Software using Nemo
- 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.
- SageMathCloud 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
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