Algorithms for solving linear systems over cyclotomic fields

DOI10.1016/j.jsc.2010.05.001zbMath1195.65029OpenAlexW2045078718MaRDI QIDQ987701

Liang Chen, Michael B. Monagan

Publication date: 13 August 2010

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2010.05.001

zbMATH Keywords

linear systemsnumerical examplescyclotomic fieldscyclotomic polynomialsMaplecomputational group theoryChinese remainderinglinear \(p\)-adic liftingmodular algorithmsmultiple primes

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Polynomials over finite fields (11T06) Direct numerical methods for linear systems and matrix inversion (65F05)

Uses Software

• IML - Integer Matrix Library
• Maple

Cites Work

• Exact solution of linear equations using p-adic expansions
• Efficient rational number reconstruction
• The shifted number system for fast linear algebra on integer matrices
• Maximal quotient rational reconstruction
• A BLAS based C library for exact linear algebra on integer matrices
• On the coefficients of the cyclotomic polynomial
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