More About Grobner Bases

The following is a general explanation, as to what I mean by the term "Grobner Bases," in my discussions about cohomology.:

Let's initially consider the following mathematical concept; while I will subsequently work to apply such a concept, to an improved explanation as to the general idea that I am trying to portray.:

Let us initially consider an overall value of "2021."  One is to achieve such a value, via a combination in the quantity of the values of three different types of variables.  One of such variables is worth the value of "4," another of such variables is worth the value of "13," while the other of such variables is worth the value of "17." Now; work to determine what combination in the quantity of the values of these three different types of variables, -- is to achieve the overall value of "2021." Since (4*6 + 13*66 + 17*67) = 2021, this respective situation may consequently be described of, via a Grobner Basis, as being of (6, 66, 67). This just mentioned idea; works to help describe the general numerical concept, behind the idea -- as to what "Grobner Bases" are.
Next, an explanation as to an application of the just illustrated concept -- to the idea of cohomology;  Let us say, one is to have an orbifold eigenset, -- that is here to be of a particular overall net quantum of energy.  This inferred cohesive set of discrete energy quanta, is here to be traveling via the Lagrangian-based path of a De Rham cohomology -- via a projected trajectory, that is here to be in relation to its theoretical holomorphic tendency of directional wave-tug. The herein mentioned cohesive set of discrete energy quanta, is to be of a Calabi-Yau organization of stringular-related phenomenology, that is to work to bear both a specific angular momentum vector/tensor wave-tug (potentially tensor-based, if one is to arbitrarily consider an ulterior-related Nijenhuis angling of the correlative discrete quantum of energy, in this particular situation), and a set of spin-orbital tensor-related wave-tug activity -- that is here to be of an overall net gauged-action.  Given the overall general behavior and energy of the said cohesive set of discrete energy quanta, one is then to work to determine the idea, -- as to what the delineation of the cohomology of such an inferred orbifold eigenset is consequently then to be.  Such a determination of the delineation of the cohomology, based upon the respective considered ulterior Ward-Cauchy-related conditions of the said eigenset, as you can now see, -- is geometrically tantamount to what the idea behind the "Grobner Bases" is thence to be.  I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.