Membership problem for differential ideals generated by a composition of polynomials

Programming and Computer Software (Impact Factor: 0.19). 04/2006; 32(3):123-127. DOI: 10.1134/S0361768806030017
Source: DBLP


The question of whether a polynomial belongs to a finitely generated differential ideal remains open. This problem is solved
only in some particular cases. In the paper, we propose a method, which reduces the test of membership for fractional ideals
generated by a composition of differential polynomials to another, simpler, membership problem.

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    ABSTRACT: We generalize Hoon Hong’s theorem on Gröbner bases under composition to the case of differential standard bases in the ordinary ring of differential polynomials {ie4152-01}. In particular, we prove that some ideals have finite differential standard bases. We construct special orderings on differential monomials such that ideals generated by some power of a quasi-linear polynomial acquire finite differential standard bases.
    Journal of Mathematical Sciences 01/2008; 152(4):522-539. DOI:10.1007/s10958-008-9080-9