Show the polynomials in the Groebner Basis as they are found
This is more a question about singular, since that is what Sage uses to computer the Groebner Basis. In Singular, you can use option(prot) and then, upon using the groebner function of your choice, you will see verbose output. From the Singular manual, we are told that when "s" is printed in the verbose output, a new element of the standard basis has been found. It is sometimes enough, and in particular very useful for my needs, to know that a certain polynomial is in the groebner basis.
I am working with an overdetermined system of polynomials for which the full groebner basis is too difficult to compute, however it would be valuable for me to be able to print out the groebner basis elements as they are found so that I may know if a particular polynomial is in the groebner basis. Is there any way to do this?
My question is above, but more details specifically related to my problem are below, which may be useful in providing an alternate answer.
The problem is as follows: I have a system of (not necessarily homogeneous) multivariate polynomials $f_1(x_1,\dots,x_n)=0,\dots f_m(x_1,\dots,x_n)=0$. I would like to prove that a few of the $x_i$ must be equal to zero. I was able to uncomment lines 240, 241, and 242 in this toy implementation library of Faugere's f5 algorithm for Singular and remove the "lead" function around the to-be-printed output on line 241. After just a couple of seconds while running this command, $x_7^5$ was printed out as a member of the basis.
This would seem to imply that $x_7$ must equal zero. The toy library is useful in this regard, since it was able to be modified to print out the members of the basis as they were discovered, however it is still a toy implementation and is not as efficient as slimgb, for instance. My question is, how can I get this same behavior from slimgb?