Here's a pure python implementation of an algorithm to factor polynomials over ZZ using kronecker's trick (specializing a variable to a large prime reduces you to a poly of fewer variables). Note that this also fills in an implementation of factoring over ZZ[x,y] --- we don't have any implementation at all for this currently. It's also faster than singular (over QQ) for some cases.
Here's an example with my favorite trouble-maker for singular.
this patch:
sage: R.<p10,g0,g1,g2,g3,g4,X1,X2>=ZZ[]
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 0.11 s, sys: 0.00 s, total: 0.12 s
Wall time: 0.12
(-1) * (p10^8*X2 - 1) * (p10^8*X1 - 1) * (p10^18*X1*X2 - 1) * (p10^32*X2^4 + p10^24*X2^3 + p10^16*X2^2 + p10^8*X2 + 1) * (p10^32*X1^4 + p10^24*X1^3 + p10^16*X1^2 + p10^8*X1 + 1) * (p10^72*X1^4*X2^4 + p10^54*X1^3*X2^3 + p10^36*X1^2*X2^2 + p10^18*X1*X2 + 1)
singular:
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: <longer than I wanted to wait>
