default(realprecision,38);
test(a,b)= if(a==b,oo, ceil(log(abs(a-b))/log(10)));
test(zetamult([2,1]), zeta(3))
test(zetamult([4,2]), (zeta(3)^2 - 4*zeta(6)/3))
test(zetamult([4,4]), (zeta(4)^2 - zeta(8))/2)
test(zetamult([2,2,2]), zeta(2)^3/6 + zeta(6)/3 - zeta(2)*zeta(4)/2)
zetamult("a")
zetamult(2)
zetamult([])
zetamult([1,2])

default(realprecision,57);
for(k=1,10, print(Pi^(4*k) / zetamult(vector(2*k, j, 1+2*(j%2)))));

v = [zeta(9),Pi^2*zeta(7),Pi^4*zeta(5),Pi^6*zeta(3)];
LD=[2,2,2,2];
{
  for(i=1,4,
    LE=LD; LE[i]=3;
    z = lindep(concat(zetamult(LE),v));
    if (z[1] < 0, z = -z); print(z);
  );
}
