General Jacobi identity revisited again - Grobner bases in differential geometry

Synthetic di¤erential geometry occupies a unique position in topos-theoreticphysics. Nevertheless it has appeared somewhat too conceptual to physicistsin general, partly because it has appeared to lack computational aspects. Itscomputational facets are really concerned with computation of the quasi-colimitof a nite diagram of innitesimal spaces, or equivalently, with computation ofthe limit of a nite diagram of Weil algebras. Indeed we have been forced todo a highly invovled computation of the above kind by hand in our previouspapers ([International Journal of Theoretical Physics, 36 (1997) , 1099-1131]and [International Journal of Theoretical Physics, 38 (1999) , 2163-2174]). Theprincipal objective in this paper is to show that Gröbner bases techniques pro-vide us with means that relegate such computations to computers