I have a question like this:
Given a polynomial $f$, and a set $F = \{f_1, f_2\}$,
(for example, $f = x^2y + y^2$, and $f_1 = x^2, f_2 = y^2$)
using LEX, compute $\bar f^{(f_1,f_2)} = \_\_\_\_\_\_.$
Any idea what does $\bar f^{(f_1,f_2)}$ mean here?
Does it mean to do the polynomial division first, and then write $f$ in the form of $f = q_1*f_1 + q_2*f_2 + r$ where $r$ is the remainder?
Just found it in Chapter 2.6 of this book:
Ideals, Varieties, and Algorithms, Fourth Edition, 2015 (https://dacox.people.amherst.edu/iva.html)
It means the remainder of the division.