Free Math! the Sage Software Project for Free and Open-Source Computation

Free Math! The Sage Software Project for Free and Open-Source Computation

Sage Wiki: General Coordination and Information Marshall Hampton University of Minnesota, Duluth

Abstract: Three years ago William Stein released the first version of Sage, a free and open source computational platform based on the popular scripting language Python. Sage unifiesOctober a huge 28, collection 2008 of mathematical software projects into a coherent and powerful system for mathematics, statistics, and scientific computation. In this talk I will give a brief overview of its present capabilities and future directions.

Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 28, 2008 1 / 2

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 2 / 10 Thoughts on Open-Source Software

“You can read Sylow’s Theorem and its proof in Huppert’s book in the library...then you can use Sylow’s Theorem for the rest of your life free of charge, but for many computer algebra systems license fees have to be paid regularly....You press buttons and you get answers in the same way as you get the bright pictures from your television set but you cannot control how they were made in either case. With this situation two of the most basic rules of conduct in mathematics are violated: In mathematics information is passed on free of charge and everything is laid open for checking. Not applying these rules to computer algebra systems that are made for mathematical research ... means moving in a most undesirable direction. Most important: Can we expect somebody to believe a result of a program that he is not allowed to see? Moreover: Do we really want to charge colleagues in Moldava several years of their salary for a computer algebra system?” – J. Neub¨userin 1993 (founded GAP in 1986).

TerminologyMarshall Hampton and University basic of factsMinnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 28, 2008 3 / 3

2 2 Vol(λ1P1 + λ2P2)=a1λ1 + (mixed volume)λ1λ2 + a2λ2

These deﬁnitions follow Anders Jensen thesis (Algorithmic Aspects of Gr¨obner Fans and Tropical Varieties (2007), which is recommended reading.

The face of a polyhedron P maximizing a form ω Rn is ∈

faceω(P ) := p P :< ω, p >= maxq P < ω, q > . { ∈ ∈ }

The normal cone of a face F of a polyhedron P is

n NP (F ) := ω R : faceω(P )=F { ∈ }

The normal fan of a polyhedron P is the polyhedral fan of the normal cones NP (F ) for all faces F of P .

