Asymptotically fast triangularization of matrices over rings
SIAM Journal on Computing
Fast construction of irreducible polynomials over finite fields
Journal of Symbolic Computation
Preconditioning of rectangular polynomial matrices for efficient Hermite normal form computation
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Computing Popov and Hermite forms of polynomial matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Modern computer algebra
Diophantine linear system solving
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Rational solutions of singular linear systems
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Approximate algorithms to derive exact solutions to systems of linear equations
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
On computing the determinant and Smith form of an integer matrix
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On lattice reduction for polynomial matrices
Journal of Symbolic Computation
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Improved algorithms for computing determinants and resultants
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
Essentially optimal computation of the inverse of generic polynomial matrices
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
Computing the rank and a small nullspace basis of a polynomial matrix
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Processor efficient parallel matching
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
The shifted number system for fast linear algebra on integer matrices
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Some recent progress in exact linear algebra and related questions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Maximum weight bipartite matching in matrix multiplication time
Theoretical Computer Science
The shifted number system for fast linear algebra on integer matrices
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Kaltofen's division-free determinant algorithm differentiated for matrix adjoint computation
Journal of Symbolic Computation
Computing hermite forms of polynomial matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Fast computation of common left multiples of linear ordinary differential operators
ACM Communications in Computer Algebra
Shortest paths in matrix multiplication time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Weighted bipartite matching in matrix multiplication time
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic Computation
Relaxed p-adic Hensel lifting for algebraic systems
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Fast computation of common left multiples of linear ordinary differential operators
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Fast computation of Smith forms of sparse matrices over local rings
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Theoretical Computer Science
Complexity estimates for two uncoupling algorithms
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Reductions to polynomial matrix multiplication are given for some classical problems involving a nonsingular input matrix over the ring of univariate polynomials with coefficients from a field. High-order lifting is used to compute the determinant, the Smith form, and a rational system solution with about the same number of field operations as required to multiply together two matrices having the same dimension and degree as the input matrix. Integrality certification is used to verify correctness of the output. The algorithms are space efficient.