Interesting Stuff As To Grobner Bases

Let's consider what is meant to be determined as a Grobner Basis:

Let's say that one is to have a point particle.  It is theoretically to be of zero spatial dimensions.  Consequently; its surrounding spatial dimensionality, is theoretically here to be "infinite" in its number of spatial dimensions.  Next; one may take certain basic differential geometrical-related mathematical stipulations, about the dimensional relationships of certain spaces, that are here to be related to both the existence and the motion of such a theoretical point particle, both as to what may potentially be an element of what, what may be in union to what, what may intersect what, etc., -- based upon the basic mathematical operations of addition, division, multiplication, and subtraction.  Consequently; one may then work to determine an eigenbasis, that is here to work upon a given arbitrary space, in a Laplacian-related manner -- that is here to work to involve a stipulation, that involves the relationship of one point particle To a stipulation that involves the relationship of another point particle, -- to where the relationship that is here to work to involve the two inferred point particles, is then to be of either a Real Riemann Gaussian-related association, or of a Li-based Gaussian-related association.  Such a general tense of an eigenbasis, may then be utilized, to work to determine as to what actual point-like spaces are more likely to be relatively adjacent to other actual point-like spaces, -- given how such point-like spaces are here to be acting, over time. Such a general tense of an eigenbasis, may be thought of as a Grobner Basis.  Sincerely, Samuel David Roach.