The common reﬁnement of two fans and is deﬁned as F1 F2

1 2 = C1 C2 (C1,C2) 1 2 F ∧ F { ∩1 } ∈F ×F Sage Timeline Sage Timeline 1 1980 Maple created1 as1980 an accessible Maple created alternative as to an Macsyma. accessible alternative to Macsyma. 2 1984 Matlab-based company2 1984 Matlab-basedMathWorks founded. company MathWorks founded. 3 1984 Maple becomes commercial. 3 1984 Maple becomes commercial. 4 1988 Mathematica releases version 1.0. 4 1988 Mathematica releases version 1.0. 5 1993 Magma 1.0 released. 5 6 2005 Sage created 1993 Magma 1.0 released. 7 2005 (November) Version6 2005 0.9.10 Sage of Sage created made publicly available. 8 2006 (February) version7 November 1.0.0 of Sage 2005: (38th Version release). 0.9.10 of Sage made publicly available. 9 2007 (January) Mathematica8 February 6.0: Rewrite 2006: version of graphics 1.0.0 for of Sage (38th release). Manipulate/interactive displays. 9 2007 Mathematica 6.0: Rewrite of graphics for 10 2007 (January) version 2.0.0 of Sage (118th release). Interactive 3D graphics. Manipulate/interactive displays. 10 11 2007 (November) SageJanuary wins 1st place 2007: in version the Trophees 2.0.0 du of Libre Sage (118th release). Interactive competition. 3D graphics. 12 2008(March) Interact11 commandMarch 2008: created. Interact command created. 13 2008 (April) version12 3.0.0April of Sage 2008: (176th version release). 3.0.0 R of support Sage and (176th release). R support and massively improved testing. massively improved testing. 14 2008 (November) 188th release of Sage, version 3.2. 13 November 2008: 188th release of Sage, version 3.2. Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 5 / 6 Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 29, 2008 5 / 5 Sage Timeline Sage Timeline 1 1980 Maple created1 as1980 an accessible Maple created alternative as to an Macsyma. accessible alternative to Macsyma. 2 1984 Matlab-based company2 1984 Matlab-basedMathWorks founded. company MathWorks founded. 3 1984 Maple becomes commercial. 3 1984 Maple becomes commercial. 4 1988 Mathematica releases version 1.0. 4 1988 Mathematica releases version 1.0. 5 1993 Magma 1.0 released. 5 6 2005 Sage created 1993 Magma 1.0 released. 7 2005 (November) Version6 2005 0.9.10 Sage of Sage created made publicly available. 8 2006 (February) version7 November 1.0.0 of Sage 2005: (38th Version release). 0.9.10 of Sage made publicly available. 9 2007 (January) Mathematica8 February 6.0: Rewrite 2006: version of graphics 1.0.0 for of Sage (38th release). Manipulate/interactive displays. 9 2007 Mathematica 6.0: Rewrite of graphics for 10 2007 (January) version 2.0.0 of Sage (118th release). Interactive 3D graphics. Manipulate/interactive displays. 10 11 2007 (November) SageJanuary wins 1st place 2007: in version the Trophees 2.0.0 du of Libre Sage (118th release). Interactive competition. 3D graphics. 12 2008(March) Interact11 commandMarch 2008: created. Interact command created. 13 2008 (April) version12 3.0.0April of Sage 2008: (176th version release). 3.0.0 R of support Sage and (176th release). R support and massively improved testing. massively improved testing. 14 2008 (November) 188th release of Sage, version 3.2. 13 November 2008: 188th release of Sage, version 3.2. Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 5 / 6 Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 29, 2008 5 / 5 Sage Timeline Sage Timeline 1 1980 Maple created1 as1980 an accessible Maple created alternative as to an Macsyma. accessible alternative to Macsyma. 2 1984 Matlab-based company2 1984 Matlab-basedMathWorks founded. company MathWorks founded. 3 1984 Maple becomes commercial. 3 1984 Maple becomes commercial. 4 1988 Mathematica releases version 1.0. 4 1988 Mathematica releases version 1.0. 5 1993 Magma 1.0 released. 5 6 2005 Sage created 1993 Magma 1.0 released. 7 2005 (November) Version6 2005 0.9.10 Sage of Sage created made publicly available. 8 2006 (February) version7 November 1.0.0 of Sage 2005: (38th Version release). 0.9.10 of Sage made publicly available. 9 2007 (January) Mathematica8 February 6.0: Rewrite 2006: version of graphics 1.0.0 for of Sage (38th release). Manipulate/interactive displays. 9 2007 Mathematica 6.0: Rewrite of graphics for 10 2007 (January) version 2.0.0 of Sage (118th release). Interactive 3D graphics. Manipulate/interactive displays. 10 11 2007 (November) SageJanuary wins 1st place 2007: in version the Trophees 2.0.0 du of Libre Sage (118th release). Interactive competition. 3D graphics. 12 2008(March) Interact11 commandMarch 2008: created. Interact command created. 13 2008 (April) version12 3.0.0April of Sage 2008: (176th version release). 3.0.0 R of support Sage and (176th release). R support and massively improved testing. massively improved testing. 14 2008 (November) 188th release of Sage, version 3.2. 13 November 2008: 188th release of Sage, version 3.2. Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 5 / 6 Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 29, 2008 5 / 5 Sage Architecture

