Modern computer algebra
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Acceleration of Euclidean algorithm and extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Exploiting fast hardware floating point in high precision computation
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
The Mathematica Book
FFPACK: finite field linear algebra package
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
A BLAS based C library for exact linear algebra on integer matrices
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Implementation techniques for fast polynomial arithmetic in a high-level programming environment
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast rational function reconstruction
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Jebelean--Weber's algorithm without spurious factors
Information Processing Letters
Solving Very Sparse Rational Systems of Equations
ACM Transactions on Mathematical Software (TOMS)
Exact solutions to linear systems of equations using output sensitive lifting
ACM Communications in Computer Algebra
Vector rational number reconstruction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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Over the past few decades several variations on a "half GCD" algorithm for obtaining the pair of terms in the middle of a Euclidean sequence have been proposed. In the integer case algorithm design and proof of correctness are complicated by the effect of carries. This paper will demonstrate a variant with a relatively simple proof of correctness. We then apply this to the task of rational recovery for a linear algebra solver.