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References

Software using Nemo

• Oscar.jl uses Nemo for many of its basic types and AbstractAlgebra for the backbone of much of its generic system.
• Hecke.jl uses Nemo for number fields and basic arithmetic including Hermite normal form.
• Singular.jl provides a C++ wrapper of the Singular kernel and is tightly integrated with Nemo, supporting all Nemo field types as coefficient rings.
• CoCalc supports Julia in Jupyter notebooks with a Julia kernel. Nemo is available.

References to Nemo in the literature and online

• Exact seimidefinite programming bounds for packing problems, Maria Dostert, David de Laat, Philippe Moustrou
• Lattice of compatibly embedded finite fields in Nemo/Flint, Luca De Feo, Hugues Randriambololona, Edouard Rousseu
• Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms, Fredrik Johansson
• Imaginary multiquadratic number fields with class group of exponent 3 and 5, Jurgen Kluners, Toru Komatsu
• Solving p-adic polynomial systems via iterative eigenvector algorithms, Avinash Kulkarni
• k-Point semidefinite programming bounds for equiangular lines, David de Laat, Fabrício Caluza Machado, Fernando a¡rio de Oliveira Filho & Frank Vallenti
• Probably faster multiplication of sparse polynomials, Joris van der Hoeven
• On the computation of overorders, Tommy Hofmann, Carlo Sircana
• Towards practical key exchange from ordinary isogeny graphs, Luca De Feo, Jean Kieffer, Benjamin Smith
• Interpretable exact linear reductions via positivity, Gleb Pogudin, Xingjian Zhang
• On the possibility of using the Julia programming language for scientific and technical tasks (Russian), G. V. Belov, N. M. Aristova
• Computer Algebra and Number Theory Packages for the Julia Programming Language, Claus Fieker, William Hart, Tommy Hofmann, Fredrik Johansson

Credits

Mathematics, algorithms and implementations

Many resources have been invaluable to us. The following is an incomplete list of papers, algorithms, implementations, websites, etc. that we credit.

• Julia: A fresh approach to numerical computing, Jeff Bezanson, Alan Edelman, Stefan Karpinski, Viral B. Shah
• Computational Algebraic Number Theory, Henri Cohen
• Division free algorithms for the determinant and the Pfaffian: Algebraic and combinatorial approaches, Gunter Rote.
• Berkowitz's algorithm and clow sequences, Michael Soltys
• On computing determinants of matrices without divisions, Erich Kaltofen
• Generalized fraction-free LU factorization for singular systems with kernel extraction, David Dureisseix
• A simplified fraction-free integer Gauss elimination algorithm, Peter Turner
• Linear Algebra: characteristic polynomial and minimum polynomial, Massoud Malek
• Bounds on the coefficients of the characteristic and minimal polynomials, Jean-Guillaume Dumas
• The minimal polynomial and some applications, Keith Conrad
• A new algorithm for the computation of canonical forms of matrices over fields, Allan Steel
• The minimal polynomials, characteristic subspaces, normal bases and the Frobenius form, Paul Camion, Daniel Augot
• A modular algorithm for computing the characteristic polynomial of an integer matrix in Maple, Simon Lo, Michael Monaghan, Allan Wittkopf
• Computing minimal polynomials of matrices, Max Neunhoffer, Cheryl Praeger
• Faster algorithms for the characteristic polynomial, Clement Pernet, Arne Storjohann

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