Remarks on Gröbner basis for ideals under composition

  • Authors:

  • Wang Mingsheng;Liu Zhuojun

  • Affiliations:

  • Chinese Academy of Sciences, Beijing, China;Chinese Academy of Sciences, Beijing, China

  • Venue:
  • Proceedings of the 2001 international symposium on Symbolic and algebraic computation
  • Year:
  • 2001

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Abstract

Let K[x1,…,xn]be a polynomial ring over a field K in variables x1,…,xn, and K[y1,…,ym] be a polynomial ring over a field K in variables y1,…,ym. m ≱ n. Let &THgr; = (&thgr;1,…,&thgr;n) be an ordered n-tuple of non-constant polynomials in K[y1,…,ym]. For any finite set F of K[x1,…,xn], let F o &THgr; be the set obtained from F by replacing xi; by &thgr;i, thus for any F e K[x1,…,xn], Fo&THgr; e K[y1,…,ym]. With the above notations, Hong's main theorem [9] and the main theorem of [6] are generalized to general cases with some new proofs.