r""" <Very short 1-line summary> <Paragraph description> ... AUTHORS: - YOUR NAME (2005-01-03): initial version - person (date in ISO year-month-day format): short desc ... - person (date in ISO year-month-day format): short desc \section{Tutorial} ... Lots and lots of examples. """ #***************************************************************************** # Copyright (C) 2006 William Stein <wstein@gmail.com> # 2006 YOUR NAME <your email> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #*****************************************************************************
The following is top of the ssmod.py file, which contains the
SupersingularModule code and is located at
SAGE_ROOT/devel/sage/sage/modular/ssmmod/ssmod.py
.
""" Module of Supersingular Points AUTHORS: -- William Stein -- David Kohel -- Iftikhar Burhanuddin EXAMPLES: sage: x = SupersingularModule(389) sage: m = x.T(2).matrix() sage: a = m.change_ring(GF(97)) sage: D = a.decomposition() sage: D[:3] [ (Vector space of degree 33 and dimension 1 over Finite Field of size 97 Basis matrix: [ 0 0 0 1 96 96 1 0 95 1 1 1 1 95 2 96 0 0 96 96 0 0 96 2 96 96 2 0 0 1 1 95 0], 1), (Vector space of degree 33 and dimension 1 over Finite Field of size 97 Basis matrix: [ 0 1 96 16 75 22 81 0 0 17 17 80 80 0 0 16 1 40 74 23 57 96 81 0 23 74 0 0 0 24 73 0 0], 1), (Vector space of degree 33 and dimension 1 over Finite Field of size 97 Basis matrix: [ 0 1 96 90 90 7 7 0 0 6 91 6 91 0 0 7 13 0 91 6 0 84 90 0 91 6 0 0 0 90 7 0 0], 1) ] sage: len(D) 9 We compute a Hecker operator on a space of huge dimension! sage: X = SupersingularModule(next_prime(100000)) sage: t = X.T(2).matrix() # long time (but still less than a minute!) sage: t.nrows() # long time 8334 """ #***************************************************************************** # Copyright (C) 2004,2006 William Stein <wstein@gmail.com> # Copyright (C) 2006 David Kohel <kohel@maths.usyd.edu.au> # Copyright (C) 2006 Iftikhar Burhanuddin <burhanud@usc.edu> # Distributed under the terms of the GNU General Public License (GPL) ...
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