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
- None yet.
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