Solving systems of nonlinear polynomial equations faster
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Multipolynomial resultant algorithms
Journal of Symbolic Computation
Sparsity considerations in Dixon resultants
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Subresultants under composition
Journal of Symbolic Computation
The structure of sparse resultant matrices
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Groebner basis under composition I
Journal of Symbolic Computation
Solving degenerate sparse polynomial systems faster
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Solving the recognition problem for six lines using the Dixon resultant
Mathematics and Computers in Simulation - Special issue on high performance symbolic computing
A subdivision-based algorithm for the sparse resultant
Journal of the ACM (JACM)
Sparse resultant of composed polynomials I* mixed-unmixed case
Journal of Symbolic Computation
Factoring sparse resultants of linearly combined polynomials
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Sparse Resultant under Vanishing Coefficients
Journal of Algebraic Combinatorics: An International Journal
MR: Macaulay Resultant package for Maple
ACM SIGSAM Bulletin
MR: macaulay resultant package for maple
ACM SIGPLAN Notices - Best of PLDI 1979-1999
Resultants of skewly composed polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Cayley-Dixon projection operator for multi-univariate composed polynomials
Journal of Symbolic Computation
Resultants of partially composed polynomials
Journal of Symbolic Computation
Hi-index | 0.00 |
The main question of this paper is: What is the dense (Macaulay) resultant of composed polynomials? By a composed polynomial f (g1,...,gn), we mean the polynomial obtained from a polynomial f in the variables y1,...,yn by replacing yj by some polynomial gj. Cheng, McKay and Wang and Jouanolou have provided answers for two particular subcases. The main contribution of this paper is to complete these works by providing a uniform answer for all subcases. In short, it states that the dense resultant is the product of certain powers of the dense resultants of the component polynomials and of some of their leading forms. It is expected that these results can be applied to compute dense resultants of composed polynomials with improved efficiency. We also state a lemma of independent interest about the dense resultant under vanishing of leading forms.