Sage Architecture Common compiled libraries in C, C++, Fortran (e.g. GMP, NTL, GHMM) Compiled components with Python/Sage wrappers (e.g. Singular, Pari, GAP, GSL) Common compiled libraries in C, C++, Fortran (e.g. GMP, NTL, GHMM) Python/Sage librariesSage (e.g. Numpy, Architecture Scipy, matplotlib) SageSage Architecture ArchitectureCompiled components with Python/Sage wrappers (e.g. Singular, Pari, GAP, ? - Java, javascript,GSL) notebook.Common compiled Twisted, jquery. libraries in C, C++, Fortran (e.g. GMP, NTL, GHMM) Sage Architecture Python Sage Architecture Python/SageCompiled libraries components (e.g. Numpy, with Scipy, Python/Sage matplotlib) wrappers Common compiled libraries in C,(Singular, C++, Fortran Pari, (e.g. GAP, GMP, GSL, NTL, ...) GHMM) Sage Preparser/IPython? - Java, javascript, shell notebook. Twisted, jquery. Common compiled libraries in C, C++, Fortran (e.g. GMP, NTL, GHMM) Compiled components with Python/SagePython/Sage wrappers native libraries Common compiled libraries in C, C++, Fortran (e.g.Python GMP, NTL, GHMM) Compiled components(Singular, with Python/Sage Pari, GAP, wrappers GSL, ...) (Numpy, Scipy, matplotlib, ...) Compiled(Singular, components Pari, GSL, M4RI, with Python/Sage Linbox, ...) wrappersSage Preparser/IPython shell Python/SageSage native Architecture libraries Cython modules (Singular, Pari, GAP, GSL, ...) Python/Sage native libraries(Numpy, Scipy, matplotlib, ...) (C with Python wrappers) Common compiled libraries in C, C++, Fortran (e.g. GMP, NTL, GHMM) Python/Sage(Numpy, Scipy, native matplotlib, libraries ...) pexpect interfaces pexpect interfaces (Numpy, Scipy, matplotlib, ...) Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 3 / 6 Cython modules Compiled components with Python/Sage wrappers ? - Java,(GMP, javascript, Singular, notebook. Pari, GSL, Twisted,external M4RI, jquery. Linbox, libraries ...) pexpect(C with Python interfaces wrappers) (Maxima, Gfan, R, Axiom, Phcpack, ...) PythonPython/Sage native libraries ?pexpect - Java, interfaces javascript, notebook. Twisted, jquery. (Numpy, Scipy, matplotlib,Marshall Hampton University ...)? - Java, of Minnesota, javascript, Duluth () Free Math! notebook. The Sage Software Twisted, Project for Free jquery. and Open-Source Computation October 29, 2008 3 / 6 Sage Preparser/IPython shell Pythonexternal programs Python (Maxima, GAP, Gfan, R, Axiom,Cython Phcpack, modules ...) Sage Preparser/IPython shell (C with Python wrappers) Sage Preparser/IPython shell ? - Java, javascript, notebook. Twisted, jquery. pexpect interfaces Python external programs Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 3 / 6 Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 3 / 6 Sage Preparser/IPython shell(Maxima, GAP, Gfan, R, Axiom, Phcpack, ...)

Marshall Hampton University of Minnesota, Duluth () Free Math!? The - Java, Sage Software javascript, Project for Free and notebook. Open-Source Computation Twisted,October jquery. 29, 2008 3 / 6 Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 3 / 6 Python Sage Preparser/IPython shell

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 3 / 6 Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 29, 2008 3 / 4 Sage notebook architecture

SageSage notebook notebook architecture architectureSageSage notebook notebook architecture architecture Sage notebookSage notebook architecture architecture

Worksheet web browser interface Worksheet web browser interface Worksheet web browser interface Client-side Worksheet webWorksheet browser interface web browserWorksheet interface web browser interface JavascriptSage and Java notebookSage architecture notebookJavascript andSage architecture Java notebook architecture Javascript andClient-side Java Javascript and Java Javascript andTwisted/Python Java framework for server-clientTwisted/Python interaction framework for server-client interaction Twisted/PythonJavascript framework and for Java server-clientTwisted/Python interaction framework for server-client interaction secure connections Sage notebooksecuresecure connections architecture connections secure connections Twisted/Python frameworkWorksheetSage for notebook webTwisted/Python server-client browserWorksheet interface architecture framework interaction web browser forWorksheet interface web browser interface secure connections server-client interaction Client-side (secureClient-side connections) Client-side Server-side Server-side Server-side Worksheet web browserWorksheet interface web browser interface Sage server Sage server Sage server Client-side Client-side Sage instance Sage instance Sage instance Server-side JavascriptServer-side and JavaJavascript and JavaJavascript and Java Marshall Hampton University of Minnesota, Duluth () Free Math! The SageMarshall Software Hampton Project for University Free and of Open-Source Minnesota, Duluth Computation () FreeOctober Math! The 30, 2008 Sage Software 3 / 11 Project for Free and Open-Source ComputationOctober 30, 2008 3 / 11 Marshall Hampton University of Minnesota, Duluth () Free Math! The SageMarshall Software Hampton Project for University Free and of Open-Source Minnesota, Duluth Computation () FreeOctober Math! The 30, 2008 Sage Software 3 / 11 Project for Free and Open-Source ComputationOctober 30, 2008 3 / 11 Twisted/PythonSage server frameworkTwisted/Python for frameworkTwisted/Python for framework for Sage server Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 3 / 11 server-client interactionserver-client interactionserver-client interaction (secureSage instance connections)(secure connections)(secure connections) MarshallSage Hampton instanceUniversity of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 3 / 11 Javascript and Java Javascript and Java Twisted/Python framework for Twisted/Python frameworkserver-client for interaction server-client interactionMarshall(secure Hampton University connections) of Minnesota,Marshall Duluth Hampton () Free University Math! The of Sage Minnesota, SoftwareMarshall Duluth Project Hampton () Free for Free University Math! and The Open-Source of Sage Minnesota, Software Computation Duluth Project () FreeOctober for Free Math! and 30, The 2008 Open-Source Sage Software 3 / 11 Computation ProjectOctober for Free and 30, 2008 Open-Source 3 / 11 ComputationOctober 30, 2008 3 / 11

