CoCoA » CoCoA-5

Here is an example which shows that RationalSolve can be unreasonably slow:

use P ::= ZZ/(32003)[x,y,z];
use P ::= QQ[x,y,z];

X := indets(P);
S := support((1+sum(X))^3);  --> deg = 3
define rndpoly(S)
  return sum([random(-9,9)*t | t in S]);
enddefine; -- rndpoly

L := [rndpoly(S) | i in 1..3];
I := ideal(L);
//SetVerbosityLevel(100);

println "=======================================================";
println "ReducedGBasis";
println "=======================================================";
t0 := CpuTime();
RGB := ReducedGBasis(I);
println "RGB TIME ", TimeFrom(t0); println; println;

J := ideal(L);
println "=======================================================";
println "MinPolyQuot";
println "=======================================================";
t0 := CpuTime();
mu := MinPolyQuot(x,J,x);
println "MPQ TIME ", TimeFrom(t0); println; println;

println "=======================================================";
println "ApproxSolve";
println "=======================================================";
t0:=CpuTime();
solns:=ApproxSolve(L);
println "ApproxSolve TIME ", TimeFrom(t0); println; println;

println "=======================================================";
println "RationalSolve";
println "=======================================================";
t0 := CpuTime();
RationalSolve(L);
println "RatSolve TIME ", TimeFrom(t0); println; println;

On my computer, typical timings are about RGB 0.04, MPQ 0.08, ApproxSolve 1.0, RatSolve 2.1.
Increasing deg to 4 makes RationalSolve unreasonably slow: RGB 0.06, MPQ 1.2, ApproxSolve 22, RatSolve 2250

I have just tried the example from comment 5, and RationalSolve is now tolerably fast (less than 2s).

tested on Mac, ~0.1s