-----------------------------------------Random Systems----------------------------------------------- 1) p1:=-5*x+8*x^2+5*z^2-x*y; p2:=-9*z+5*x^2+8*z^2+4*y*z-3*u^2; p3:=2*x+5*u-5*z+9*x*y-9*y^2; p4:=-9*z+5*x^2+7*x*u-8*y^2+3*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,y,z,u)| 124 | | ------------------------------------ 2) (good) p1:=-2+7*x*y+3*x*u-7*y^2; p2:=-9-4*y-u-2*z+z*x; p3:=4*x+4*u+6*z+6*x*y-8*z*x; p4:=3*u-8*x^2-5*z^2+4*u*z+9*z*x; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,z,y,u) | 2 | | ------------------------------------ ----------------------------------------------------- 3) p1:=-1-2*y*z+5*y*u-7*u*z-5*z*x; p2:=2*y+6*z-7*x^2+9*x*u+3*y*z; p3:=9*y+x^2+3*z^2+7*y*z-5*u*z; p4:=3*x-2*x^2-y*z-u^2-3*y^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,z,y,u) | 411 | | ------------------------------------ --------------------------------------------------- 4) p1:=8*x-5*x*u-5*u*z-4*z*x; p2:=-7*y-9*y*z-7*u^2-6*y^2+6*y*u; p3:=4+8*x-4*z-2*y^2-7*u*z; p4:=4*x^2-3*z^2+9*x*u-u^2+9*y^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,u,z,x) | 176 | | ------------------------------------ ----------------------------------------------------- 5) p1:=4*u+9*z^2-8*x*u-6*u^2+3*z*x; p2:=-x+3*z+9*y^2-7*y*u+8*z*x; p3:=9*y+8*y*z-6*u*z-9*z*x; p4:=-9*y-9*z+2*x^2-7*x*u-7*y^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,z,x,u)| 214 | | ------------------------------------ ----------------------------------------- 6) p1:=9+8*z^2-3*y*z+7*u^2+9*u*z; p2:=9*x+5*u+5*y^2-5*y*u; p3:=-5*x*y-8*y*z+7*u^2-6*y*u-7*u*z; p4:=-3*x+u-3*x^2-7*x*y; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (u,y,z,x)| 48 | | ------------------------------------ ---------------------------------------------- 7) p1:=5*x-8*z^2-6*x*u-2*y*z-9*y*u; p2:=9-9*y-u^2+4*y*u; p3:=-6*x+3*x^2-2*z^2+4*y^2+u*z; p4:=-9+5*x*y-u^2+4*y^2+2*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,z,u,x) | 24 | | ------------------------------------ ------------------------------------------------- 8) p1:=-5*x+8*x^2+5*z^2-x*y+1; p2:=-9*z+5*x^2+8*z^2+4*y*z-3*u^2; p3:=2*x+5*u-5*z+9*x*y-9*y^2; p4:=-9*z+5*x^2+7*x*u-8*y^2+3*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,y,z,u)| 65 | | ------------------------------------ ------------------------------------------------- 9) p1:=-5*z+6*z^2+y^2-7*z*x; p2:=-7*y-2*z^2-7*x*u+8*u^2+5*z*u; p3:=x+9*z+5*y*z+u^2+3*z*u; p4:=-2*z^2-7*x*y-y*z-2*u^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (z,u,y,x) | 70 | | ------------------------------------ ------------------------------------- 10) p1:=4*x-8*x^2+8*z^2+7*x*y+9*y^2; p2:=8*y-9*z-4*x*y-6*y*z-9*y^2; p3:=-7*x-z-3*y*z-9*y^2-8*z*x; p4:=-2*x^2-6*x*y-2*x*u+6*u^2+y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,x,z,u)| 2 | | ------------------------------------ --------------------------------------- 11) p1:=-8*y-5*u+4*x^2+9*z*x+5*z*u; p2:=-1-2*y*z+5*y*u-7*z*x-5*z*u; p3:=2*y+6*z-7*x^2+9*x*u+3*y*z; p4:=9*y+x^2+3*z^2+7*y*z-5*z*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,z,y,u)| 24 | | ------------------------------------ --------------------------------------- 12) p1:= x+5*u-3*x*u+9*y^2+7*z*u; p2:=8*y-9*x^2+6*x*y-2*y*z+9*u^2; p3:=6+7*z-x^2+9*y^2-2*y*u; p4:=9*x+5*z^2-5*u^2-z*x; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,y,u,z) | 1346 | | | ------------------------------------ ------------------------------------------- 13) p1:=-5*x+8*x^2+5*z^2-x*y^2; p2:=-9*z+5*x^2+8*z^2+4*y*z-3*u^2; p3:=2*x+5*u-5*z+9*x*y-9*y^2; p4:=-9*z+5*x^2+7*x*u-8*y^2+3*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,y,z,u)| 72 | | ------------------------------------ ------------------------------------------ 14) p1:=5*x+u+3*z+4*y*z; p2:=-z^2-2*x*u+3*y*z+u^2; p3:=-5*x*u-4*u^2+y^2-u*z; p4:=-2*x+y+7*z^2+x*y-7*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (u,z,y,x)| 14 | | ------------------------------------ -------------------------------------------- 15) p1:=-4+8*y+9*z-7*x^2-y^2; p2:=-9*z+2*x^2+9*z^2-5*x*u-2*y^2; p3:=-6*y+8*u-9*z+9*u^2-3*z*x; p4:=7*x+3*y-7*x*u-6*y^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,x,z,u) | 48 | | ------------------------------------ -------------------------------------------- 16) p1:=5+2*x-y-6*u+4*y*u; p2:=7*u-9*z^2+5*x*y-4*x*u+7*y^2; p3:=6+7*y+3*x^2+4*y*z-9*y*u; p4:=-5*x+8*z+3*z^2-y*z+7*u^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (z,y,u,x)| 49 | | ------------------------------------ -------------------------------------------- 17) p1:=-9*y+9*z+x^2+3*z^2+7*y*z; p2:=2*x+3*x^2-2*y*z-y^2-z*x; p3:=6*y+5*y*z-y*u+2*u*z-5*z*x; p4:=4*x+u+5*y*z-3*y^2+9*u*z; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,x,z,u)| 15 | | ------------------------------------ ------------------------------------ 18) p1:=2+6*y+3*x^2-7*z^2+6*x*y; p2:=3+9*z-3*z^2+6*y*u+9*u*z; p3:=x-9*z-9*x^2-9*x*u+8*y*z; p4:=7+9*x-4*y-8*y*z+9*u*z; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (z,x,y,u)| 12 | | ------------------------------------ ----------------------------------------- 19) p1:=-5*x+8*x^2+5*z^2-x*y; p2:=-9*z+5*x^2+8*z^2+4*y*z-3*u^2; p3:=2*x+5*u-5*z^2+9*x*y-9*y^2; p4:=-9*z+5*x^2+7*x*u-8*y^2+3*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,z,y,u) | 150 | | ------------------------------------ --------------------------------------- 20) (good) p1:=-5*z+6*z^2+y^2-7*z*x; p2:=-7*y-2*z^2-7*x*u+8*u^2+5*z*u; p3:=x+9*z+5*y*z+u^2+3*z*u; p4:=-2*z^2-7*x*y-y*z-2*u^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (z,u,y,x) | 69 | | ----------------------------------- -------------------------------- 21) p1:=7+9*x+4*x*y+6*x*u-3*y*z; p2:=-6*y-9*x^2-6*x*y-9*x*u-4*y^2; p3:=-8*z+9*x^2-4*z^2+y*z-9*z*x; p4:=-2*u+6*x*y+u^2+4*y*u-6*z*x; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,y,z,u) | 83 | | ----------------------------------- ----------------------------- 22) p1:=2*x-y-6*u+4*z+4*y*u; p2:=5*u-4*z^2+7*x*y+3*y^2-8*z*u; p3:=-9+2*x^2-y*u-2*z*x+5*z*u; p4:=-5*y+6*u-4*z+5*x^2+2*y*z; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,z,y,u) | 71 | | ----------------------------------- ------------------------------- 23) p1:=-1-3*y*z-u^2+y^2-5*z*x; p2:=5*x*y-y*z+2*y*u-5*z*x-7*z*u; p3:=4*x+u+5*y*z-3*y^2+9*z*u; p4:=8*y-9*x^2+6*x*y-2*y*z+9*u^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,u,x,z) | 190 | | ------------------------------------ 24) p1:=-7*x+4*y-6*u+6*z+9*z*u; p2:=-2*x+5*z+4*x*u-8*y*z+3*y*u; p3:=u+6*u^2-z*x+2*z*u; p4:=3+2*y+x^2+5*z^2-3*z*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (z,u,x,y) | 5 (0.3)| 0 | ----------------------------------- ------------------------------- 25) p1:=-8*x^2-6*x*u-9*u^2+4*y^2; p2:=-7*y+3*z+7*u^2-8*y^2-3*y*u; p3:=-9+8*x+3*y-7*y^2-7*y*u; p4:=3+7*u-3*z-3*x*y-9*y*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,u,x,z) | 1 | | ------------------------------------ --------------------------------- 26) p1:=9*z-2*x*u-y^2+4*y*u+5*z*u; p2:=8+7*x-4*x*y-5*z*x; p3:=-3-8*y*z-3*u^2+3*z*x-5*z*u; p4:=9*z-8*y^2+2*z*x+3*z*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,u,z,x)| 39 | | ------------------------------------ -------------------------------- 27) p1:=9*x-u-2*x^2+2*x*u-4*z*u; p2:=3*z+8*z^2-3*x*u+y^2-5*z*u; p3:=2+9*u+6*x^2+4*y*u+6*z*x; p4:=4*u+9*z^2-8*x*u-6*u^2+3*z*x; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (x,z,u,y) | 61 | | ----------------------------------- ----------------------------------- 28) p1:=-9*x-4*z^2-8*x*y+8*x*u-6*z*x; p2:=-7*x+7*z+4*x^2-6*y*z-4*y*u; p3:=1-9*y*z-6*y^2-2*z*x+3*z*u; p4:=2-6*x*u-7*y^2-9*y*u-3*z*u; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (y,x,z,u) | 188 | | ----------------------------------- ----------------------------------- 29) p1:=9*x^2+6*z^2+7*x*y-3*u^2+8*z*x; p2:=-3+x-8*u+7*x^2+4*u^2; p3:=-5+2*x+6*y+z-3*y*z; p4:=-5*u-6*z^2+8*u^2+3*z*x; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (u,x,z,y)| 10 | | ----------------------------------- ------------------------------------- 30) p1:=-9+3*z+6*x^2+5*y*z+7*z*u; p2:=-7*z-8*y*z-7*u^2+9*z*u; p3:=-2*u+6*x*y+u^2+6*z*x-6*z*u; p4:=6*x-8*u+4*z+8*x*y+2*y^2; ------------------------------------ Order | MT(gs) | MT(gb) | ------------------------------------ (u,y,x,z) | 99 | | ------------------------------------