(secure connections)Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 3 / 10

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 3 / 11

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 3 / 11 Python Quotes

Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 28, 2008 2 / 2 Python Quotes

Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 28, 2008 2 / 2 Cython

Cython A killer-app spinoff of the Sage project. Used when there is a need for speed.

A killer-app spinoff of the Sage project.

Marshall Hampton UniversityUsed of Minnesota, Duluth when () Free Math! there The Sage Software is Project a need for Free and Open-Source for speed. Computation October 30, 2008 6 / 8

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 30, 2008 6 / 8 License License

Sage components are GPL version 2 compatible. This means that anyone is free to install and modify all parts of Sage. If Sage is used in a commercial product, AND the product uses a modified version of Sage, then the modified Sage code must be made available (a reasonable fee can be chargedSage for distribution). components are GPL version 2 compatible. This means that anyone is free to install and modify all parts of Sage. If Sage is used in a commercial product, AND the product uses a modified version of Sage, then the modified Sage code must be made available (a reasonable fee can be charged for distribution).

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 4 / 12

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 4 / 12 Sage Components

1 ATLAS: Automatically Tuned Linear Algebra Software 2 BLAS: Basic Fortan 77 linear algebra routines 3 Bzip2: High-quality data compressor 4 Cddlib: Double Description Method of Motzkin 5 Common Lisp: Multiparadigm and general-purpose programming language 6 CVXOPT: Convex optimization, linear programming, least squares, etc. 7 Cython: C-Extensions for Python 8 F2c: Converts Fortran 77 to C code 9 Flint: Fast Library for Number Theory 10 FpLLL: Euclidian lattice reduction 11 FreeType: A Free, High-Quality, and Portable Font Engine 12 G95: Open source Fortran 95 compiler 13 GAP: Groups, Algorithms, Programming 14 GD: Dynamic graphics generation tool

15 Genus2reduction: CurveMarshall Hampton data University computation of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 6 16 Gfan: Grbner fans and tropical varieties 17 Givaro: C++ library for arithmetic and algebra Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 7 Sage Components

18 GMP: GNU Multiple Precision Arithmetic Library 19 GMP-ECM: Elliptic Curve Method for Integer Factorization 20 GNU TLS: Secure networking 21 GSL: Gnu Scientiﬁc Library 22 JsMath: JavaScript implementation of LaTeX 23 IML: Integer Matrix Library 24 IPython: Interactive Python shell 25 LAPACK: Fortan 77 linear algebra library 26 Lcalc: L-functions calculator 27 Libgcrypt: General purpose cryptographic library 28 Libgpg-error: Common error values for GnuPG components 29 Linbox: C++ linear algebra library 30 M4RI: Linear Algebra over GF(2) 31 Matplotlib: Python plotting library 32 Maxima: computer algebra system

33 Mercurial: RevisionMarshall control Hampton University system of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 6 34 MoinMoin Wiki 35 MPFI: Multiple Precision Floating-point Interval library Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 7 Sage Components

36 MPFR: C library for multiple-precision ﬂoating-point computations with correct rounding 37 ECLib:Cremona’s Programs for Elliptic curves 38 NetworkX: Graph theory 39 NTL: Number theory C++ library 40 Numpy: Numerical linear algebra 41 OpenCDK: Open Crypto Development Kit 42 PALP: A Package for Analyzing Lattice Polytopes 43 PARI/GP: Number theory calculator 44 Pexpect: Pseudo-tty control for Python 45 PNG: Bitmap image support 46 PolyBoRi: Polynomials Over Boolean Rings 47 PyCrypto: Python Cryptography Toolkit 48 Python: Interpreted language 49 Qd: Quad-double/Double-double Computation Package

