Singular's factorize command is immensely slow at times, but other times it is decent. I'd not report this as a bug except for the fact that it appears that some tuning of something might fix this.
Run this in singular (binary 3-0-4 from upstream as well):
ring R=0,(p10,g0,g1,g2,g3,g4,X1,X2),dp;
poly t=-p10^170*X1^10*X2^10+p10^130*X1^10*X2^5+p10^130*X1^5*X2^10-p10^90*X1^5*X2^5+p10^80*X1^5*X2^5-p10^40*X1^5-p10^40*X2^5+1;
factorize(t);
Repeat the factorize command a couple of times. You'll get extreme fluctation on the amount of time required to factor (nearly instantaneous all the way out to 5-10 minutes!).
Obviously, sage demonstrates the same bizarre timing statistics:
sage: R.<p10,g0,g1,g2,g3,g4,X1,X2>=QQ[]
sage: t=-p10^170*X1^10*X2^10+p10^130*X1^10*X2^5+p10^130*X1^5*X2^10-p10^90*X1^5*X2^5+p10^80*X1^5*X2^5-p10^40*X1^5-p10^40*X2^5+1
sage: time _=t.factor()
CPU times: user 25.63 s, sys: 0.02 s, total: 25.65 s
Wall time: 26.18
sage: time _=t.factor()
CPU times: user 5.95 s, sys: 0.00 s, total: 5.95 s
Wall time: 5.95
sage: time _=t.factor()
CPU times: user 310.76 s, sys: 0.21 s, total: 310.97 s
Wall time: 311.65
I've reported this to the upstream forum as well (with no response so far):
http://singular.mathematik.uni-kl.de/forum/viewtopic.php?t=1652
I also just now submitted the bug through the singular bug request form.
