On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
On Computing the Exact Determinant of Matrices with Polynomial Entries
Journal of the ACM (JACM)
The Algebraic Solution of Sparse Linear Systems via Minor Expansion
ACM Transactions on Mathematical Software (TOMS)
Analysis of Algorithms, A Case Study: Determinants of Matrices with Polynomial Entries
ACM Transactions on Mathematical Software (TOMS)
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm
Communications of the ACM
An efficient sparse minor expansion algorithm
ACM '76 Proceedings of the 1976 annual conference
The definition and use of data structures in REDUCE
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
A mode analyzing algebraic manipulation program
ACM '74 Proceedings of the 1974 annual ACM conference - Volume 2
Computer Aided Geometric Design
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In this paper, the use of an efficient sparse minor expansion method to directly compute the subresultants needed for the greatest common denominator (GCD) of two polynomials is described. The sparse minor expansion method (applied either to Sylvester's or Bezout's matrix) naturally computes the coefficients of the subresultants in the order corresponding to a polynomial remainder sequence (PRS), avoiding wasteful recomputation as much as possible. It is suggested that this is an efficient method to compute the resultant and GCD of sparse polynomials.