Initial ideal computation very slow for zero weight in 1.6.0 #5639
Description
In OSCAR 1.6.0 for I = grassmann_pluecker_ideal(3, 7), I get
julia> @time (for _ in 1:100
initial(I, tropical_semiring_map(QQ), rand(0:1, 35))
end);
79.891922 seconds (264.83 M allocations: 8.545 GiB, 2.14% gc time)
for a 100 random weights, but
julia> @time initial(I, tropical_semiring_map(QQ), [0 for _ in 1:35]);
820.467393 seconds (19.99 M allocations: 442.009 MiB, 0.02% gc time, 0.00% compilation time)
for the zero weight.
While this is particularly prominent for Plücker ideals, for, say, random toric ideals there is also a noticeable difference between zero and random weights (about one-two orders of magnitude). And, most importantly, this seems to have gotten much worse since version 1.5.0, where
julia> @time initial(I, tropical_semiring_map(QQ), [0 for _ in 1:35]);
15.455510 seconds (120.76 k allocations: 6.133 MiB, 0.10% compilation time)
while the average time for random weights was roughly the same.