I've been trying to calculate a groebner basis, while storing the highest degree that was reached during the computation for a bunch of ideals, using Macaulay2.
I think I do understand how to get that done with the normal strategy (here I calculate a GB for some example ideal I found online):
However, the GB's I would like to calculate will have an expensive calculation, so I would like to use the most efficient algorithm available. I found the F4 GB algorithm, and used it on the same example ideal:
My main issue with this part is that it doesn't show 'S-pairs encountered up to degree 19' anymore. As far as I understand it, the output of gb is a Groebner basis computation object, whereas the output of groebnerBasis is just the generators.
Now I would like to ask you guys:
1: Could you please correct me if I was wrong about something?
2: Is there some way to use the F4 strategy and still get the information about the highest degree that was encountered?
3: More generally, are there efficient ways to calculate the GB, and find the highest degree that was encountered, which I might have missed?
Thank in advance for your help!