links.txt

<h2>Links and references</h2>

<h3>Software using Nemo</h3>

<ul>

<li><a href="https://github.com/thofma/hecke">Hecke</a> uses Nemo for number fields and basic
arithmetic including Hermite normal form.</li>

<li><a href="http://cloud.sagemath.com/">SageMathCloud</a> supports Nemo in Jupyter notebooks with the Julia kernel.</li>

</ul>

<h3>References to Nemo in the literature and online</h3>

<ul>

<li>None yet.</li>

</ul>

<h2>Credits</h2>

<h3>Mathematics, algorithms and implementations</h3>

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

<ul>

<li><a href="http://arxiv.org/abs/1411.1607">Julia: A fresh approach to numerical computing</a>, Jeff
Bezanson, Alan Edelman, Stefan Karpinski, Viral B. Shah</li>

<li>Computational Algebraic Number Theory, Henri Cohen</li> 

<li><a href="http://www.inf.fu-berlin.de/groups/ag-ti/people/rote/Papers/pdf/Division-free+algorithms.pdf">Division free algorithms for the determinant and the Pfaffian: Algebraic and combinatorial approaches</a>, Gunter Rote.</li>

<li><a href="http://arxiv.org/pdf/math/0201315v1.pdf">Berkowitz's algorithm and clow sequences</a>, Michael Soltys</li>

<li><a href="http://www4.ncsu.edu/~kaltofen/bibliography/92/Ka92_issac.pdf">On computing determinants of matrices without divisions</a>, Erich Kaltofen</li>

<li><a href="https://hal.archives-ouvertes.fr/hal-00678543/document">Generalized fraction-free LU factorization for singular systems with kernel extraction</a>, David Dureisseix</li>

<li><a href="http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA313755">A simplified fraction-free integer Gauss elimination algorithm</a>, Peter Turner</li>

<li><a href="http://www.mcs.csueastbay.edu/~malek/Class/Characteristic.pdf">Linear Algebra: characteristic polynomial and minimum polynomial</a>, Massoud Malek</li>

<li><a href="http://www.emis.de/journals/JIPAM/images/271_06_JIPAM/271_06.pdf">Bounds on the coefficients of the characteristic and minimal polynomials</a>, Jean-Guillaume Dumas</li>

<li><a href="http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/minpolyandappns.pdf">The minimal polynomial and some applications</a>, Keith Conrad</li>

<li><a href="http://www.sciencedirect.com/science/article/pii/S074771719690142X">A new algorithm for the computation of canonical forms of matrices over fields</a>, Allan Steel</li>

<li><a href="https://hal.inria.fr/inria-00074666/document">The minimal polynomials, characteristic subspaces, normal bases and the Frobenius form</a>, Paul Camion, Daniel Augot</li>

<li><a href="http://www.cecm.sfu.ca/CAG/papers/CPpaper.pdf">A modular algorithm for computing the characteristic polynomial of an integer matrix in Maple</a>, Simon Lo, Michael Monaghan, Allan Wittkopf</li>

<li><a href="http://www-circa.mcs.st-and.ac.uk/Preprints/minpoly.pdf">Computing minimal polynomials of matrices</a>, Max Neunhoffer, Cheryl Praeger</li>

<li><a href="http://lig-membres.imag.fr/pernet/Publications/issac07_pernet.pdf">Faster algorithms for the characteristic polynomial</a>, Clement Pernet, Arne Storjohann</li>

</ul>