I tried downloading form3.0, and I find it mysterious. Maybe I am not using it correctly. My first version took 101.23 seconds. I repeated it and it took 97 seconds
This is what I did:
C:\form>form sample3.frm form sample3.frm FORM by J.Vermaseren,version 3.0(Jan 28 2001) Run at: Thu Mar 28 10:26:41 2002 Symbols x,y,z; Local q=(1+x+y+z)^20; Local q1=q+1; Local res=q*q1; .end ..... This changed program however took only 0.98 second:
C:\form>form sample7.frm form sample7.frm FORM by J.Vermaseren,version 3.0(Jan 28 2001) Run at: Thu Mar 28 10:50:53 2002 Symbols x,y,z; Local q2=(1+x+y+z)^20*(1+(1+x+y+z)^20); .end
Time = 1.04 sec Generated terms = 14112
q2 Terms in output = 12341
Bytes used = 305378
The reason might be that the first power is expanded as (1+x+y+z)*(1+x+y+z)*...*(1+(1+x+y+z)*...*(1+x+y+z)) which will expand much faster than making the product of 1+x+y+z expanded. This would be the same reason why it is never a good idea to use the chinese powering algorithm for expansion of power of multivariate polynomials.