Grobner Bases Versus Grobner Basis

 One may often consider what can be construed of, as to what the necessary differential geometrical configuration of those cohomology-related eigenstates, that work to comprise the overall cohomology of a given arbitrary superstring of discrete energy permittivity -- in order for this inferred string to behave in a proscribed respective given arbitrary manner -- as a geometric Grobner Basis, -- to where the resultant needed differential configuration of the cohomology-related eigenstates, that are here to be of the individually taken superstrings of discrete energy permittivity, that are here to come together, in so as to appertain to the integrable net sum whole of all of those composite superstrings, that are to work to be comprising the self-same directly corresponding cohesive set of discrete energy quanta, to where this will tend to consequently be appertaining, to what may be thought of, as being a geometric Grobner Bases. However; if one is here to consider, quite simply, just the net overall necessary geometrical configuration of those cohomology-related eigenstates, that is necessary, in order for the given arbitrary respective cohesive set of discrete energy quanta, to behave in the earlier inferred proscribed manner, then, one may often construe such a consequently proscribed delineation of eigenstates, as taken along the topological surface of the external shell of such a said cohesive set of discrete energy quanta, to tend to be deemed of as being a geometric genus of a Grobner Basis. A geometric Grobner Basis (Bases), has more to do with determining a means of how cohomology-related eigenstates are to be delineated, in so as to be able to be fitted-into a space -- to where a set of discrete energy quanta may be able to function as it is needed to; whereas, a Cox Ring has more to do with determining the mapped-out chain, that is appertaining to the delineation of the cohomology-related eigenstates, that are of a set of discrete energy quanta. To Be Continued! Sincerely,, SAM ROACH.