Sorry to jump in late; I just found this discussion by googling
something else..
Maxima was berated for being too slow in factoring this..
-p10^170*X1^10*X2^10+p10^130*X1^5*X2^10+p10^130*X1^10*X2^5-
p10^90*X1^5*X2^5+p10^80*X1^5*X2^5-p10^40*X2^5-p10^40*X1^5+1
which apparently did not terminate after more than 15 minutes.
After observing that the polynomial is actually a polynomial in x1,
x2, and x3=p10^10, I made that substitution and tried factoring.
Maxima 5.14.0 factored it into 3 factors in 0.8 seconds on my 3GHz
pentium.
The remaining decomposition, factoring these factors further with
p10^10 restored, took 18 seconds more.
Factoring the polynomial as given, took 600 seconds.
Whether the observation of slowness was caused by CLISP rather than
GCL, or hardware differences or ....
a bad algorithm, easily improved, it is hard to say.
If Maxima's factoring program is too slow, it could always call some
other program. Maybe it should be set up to call SAGE? That way the
programmer would have the advantage of all the interactivity of
Maxima, error messages, debugging, graphical front end, as well as
programming Maxima language and lisp, which are compilable languages.
I also noticed a discussion of multivariate GCD heuristics and
simulated annealing. If you think that you can characterize the
domain of GCD inputs in such a way as to cluster inputs that are best
done by a particular algorithm, lots of luck. The choice of the best
GCD algorithm seems to depend most heavily on the ANSWER, not the
input. That is, if the GCD result is 1, you have one choice. If the
GCD(p,q) is p, you have another.
Regards
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