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On the construction of Gröbner basis of a polynomial ideal based on Riquier-Janet theory. (English) Zbl 0802.13006

Summary: As a consequence of a previous study of algebraic differential geometry [see ibid. 2, No. 4, 289-312 (1989; Zbl 0739.14001)] there may be associated to certain special kinds of differential ideals some well- behaved basis enjoying some well-behaved properties. If the differential ideals are further specialized so that they correspond to ordinary polynomial ideals then such a well-behaved basis will become the usual Gröbner basis of the polynomial ideals while the latter is not known for differential ideals.

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13N05 Modules of differentials

Citations:

Zbl 0739.14001
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