Timings below are for the following four sets of test problems. The timings were obtained by running evala(Gcd(f,h)) in rmaple (Maple 11) on the 64 bit machine called "maple" in the CECM. This is Sun wz2100 with an AMD 248 Opteron CPU running at 2.2 GHz. Test 1: m = z^2-s*z-3 DENSE Q(s,alpha(s))[x,y] file: multivar.tst7 for n from 1 to 10 do a,b,g = randpoly([x,y,s,alpha],dense,degree=n) f,h = a*g, b*g; Test 2: m = z^2-s*z-3 DENSE Q(s,alpha(s))[x,y] file: multivar.tst8 for n from 0 to 10 do g = randpoly([x,y,s,alpha],dense,degree=n); a,b = randpoly([x,y,s,alpha],dense,degree=10-n); f,h = a*g, b*g; Test 4: m := z^3-s*z^2-t^2*z-3*u-5; Q(alpha(s,t,u))[x,y,z] file multivar.semis r = rand(1..99); for n from 1 to 10 do g = s*x^n+t*y^n+u*z^n + add( add( r()*alpha^(j-1)*X[j]^i, i=0..n-1 ), j=1..3 ) + add( add( r()*w^j, j=0..n ), w=[s,t,u] ); a = t*x^n+u*t*y^n+s*z^n + add( add( r()*alpha^(j-1)*X[j]^i, i=0..n-1 ), j=1..3 ) + add( add( r()*w^j, j=0..n ), w=[s,t,u] ); b = u*x^n+s*y^n+t*z^n + add( add( r()*alpha^(j-1)*X[j]^i, i=0..n-1 ), j=1..3 ) + add( add( r()*w^j, j=0..n ), w=[s,t,u] ); f,h = a*g, b*g; Test 5: m := z^3-s*z^2-t^2*z-3*u-5; Q(alpha(s,t,u))[x,y,z] file multivar.semis2 r = rand(1..99); for n from 0 to 10 do m := 10-n; g = add( add(r()*w^i,i=0..n), w=X ) + add( add(r()*w^j,j=0..n), w=T ) + add(r()*alpha^j,j=0..2); a, b = add( add(r()*w^i,i=0..m), w=X ) + add( add(r()*w^j,j=0..m), w=T ) + add(r()*alpha^j,j=0..2); f,h = a*g, b*g; Q(alpha(s))[x,y] Q(alpha(s,t,u))[x,y,z] DENSE SPARSE n 1 mod 1 div 1 sub 2 mod 2 sub 4 mod 4 sub 5 mod 5 sub 0 - - - 0.368 - - - 0.154 - 1 0.034 0.004 0.044 0.434 - 0.50 0.503 1.252 - 2 0.063 0.020 0.387 0.445 - 2.30 288.1 4.073 - 3 0.135 0.058 2.770 0.398 - 8.31 >2,000 10.73 - 4 0.282 0.148 29.55 0.509 - 24.57 - 23.80 - 5 0.745 0.310 444.5 0.541 >1000 63.41 - 46.68 - 6 0.965 0.558 >1000 0.808 371.0 149.3 - 85.88 - 7 2.022 0.995 - 0.900 57.81 324.3 - 144.7 >19,000 8 3.178 1.650 - 0.966 10.59 652.0 - 223.1 81.24 9 4.929 2.647 - 1.051 1.443 1493. - 319.6 8.437 10 7.494 4.227 - 0.189 0.220 2749. - 0.129 0.129