 
cb = x^198*[expanded (m1^2-m2^2)^99]

> and e1/e2 gets simplified to  (-m2^2*x^2+m1^2*x^2)^(-99) 
> by power::eval() even before normal() is invoked.

In ginsh:

$ test = (x^2*m2^2-x^2*m1^2)/(x^2*m1^2-x^2*m2^2)^100;
(-x^2*m1^2+x^2*m2^2)*(x^2*m1^2-x^2*m2^2)^(-100)
$ test2 = (x^2*m1^2-x^2*m2^2)/(x^2*m1^2-x^2*m2^2)^100;
(x^2*m1^2-x^2*m2^2)^(-99)

> Besides, gcd() already has heuristics for the cases b==a^n (or a==b^n).

Unfortunately, gcd() does not play well with a==e*something^n (e is
something simple, n >> 1), as my example demonstrates.


> Hm, which version of GiNaC are you using?

I use GiNaC 1.3.0 from CVS.


Thanks,
	Alexei.