Subresultants Under Composition

@article{Hong1997SubresultantsUC,
  title={Subresultants Under Composition},
  author={Hoon Hong},
  journal={J. Symb. Comput.},
  year={1997},
  volume={23},
  pages={355-365}
}
  • H. Hong
  • Published 1 April 1997
  • Mathematics
  • J. Symb. Comput.
Composition is an operation of replacing a variable in a polynomial with another polynomial. The main question of this paper is:What happens to subresultants under composition? The main contribution of the paper is to show that the subresultants ``almost'' commute with composition. This generalizes the well-known fact that the resultant is invariant under translation. 

Groebner Basis Under Composition I

  • H. Hong
  • Mathematics
    J. Symb. Comput.
  • 1998
It is proved that this happens iff the composition is compatible with the term ordering and the nondivisibility of Groebner basis computation.

Groebner basis under composition II

It is proved that this happens i the composition is ‘compatible’ with the term ordering and the nondivisibility of Groebner basis computation.

Subresultants revisited

An elementary approach to subresultants theory

Birational properties of the gap subresultant varieties

Double Sylvester sums for subresultants and multi-Schur functions

Resultants of partially composed polynomials

D-resultant and subresultants

We establish a connection between the D-resultant of two polynomials f(t) and g(t) and the subresultant sequence of f(t)-x and g(t)-y. This connection is used to decide in a more explicit way whether

Various New Expressions for Subresultants and Their Applications

New expressions for Subresultant Polynomials, written in terms of some minors of matrices different from the Sylvester matrix are presented, providing new proofs for formulas which associate the Sub resultant polynomials and the roots of the two polynmials.

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In conclusion, the leading coefficient of P(@@@@), the integral domain of polynomials over @@@@, exists uniquely R(P), S (S), and P (@@@@) such that R(R) = 1 and S(S) = 3.