caa a22 4500 463197623 CHVBK 20180406164927.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s10773-007-9397-z doi (NATIONALLICENCE)springer-10.1007/s10773-007-9397-z General Jacobi Identity Revisited Again [Elektronische Daten] Gröbner Bases in Differential Geometry [Hirokazu Nishimura, Takeshi Osoekawa] Synthetic differential geometry occupies a unique position in topos-theoretic physics. Nevertheless it has appeared somewhat too conceptual to physicists in general, partly because it has appeared to lack computational aspects. Its computational facets are really concerned with computation of the quasi-colimit of a finite diagram of infinitesimal spaces, or equivalently, with computation of the limit of a finite diagram of Weil algebras. Indeed we have been forced to do a highly involved computation of the above kind by hand in our previous papers (Nishimura, H. in Int. J. Theor. Phys. 36:1099-1131, 1997 and Nishimura, H. in Int. J. Theor. Phys. 38:2163-2174, 1999). The principal objective in this paper is to show that Grö bner bases techniques provide us with means that relegate such computations to computers. Springer Science+Business Media, LLC, 2007 Weil algebra nationallicence Limit nationallicence Equalizer nationallicence Gröbner basis nationallicence Elimination theory nationallicence Synthetic differential geometry nationallicence Zero-dimensional ideal nationallicence Topos-theoretic physics nationallicence Nishimura Hirokazu Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Ibaraki, Japan aut Osoekawa Takeshi Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Ibaraki, Japan aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/11(2007-11-01), 2843-2862 0020-7748 46:11<2843 2007 46 10773 https://doi.org/10.1007/s10773-007-9397-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9397-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nishimura Hirokazu Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Ibaraki, Japan aut NATIONALLICENCE 700 1- Osoekawa Takeshi Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Ibaraki, Japan aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/11(2007-11-01), 2843-2862 0020-7748 46:11<2843 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer