Information Processing Letters
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Asymptotically fast triangularization of matrices over rings
SIAM Journal on Computing
Algorithms for computer algebra
Algorithms for computer algebra
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Nearly optimal algorithms for canonical matrix forms
Nearly optimal algorithms for canonical matrix forms
Nearly Optimal Algorithms For Canonical Matrix Forms
SIAM Journal on Computing
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Rectangular matrix multiplication revisited
Journal of Complexity
Fast deterministic computation of determinants of dense matrices
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Fast computation of the Smith form of a sparse integer matrix
Computational Complexity
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
Randomized Acceleration of Fundamental Matrix Computations
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Approximate algorithms to derive exact solutions to systems of linear equations
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
An output-sensitive variant of the baby steps/giant steps determinant algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Proceedings of the 2002 international symposium 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
Modern Computer Algebra
High-order lifting and integrality certification
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
On Rational Number Reconstruction and Approximation
SIAM Journal on Computing
Improved algorithms for computing determinants and resultants
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
On the complexity of computing determinants
Computational Complexity
A BLAS based C library for exact linear algebra on integer matrices
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Safe and effective determinant evaluation
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Algorithms for solving linear systems over cyclotomic fields
Journal of Symbolic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Exact solutions to linear systems of equations using output sensitive lifting
ACM Communications in Computer Algebra
Kaltofen's division-free determinant algorithm differentiated for matrix adjoint computation
Journal of Symbolic Computation
Recent progress in linear algebra and lattice basis reduction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Quadratic-time certificates in linear algebra
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic Computation
Deterministic unimodularity certification
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Computing the invariant structure of integer matrices: fast algorithms into practice
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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The shifted number system is presented: a method for detecting and avoiding error producing carries during approximate computations with truncated expansions of rational numbers. Using the shifted number system the high-order lifting and integrality certification techniques of Storjohann 2003 for polynomial matrices are extended to the integer case. Las Vegas reductions to integer matrix multiplication are given for some problems involving integer matrices: the determinant and a solution of a linear system can be computed with about the same number of bit operations as required to multiply together two matrices having the same dimension and size of entries as the input matrix. The algorithms are space efficient.