Date: Mon, 10 Jul 2000 16:07:18 +0200
From: John Abbott
Subject: challenge multivariate factorization (in F_5) info

Hi Paul,

Here is some information pertaining to the factorization of the
multivariate challenge polynomial:

Person who ran the computation:  Bill Naylor (University of Bath)
Machine which did it:            150MHz pentium running Linux 2.0
Software which did it:           Axiom Computer Algebra System (Release 2.1)

There are two factors: F1 and F2 with degrees as follows,
  deg_x(F1) = 15       deg_x(F2) = 20
  deg_y(F1) =  5       deg_y(F2) = 10
  deg_z(F1) =  5       deg_z(F2) =  5

F1 has 21 terms, and F2 has 30.

The factors are:
z^5+
z^3*(x^3*y^2+2*x^5*y+3*x^7)+
z^2*(x^4*y^2+4*x^6*y+x^8)+
z*(3*x^4*y^5+2*x^6*y^4+4*x^8*y^3+(3*x^10+2*x^5)*y^2+(x^12+2*x^7)*y+x^14+4*x^9)+
2*x^5*y^5+3*x^6*y^2+4*x^8*y+x^15+2*x^5

z^5*x^5+
z^3*(3*x^4*y^4+3*x^6*y^3+x^8*y^2+4*x^12)+
z^2*(3*x^5*y^4+4*x^7*y^3+4*x^9*y^2+3*x^11*y)+
z*(2*x*y^9+2*x^3*y^8+2*x^5*y^7+2*x^7*y^6+2*x^9*y^5+2*x^11*y^4+
   (2*x^13+3*x^8)*y^3+y^2*(2*x^15+4*x^10)+y*(2*x^17+4*x^12)+2*x^19+3*x^14)+
3*y^10+2*x^5*y^5+4*x^7*y^4+x^11*y^2+3*x^13*y+2*x^20+4*x^10


John.