SAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportSAGE: Software for Algebra and GeometryExperimentationWilliam SteinAugust 14, 2006William SteinSAGE: Software for Algebra and Geometry Experimentation

OutlineWhat is SAGE?Technology OverviewHistory and Status Report1 What is SAGE?2 Technology Overview3 History and Status ReportWilliam SteinSAGE: Software for Algebra and Geometry Experimentation

The GOALWhat is SAGE?Technology OverviewHistory and Status ReportGOAL: Create the best available software foralgebraic and geometric computation.And give it away to everybody for free.William SteinSAGE: Software for Algebra and Geometry Experimentation

Open SourceWhat is SAGE?Technology OverviewHistory and Status Report1With SAGE everything is open source and thesystem is setup to strongly encourage looking at code.2Most serious users of SAGE are programmers, sothey understand and benefit from having access tocomplete source code.3Anecdotes...William SteinSAGE: Software for Algebra and Geometry Experimentation

Linus QuoteWhat is SAGE?Technology OverviewHistory and Status Report’’I think, fundamentally, open source does tendto be more stable software. It’s the right wayto do things. I compare it to science vs.witchcraft. In science, the whole systembuilds on people looking at other people’sresults and building on top of them. Inwitchcraft, somebody had a small secret andguarded it -- but never allowed others toreally understand it and build on it.Traditional software is like witchcraft. Inhistory, witchcraft just died out. The samewill happen in software.’’ -- Linus TorvaldsWilliam SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportWho is Writing SAGE?Professors, Postdocs, Graduate students, Undergraduates,High school teachers, Retired tech workers, and YOU.Contributors Include: Tom Boothby, Robert Bradshaw, DavidHarvey, Craig Citro, Bobby Moretti, Emily Kirkman, Yi Qiang, JoshKantor, David Kohel, David Joyner, Iftikhar Burhanuddin, JohnCremona, Martin Albrecht, Wilson Cheung, Alex Clemesha, DougCutrell, Didier Deshommes, Naqi Jaffery, Kiran Kedlaya, David Roe,David Kirkby, Jon Hanke, Gregg Musiker, Kyle Schalm, Steven Sivek,Jaap Spies, Gonzalo Tornaria, Justin Walker, Mark Watkins, JoeWeening, Joe WetherellWilliam SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportBig Iron: http://sage.math.washington.eduThe SAGE “sandbox”: 64GB RAM, 8-way dual core Opteron server.You can browse the developer working directories over the web here!William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportTechnology OverviewWilliam SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportPython: the glue that holds SAGE togetherPython is a free open language that is on the rise.From www.python.org:Python is a dynamic object-oriented programming language thatcan be used for many kinds of software development.It offers strong support for integration with other languages andtools, comes with extensive standard libraries, and can be learnedin a few days.Many Python programmers report substantial productivity gainsand feel the language encourages the development of higherquality, more maintainable code.You interact with SAGE (essentially) via Python.William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportIPython: The SAGE Command Linewas@sha:~$ sage--------------------------------------------------------| SAGE Version 1.3.6.3, Build Date: 2006-08-13-1150 || Distributed under the GNU General Public License V2. |--------------------------------------------------------sage: 2^381IPython: an amazing shell (history, completions, etc.)2There is also an emacs command-line interface.3Ipython provides a very nice debugger (interface to pdb).William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportGUI: The SAGE NotebookVery Surprising (to me) FACT: Most people I’ve polled vastly preferusing a good GUI for interacting with math software, if available.So now SAGE has one. Creating this was not easy (for me).1The SAGE Notebook – An “AJAX application” like Googlemaps or gmail: lots of CSS, Javascript, and XMLHTTPRequest.2Written from scratch recently by me, Alex C. and Tom B.3Uses Python’s built-in BaseHTTPServer web server.4Uses your web browser (e.g., Firefox, Safari, Opera) to providea GUI.5Client/server model which works over network or locally.6A very usable and (mostly) robust version is done. There is a bigidea list that will influence the next version.7http://sage.math.washington.edu:8100William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportInterfaces: You can use anything from SAGEContinue to use your favorite programs and code from within SAGE:SAGE includes (mostly pseudo-tty) interfaces toGAP, GP/PARI, Kash, Macaulay2, Magma, Maple,Mathematica, Maxima, Octave, Singular, etc.Red systems are included standard with SAGE.Get access to 100% of the functionality of the othersystems via interfaces. (But there is some overhead.)Get tab completion and online help.People have written fairly nontrivial SAGE programsthat combine MAGMA and PARI, e.g., Dimitar Jetchevat Microsoft Research this summer (for Heegnerpoints).William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportPyrex: Fast compiled codeIs SAGE “impossible”???:Date: Mon, 14 Aug 2006 15:26:36 +0100 (BST)I’ve never understood how you can think something thatsits on top of python can beat some custom code likemagma. How does SAGE multiply two numbers? Does it usepython to do it? I was trying to explain SAGE andfailed miserably.If SAGE were written in pure Python it would be slow (tryNZMATH to see what I mean).SAGE can be very fast, since it is partly written in Pyrex, whichis a Python-like language that is converted to C and compiled:http://www.cosc.canterbury.ac.nz/greg.ewing/python/Pyrex/Much more of SAGE’s basic arithmetic types will be (re-)writtenthis way in the next few months.William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportSAGE multiplies two integersSAGE creates and multiplies two integers as follows:1 Create two integers via a direct C-level wrapping of the GMP C library,i.e., using the functions mpz_init and mpz_set...2 Multiply them using the GMP function mpz_mul.The C code gets compiled and becomes an "extension" to the Pythonlanguage. These "extensions" are potentially just as powerful as anythingwritten in the core of Python.def __mul_(Integer self, Integer other):cdef Integer xx = Integer()_sig_on # so ctrl-c always works perfectly.mpz_mul(x.value, self.value, other.value)_sig_offreturn xWilliam SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportRevision Control: DARCSAfter SAGE Days 1 Gonzalo Tornario convinced me touse DARCS for SAGE development. Doing so was anexcellent decision.http://abridgegame.org/darcs/Darcs is a distributed revision control systemwritten by physicist David Roundy. Darcs is simple tolearn and use, with a powerful new approach to meetthe needs of today’s distributed software projects.Darcs is decentralized, based on a "theory of patches"with roots in quantum mechanics.Symmetric: Anybody’s repository is just as much the“master repository” as anybody else’s.William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportHistory and Status ReportWilliam SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportHistory: SAGE 0.1 to SAGE 1.3.6.1Feb 2005: I got job offers with tenure – SAGE 0.1April 2005: Created interfaces to Mathematica,Magma, etc.Feb 2006: SAGE Days 1 workshop – SAGE 1.0June 2006: High school workshop – SAGE NotebookAugust 2006: MSRI Workshop – two weeksuper-intense graduate student coding sprint.SAGE now has a huge range of functionality. It wasthe only system to do all the math-polyglot problems.But for much of importance to me it is not as fast asMAGMA. This is unacceptable.William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportThe SAGE Library (new code)algebras edu lfunctions monoids setscategories ext libs plot structurecoding functions matrix quadratic_forms testscombinat geometry misc ringscrypto groups modular schemesdatabases interfaces modules serverwas@sha:~/d/sage$ cat */*.py */*/*.py */*/*/*.py */*.pyx \*/*/*.pyx */*/*.pyx |wc -l182192was@sha:~/d/sage$ cat */*.py */*/*.py */*/*/*.py */*.pyx \*/*/*.pyx */*/*.pyx |grep "sage:" | wc -l14221Over 250 (of the about 1100) patches were not written by me.William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportWhat is included in SAGE1 Standard (GPL compatible; easy build on Linux and OS X; 52MB):cddlib, clisp, conway_polynomials, cremona_mini, doc, ecm, examples,extcode, freetype, gap, genus2reduction, gfan, givaro, gmp, gnuplotpy,ipython, lcalc, libpng, matplotlib, maxima, mpfr, mwrank, ntl, numeric,pari, pexpect, pyrex, pyrexembed, python, readline, sage, singular,sympow, tachyon, termcap, zlib, zodb32 Optional Packages: sage -i package_namedarcs, database_cremona_ellcurve, database_gap,database_jones_numfield, database_kohel, database_odlyzko_zeta,database_sloane_oeis, database_stein_watkins_mini, dvipng,extra_docs, gap_packages, gd, gnuplot, hermes, kash3_linux,kash3_osx, lie, linbox, macaulay2, mayavi, moin, numarray, numpy,nzmath, polymake pygtk, RealLib3, scipy, soya3 Other:Install almost any Python package: sage -python setup.py.Ubuntu: Use any standard system-wide Python code in SAGE:import sys;sys.path.append(’/usr/lib/python2.4/site-packages’)William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportGoals for SAGE 2.0Goals for SAGE 2.0 – December 20061Very fast basic arithmetic, e.g., finite fields,polynomials, etc.2Very fast everyday linear algebra (much work doneby David Harvey and Robert Bradshaw last week).3Stable release – feature freeze, bug fixing, etc.4Goal: Release SAGE 2.0 in December 2006. Sendme a patch!!5Also – create a SAGE Foundation, since doingSAGE right will cost about $100K/year, and it is verydifficult to cover that all with grants: (4 undergrademployees, 2 workshops, grad student support,hardware, visitors, teaching reduction).William SteinSAGE: Software for Algebra and Geometry Experimentation

What is SAGE?Technology OverviewHistory and Status ReportThe Future (2007) – SAGE 3.0: Very easy to useparallelism1I get regular email from people very enthusiasticabout making SAGE take extensive advantage ofparallel computers.2Hopefully a workshop in January at MSRI on this.3Hopefully followed by a series of intense 2-weekcoding sprints, probably in San Diego.4Fernando Perez et al., Yi Qiang, Jason Martin, etc.Any Questions?William SteinSAGE: Software for Algebra and Geometry Experimentation