C Y wrote: > --- Gabriel Dos Reis <[EMAIL PROTECTED]> wrote: > > (1) As a law, useful software evolve; otherwise they die. > > Certainly. If actual new ideas appear, they should be incorporated. I > would hope that these would be in areas like new mathematics, new > output formats, new graphics backends, etc - i.e. changes not involving > the core of the system. >
A little example: integrate(simplify(D((((((2-(a+log(1)))+sqrt(x)/exp(1))/((exp(x)-sqrt(log(x)-x)-(1-log(exp(sqrt(a)))))+2*(log(x)+1)))+(x))+2)+sqrt(x+2), x)), x) if you wait long enough (IIRC about 1 hour on my machine), it will run out of memory. Checking why shows that Axiom is unable to compute GCD of two polynomials. The polynomials when printed are few kilobytes in size and of relativly low degree (11 in main variable, 40 in an auxilary one) but involve algbraic quantities (square roots). Axiom uses Lazard version on polynomial remainder sequence algorithm, which IIUC was considered state of the art around 95. But today we know about modular algorithm for problem -- my understanding is that modular algorithm is supposed to compute this GCD in few seconds (possible even in fraction of second). So while old algorithm remains correct, a superior one may be invented and replace the old. There is an extra twist to this: I suspect that polynomials in question are relatively prime. With high probability a simple modular method will discover this. But there is a question how to hook modular method so that it gets used. I belive that the polynomials have type 'UP(Expression Integer)' and you need some extra work to determine if modular method is applicable. In short: new algorithms are discovered and to use new algorithm you may be forced to change parts of the system which at first glance have nothing to do with new code. -- Waldek Hebisch [EMAIL PROTECTED] _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer