Profesor Avinash Sathaye pointed out to me an apparent problem with the factor command in release 5 which was at least formally not there in earlier releases. He was calculating with 5.1 on an NT system.
The command Factor (factor mod a prime) is broken! It used to work in old versions.
Try the following commands:
> f:=x^5-3; g:=(z-x)^4-5; r:=resultant(f,g,x);
Maple produces the strange results as shown:
5 f := x - 3 4 g := (z - x) - 5 20 16 15 12 11 10 8 r := z - 25 z - 12 z + 250 z - 3900 z + 54 z - 1250 z 7 6 5 4 3 - 46500 z - 15300 z - 108 z + 3125 z - 52500 z 2 + 24750 z - 2700 z - 3044 > factor(r); 20 16 15 12 11 10 8 z - 25 z - 12 z + 250 z - 3900 z + 54 z - 1250 z 7 6 5 4 3 - 46500 z - 15300 z - 108 z + 3125 z - 52500 z 2 + 24750 z - 2700 z - 3044 > Factor(r) mod 241; 20 16 15 12 11 10 8 7 z + 216 z + 229 z + 9 z + 197 z + 54 z + 196 z + 13 z 6 5 4 3 2 + 124 z + 133 z + 233 z + 38 z + 168 z + 192 z + 89 > Irreduc(r) mod 241; false > sol:=Berlekamp(r,z) mod 241; 10 8 6 5 4 3 2 sol := {z + 208 z + 50 z + 235 z + 152 z + 86 z + 125 z 10 8 6 5 4 3 + 91 z + 85, z + 33 z + 50 z + 235 z + 89 z + 155 z 2 + 125 z + 91 z + 174} > expand(sol[1]*sol[2]-r) mod 241;
0 It is corrected with Maple 6. (U. Klein)