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1998 Extended GCD and Hermite normal form algorithms via lattice basis reduction
George Havas, Bohdan S. Majewski, Keith R. Matthews
Experiment. Math. 7(2): 125-136 (1998).


Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers $x_1,\dots,x_m$ for the equation $s=\gcd{(s_1,\dots,s_m)}=x_1s_1+\cdots+x_ms_m$, where $s_1,\dots,s_m$ are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.


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George Havas. Bohdan S. Majewski. Keith R. Matthews. "Extended GCD and Hermite normal form algorithms via lattice basis reduction." Experiment. Math. 7 (2) 125 - 136, 1998.


Published: 1998
First available in Project Euclid: 24 March 2003

zbMATH: 0922.11112
MathSciNet: MR1700579

Primary: 11Y16
Secondary: 11H06

Rights: Copyright © 1998 A K Peters, Ltd.

Vol.7 • No. 2 • 1998
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