Dear Waldek,
many thanks for looking into this. Unfortunately, I'm an absolute beginner concerning factorization and number theory, as you probably noticed... Waldek Hebisch <[EMAIL PROTECTED]> writes: > Martin Rubey wrote: > > Dear all, > > > > regarding Issue #352 and possibly #351, I experimented a little. The > > starting > > point is the documentation of PFECAT, in catdef.spad: [...] > I think that this requres deeper investigation. Namely, gcd and > factorization is currently provided by different packages using somewhat > different method. We have to check which method is better and turn it on. > Also, it looks that in the meantime better algorithms appeared, so we may > prefer to implement them and forget abot old ones. Definitively. But, lacking somebody who knows about these things (or do you?), what can we do? For myself, it's also a matter of time. By the way, a collegue (Dietrich Burde, a number theorist) experimented a little with various packages like pari, maple, mathematica, reduce, etc., what algorithms they use for factoring integers. It turned out that pari is by far the most intelligent package. I believe we should interface to pari, therefore... > > diff -c > > /home/martin/lib/axiom/target/i686-pc-linux/src/algebra/gaussian.spad > > /home/martin/gaussian.spad > > *** /home/martin/lib/axiom/target/i686-pc-linux/src/algebra/gaussian.spad > > 2007-05-02 20:39:25.000000000 +0200 > > --- /home/martin/gaussian.spad 2007-05-03 09:30:12.000000000 +0200 > > *************** > > *** 91,96 **** > > --- 91,97 ---- > > ++ "failed" if x is not a rational number. > > if R has PolynomialFactorizationExplicit and R has EuclideanDomain > > then > > PolynomialFactorizationExplicit > > + if R has UniqueFactorizationDomain then UniqueFactorizationDomain > > ^^^^^^^^^^^^^^^^^^^^^^^^^ > > That looks like overgeneralization. First, Complex R may have zero > divisors (so we will hit bug 351). Even if Complex R is an integral > domain, it is not clear if it has unique factorization (do you know > about any theorem asserting this?). Finally, even if Complex R > has unique factorization AFAICS we do not have any factorization > algorithm working in Complex R. So I would just write: > > if R is Integer then UniqueFactorizationDomain > > which seem to agree with implementation. Yes. Maybe, IntegerNumberSystem, though. (I think we want to support factorization in Complex SingleInteger, too. Martin _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
