{{{#!rst
Schedule for Sage Days 49 (June 17-21, 2013)
============================================
**For the main Sage Days 49 page go** `here <http://wiki.sagemath.org/combinat/FPSAC13>`_
Monday
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**Morning Session**:
* 09h00 : Welcome, Sage installation, coffee
* 10h00 : Introduction to Sage*, Tom Denton `(Slides!) <http://wiki.sagemath.org/days49_schedule?action=AttachFile&do=view&target=TDintroSlides.pdf>`_
* 10h45 : Tutorial I: *Using the Sage notebook and navigating the help system*, Mathieu Guay-Paquet (UQAM)
* 11h30 : Talk I: *Find me a basis that....*, Mike Zabrocki (York)
*Abstract*. This talk will start with an introduction to combinatorial
Hopf algebras (CHAs). Ironically, one of the main open problems
related to this area is to give a good definition of a CHA. A
question that I think that Sage will help us answer is "what is the
fundamental basis of a combinatorial Hopf algebra?" `slides available for talk <http://wiki.sagemath.org/days49_schedule?action=AttachFile&do=view&target=MZslides.pdf>`_
**Lunch Break**: 12h30 - 14h30
**Afternoon Session**, 14h30-17h30:
* 14h30 : *Round table and discussion of programming projects* Anne Schilling (UC Davis)
* 15h30 : Coffee Break
* 16h00 : Coding Sprints
* 17h00 : Coding Sprints
Tuesday
-------
**Morning Session**:
* 09h00 : Talk II: *Combinatorial Actions, Orbit Averages, and Sage Implementation*, Tom Roby (U. Connecticut) `slides!! <http://www.math.uconn.edu/~troby/homomesySageOrsay2013.pdf>`_ (open in Adobe Acrobat Reader to see animations)
*Abstract*. We consider a variety of combinatorial actions on finite sets whose
orbits have unexpected properties. Starting with simple examples such
as cyclic rotation of binary strings, we generalize to actions on Young
tableaux and order ideals of partially ordered sets. We identify a
particular phenomenon called *homomesy* appearing in many unrelated
combinatorial contexts: namely that the average value of some natural
statistic over each orbit is the same as the average over the entire
set. Viewing these actions as products of *toggle operations* allows
us to see how some of these actions are related and to extend much of
this picture more broadly. In particular, we can generalize the
operations of rowmotion and promotion (in Striker and Williams'
terminology) on order ideals in a poset to (1) the order polytope of a
poset (the continuous piecewise-linear category), and (2) to the
collection of maps from a poset to rational functions in $|P|$ variables
(the birational/geometrical) setting.
For this latter setting, Darij Grinberg has developed Sage code that (1)
computes the rowmotion operator; (2) checks whether this operator
appears to have finite order; (3) helps check for homomesy of particular
statistics under the action of the operator. Although we have proofs of
homomesy for a number of special cases, much remains to be done even at
the combinatorial level of order ideals on posets. For the two other
categories almost everything we have discovered via computer-based
computations is still conjectural.
This talk largely discusses recent work with Jim Propp, including ideas
and results and code from Arkady Berenstein, David Einstein, Darij
Grinberg, Shahrzad Haddadan, Jessica Striker, and Nathan Williams.
* 10h00 : Coffee Break
* 10h30 : Tutorial II: *Programming in Python and Sage*, Viviane Pons (Marne-la-Vallée) (download `tutorial <http://igm.univ-mlv.fr/~pons/docs/Introduction_to_Python_and_Sage.sws>`_, save and open through sage notebook)
* 11h30 : Talk III: *Computing Ext algebras with Sage. An F_5 algorithm for path algebra quotients* (`Slides <http://wiki.sagemath.org/days49_schedule?action=AttachFile&do=view&target=ExtF5SimonKing.pdf>`_), Simon King (Friedrich Schiller U. Jena)
*Abstract.* Basic algebras are finite dimensional path algebra quotients and naturally
occur in, e.g., representation theory of finite groups. We implement Ext algebras of
basic algebras in Sage, together with an F5 algorithm.
Given minimal projective resolutions
for the simple modules of a basic algebra, one computes the Ext algebra by dealing with homogeneous
algebraic relations in free associative algebras. Here, we use “Letterplace” from Singular. Our wrapper
in Sage revealed some severe memory leaks.
Minimal projective resolutions for modules over basic algebras
can be obtained by standard basis or linear algebra methods. The currently best implementation
(for quivers with a single vertex) is David Green’s heady Buchberger algorithm, which is part of the
optional p group cohomology spkg. We wish to replace it by a more efficient method: F5.
Faugère’s famous F5 algorithm computes standard bases for modules over polynomial rings.
It uses a “signature”, that keeps track how elements were constructed, and is efficient by
exploiting commutativity to avoid redundant constructions. We provide a non-commutative F5 algorithm,
replacing the commutativity relations by the quotient relations in a basic algebra.
Given a module over a basic algebra, the output of the F5 algorithm is not just a
standard basis but a so-called signed standard basis of the module. Our main result is:
If a negative degree monomial ordering is used, then the signed standard basis provides
enough information to read off the Loewy layers of the module. This information is not
provided in an unsigned standard basis. Hence, the F5 algorithm could not easily be
replaced by any other algorithm for the computation of standard bases.
The first Loewy layer provides a minimal generating set. Thus, the non-commutative
F5 algorithm yields more information than Green’s algorithm and in addition
is theoretically more efficient.