50 R: Statistical ComputingMarshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 6 51 Readline: Line-editing 52 Rpy: Python interface to R Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 7 Sage Components

53 Scipy: Python library for scientiﬁc computation 54 Singular: fast commutative and noncommutative algebra 55 Scons: Software construction tool 56 SQLite: Relation database 57 Sympow: L-function calculator 58 Symmetrica: Representation theory 59 Sympy: Python library for symbolic computation 60 Tachyon: lightweight 3d ray tracer 61 Termcap: Simpliﬁes the process of writing portable text mode applications 62 Twisted: Python networking library 63 Weave: Tools for including C/C++ code within Python 64 Zlib: Data compression library 65 ZODB: Object-oriented database

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 6

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 29, 2008 7 / 7

Sage Demo

Trac: bug and feature tracker

Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 29, 2008 6 / 5 Trac: bug and feature tracker

Marshall Hampton University of Minnesota, DuluthFree Math! () The Sage Software Project for Free and Open-SourceOctober Computation 29, 2008 6 / 5 Sage Wiki: General Coordination and Information

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source Computation October 30, 2008 2 / 9 Future directions for Sage

Future directionsFor the for project Sage as a whole: 1 Speed up symbolic computation. For the project as a whole: 2 Improve documentation (switch to Sphinx/ReST). 1 Speed up symbolic computation. 3 Better integration between components (R, scipy, JMol,...). 2 Improve documentation (switch to Sphinx/ReST). 4 Convenient API for sage server seperate from notebook interface. 3 Better integration between components (R, scipy, JMol,...). 5 Better distributed computing (DSage). 4 Convenient API for sage server seperate from notebook interface. 6 5 Better distributed computingCompile cleanly (DSage). on more architectures (OS X 64 bit, Windows, Solaris, AIX, ...). 6 Compile cleanly on more architectures (OS X 64 bit, Windows, Solaris, AIX, ...). For me personally: For me personally: 1 Expand its use in education. 1 Expand its use in2 education.Add more dynamical systems functionality (PyDSTool, AUTO). 2 Add more dynamical3 Create systems interfaces functionality for CellML (PyDSTool, models AUTO). (mathematical biology). 3 Create interfaces4 forMake CellML movie-making models (mathematical easier. biology). 4 Make movie-making5 Improve easier. polyhedral functionality. 5 Improve polyhedral functionality.

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 12 / 12 Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 12 / 12 Future directions for Sage

For the project as a whole: 1 Speed up symbolic computation. 2 Improve documentation (switch to Sphinx/ReST). 3 Better integration between components (R, scipy, JMol,...).

4 ConvenientFuture API for sage directions server seperate for Sage from notebook interface. 5 Better distributed computing (DSage). 6 Compile cleanlyFor the on project more architectures as a whole: (OS X 64 bit, Windows, Solaris, AIX, ...). 1 Speed up symbolic computation. For me personally: 2 Improve documentation (switch to Sphinx/ReST). 1 Expand its use in education. 3 Better integration between components (R, scipy, JMol,...). 2 Add more dynamical systems functionality (PyDSTool, AUTO). 4 Convenient API for sage server seperate from notebook interface. 3 Create interfaces for CellML models (mathematical biology). 5 Better distributed computing (DSage). 4 Make movie-making easier. 6 Compile cleanly on more architectures (OS X 64 bit, Windows, Solaris, 5 Improve polyhedralAIX, functionality. ...). For me personally:

1 Marshall Hampton University of Minnesota,Expand Duluth () Free Math! its use The Sage in Software education. Project for Free and Open-Source ComputationOctober 30, 2008 12 / 12 2 Add more dynamical systems functionality (PyDSTool, AUTO). 3 Create interfaces for CellML models (mathematical biology). 4 Make movie-making easier. 5 Improve polyhedral functionality.

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 12 / 12 Thank you!

Marshall Hampton University of Minnesota, Duluth () Free Math! The Sage Software Project for Free and Open-Source ComputationOctober 30, 2008 11 / 11