## 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, FabrÃcio 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

*Last updated: 2021-11-03 17:01:42 GMT*

*Contact: nemo-devel mailing list.*

Logo background due to Giacomo Merculiano.