Groebner Basis Under Composition I

@article{Hong1998GroebnerBU,
  title={Groebner Basis Under Composition I},
  author={Hoon Hong},
  journal={J. Symb. Comput.},
  year={1998},
  volume={25},
  pages={643-663}
}
  • H. Hong
  • Published 1 May 1998
  • Mathematics
  • J. Symb. Comput.
Composition is the operation of replacing variables in a polynomial with other polynomials. The main question of this paper is:When does composition commute with Groebner basis computation?We prove that this happens iff the composition is `compatible? with the term ordering and the nondivisibility. This has a natural application in the computation of Groebner bases of composed polynomials which often arises in real-life problems. 
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References

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It is proved that this happens i the composition is ‘compatible’ with the term ordering and the nondivisibility of Groebner basis computation.
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The main contribution of the paper is to show that the subresultants ``almost'' commute with composition, which generalizes the well-known fact that the resultant is invariant under translation.
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Composition is an operation of replacing variables in a polynomial with other poly-nomials. The main question of this paper is: What happens to multivariate resultants under composition? We prove…
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