Optimal multiplication chains for computing a power of a symbolic polynomial
ACM SIGSAM Bulletin
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)
Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations
ACM Transactions on Mathematical Software (TOMS)
Efficient Gaussian Elimination Method for Symbolic Determinants and Linear Systems
ACM Transactions on Mathematical Software (TOMS)
An efficient sparse minor expansion algorithm
ACM '76 Proceedings of the 1976 annual conference
Algebraic algorithms using p-adic constructions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Taking advantage of zero entries in the exact inverse of sparse matrices
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
ACM SIGSAM Bulletin
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We consider the problem of computing the determinant of a matrix of polynomials; we compare two algorithms (expansion by minors and Gaussian elimination), examining each under two models for polynomial computation (dense univariate and totally sparse). The results, while interesting in themselves, also serve to display two points: 1. Asymptotic results are sometimes misleading for noninfinite (e.g., practical) problems. 2. Models of computation are by definition simplifications of reality: Algorithmic analysis should be carried out under several distinct computational models, and should be supported by empirical data.