**Lunch Break**: 12h30 - 14h30
**Afternoon Session**, 14h30-17h30:
* 14h00 : `FindStat <http://wiki.sagemath.org/combinat/FPSAC13>`_ Demo (Chris Berg, Viviane Pons, Travis Scrimshaw)
* 15h30 : Coffee Break
* 17h00 : Status Reports
Wednesday
---------
**Morning Session**:
* 09h00 : Tutorial III *version control and contributing to sage* Chris Berg (UQAM)
Guides:
- `How to Referee Sage Trac Tickets`_ by William Stein
- `How to contribute to Sage`_ by Sébastien Labbé
- `Introduction to Sage Development`_ by Mike Hansen
- `Short step-by-step checklist for reviewing a patch`_ by Franco Saliola
- `Sage Developer's Guide`_:
- `Walking Through the Development Process`_
- `Review a patch`_
Videos:
- `Contributing to Sage : Who, What and How`_: video of a talk by William Stein
Related thematic tutorials:
- `Editing the Sage sources`_
* 10h00 : Coffee Break
* 10h30 : Tutorial IV: *coercion and category framework*, Simon King
`Tutorial worksheet <http://wiki.sagemath.org/days49_schedule?action=AttachFile&do=get&target=TutorialCategoriesCoercion.sws>`_, `original webpage <http://www.sagemath.org/doc/developer/walk_through.html>`_
**Lunch Break**: 12h30 - 14h30
**Afternoon Session**, 14h30-17h30: exercises and coding sprints with coffee break and status reports
* 15h30 : Coffee Break
* 17h00 : Status Reports
Thursday
--------
**Morning Session**:
* 09h00 : Talk IV: *Numerical evaluation of D-finite functions: NumGfun and beyond*, Mark Mezzarobba (RISC, Johannes Kepler U. Linz)
`Slides <http://marc.mezzarobba.net/exposes/sd49-mezzarobba-20130620-slides.pdf>`_
`Maple worksheet <http://marc.mezzarobba.net/exposes/sd49-mezzarobba-20130620-demo.mw>`_
*Abstract.* D-finite (aka holonomic) functions are complex analytic solutions of
linear ODEs with polynomial coefficients. The class of D-finite
functions encompasses most elementary functions (exp, ln, sin, sinh...)
as well as many common special functions (e.g., Bessel functions and
generalized hypergeometric functions). Its nice algebraic and
computational properties make it possible to develop a unified
framework to deal with these functions in a computer algebra system,
instead of developing ad hoc code for every single function.
My talk will focus on the multiple precision numerical evaluation of
D-finite functions. I will present NumGfun, a Maple package that
provides a guaranteed evaluator for general D-finite functions as well
as some other features related to the rigorous symbolic-numeric
manipulation of such functions. I also plan to discuss some of the
underlying algorithms and say a few words about applications to analytic
combinatorics, the reasons that made me use Maple for this work, what I
dislike about it and what role Sage may play as an alternative.
* 10h00 : Coffee Break
* 10h30 : Open Presentations
**Lunch Break**: 12h30 - 14h00
* 14h00 : `Digiteo Seminar`_, *Le génie mathématique, du théorème de quatre couleurs à la classification des groupes*, Georges Gonthier (Microsoft Research)
**Afternoon Session**,
* 15h30 : Coffee Break
* 17h00 : Status Reports
Friday
------
**Morning Session**:
* 09h00 : Open Presentations
* 10h00 : Coffee Break
* 10h30 : Open Presentations
**Lunch Break**: 11h30 - 13h30
**Afternoon Session**, 14h30-17h30: exercises and coding sprints with coffee break and status reports
* 15h00 : Final Status Reports
Open Presentations
==================
Open presentations are quick (5 to 15 minutes) presentations done by the participants. It can be demonstrations of projects done during the week. Or it can be about anything of interest to the participants including software useful for teaching or research.
.. _`Digiteo Seminar`: http://www.digiteo.fr/prochaine-seance-du-seminaire-digiteo-organisee-avec
.. _`How to contribute to Sage`: http://thales.math.uqam.ca/~labbes/Sage/how-to-contribute/
.. _`How to Referee Sage Trac Tickets`: http://sagemath.blogspot.com/2010/10/how-to-referee-sage-trac-tickets.html
.. _`Editing the Sage sources`: http://combinat.sagemath.org/doc/thematic_tutorials/tutorial-editing-sage-sources.html
.. _`Introduction to Sage Development`: http://wiki.sagemath.org/days20.5/schedule?action=AttachFile&do=view&target=sd20.5.pdf
.. _`Short step-by-step checklist for reviewing a patch`: https://www.evernote.com/shard/s16/sh/f30e5eb9-70a9-4882-818b-333c690942bf/d7a138e2705c25b8da6e2053950a89d5
.. _`Sage Developer's Guide`: http://sagemath.org/doc/developer/index.html
.. _`Walking Through the Development Process`: http://sagemath.org/doc/developer/walk_through.html
.. _`Review a patch`: http://sagemath.org/doc/developer/walk_through.html#reviewing-a-patch
.. _`Contributing to Sage : Who, What and How`: http://vimeo.com/14044496
.. _`Quick reStructuredText`: http://docutils.sourceforge.net/docs/user/rst/quickref.html
.. _`reStructuredText`: http://docutils.sourceforge.net/rst.html
.. _`Sphinx Markup Constructs`: http://sphinx.pocoo.org/markup/index.html
.. _`reStructuredText (saifoo.net)`: http://www.siafoo.net/help/reST/
.. _`ReText`: http://sourceforge.net/p/retext/home/ReText
}}}