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* ''Mclean Edwards, Scott Zhou'': '''BFGS Iterates'''. Plotting iterates, in an interactive manner, of the celebrated BFGS method applied to nonconvex and convex functions. Comparison of sage, jyscript/piscript, and our own pythonbased solutions. * ''Jakub Marecek'': '''Toy Integer Programming Solver'''. A very limited integer programming solver for instances with 3 variables, but complete with several primal heuristics in use today, and visualising the workings nicely. (Java & vtkHull?) . Further ideas: '''SVG and PDF Output for JyScript'''. A quick hack using Apache Batik (http://xmlgraphics.apache.org/batik/). '''TeX and PS and PDF Output for SAGE'''. A quick hack using Sketch (http://www.frontiernet.net/~eugene.ressler/). 
* ''Adrian Belshaw'': '''Unimodular Polynomials.''' Using Sage to draw unimodualr polynomials on the unit circle in the complex plane. * ''Arnaud Bergeron'': '''Better adaptive plotting in Sage'''. At William's request, I am working on better adaptive refinement for Sage's plot() command. * ''Drew Chorney'': '''Fundamental Domains of Congruence Subgroups and an Animation of a Geodesic :'''Some Geodesic's on the identification space of a fundamental domain for PSL(2,Z) in jyscript. And visualization of fundamental domains for congruence subgroups using SAGE. * ''Mclean Edwards, Scott Zhou'': '''BFGS Iterates'''. Plotting iterates, in an interactive manner, of the celebrated BFGS method for the minimization of nonconvex and convex functions. Comparison of sage, jyscript/piscript, and our own pythonbased solutions. * ''Adam Getchell'': '''Nonlinear Dynamics in SAGE'''. Illustrate and solve solutions to nonlinear equations. Add basic cobweb diagrams. Wrap Maxima's CTensor package and compare speed with SAGE's Christoffel symbol calculation in calculus/tests.py. * ''Yair Go1dberg'': '''3D Graphing in PiScript'''. Plotting 3 dimensional functions in PiScript. * ''Ryan Hoban'': '''Geometric Structures'''. Using sage to draw geometric structures in the Hyperbolic plane. (Slides available <a href="http://www.math.umd.edu/~rfhoban/GeometricStructures.pdf"> here</a> * ''Steve Kieffer'': '''Algebra sketches'''. Tools with which to produce sketches of a kind often drawn on blackboards to illustrate algebraic structures. * ''Avra Laarakker'': '''Properties of Digit Sets and Dilation Matrices using Sage'''. Given a dilation matrix A, and a digit set D, want to see visually if a tiling of Z^n is possible. * ''Sébastien Labbé'': '''Combinatorics on words'''. 1. Use colors and @interact of sage to study equations on words. [http://wiki.sagemath.org/Days9Projects?action=AttachFile&do=get&target=Equations_on_words_with_color.sws Equations_on_words_with_color.sws] (Next version of [http://code.google.com/p/sagewords/ sagewords package] needed to run it!!) 2. Use jyscript and jython to create a java applet to illustrate Christoffel words [http://wiki.sagemath.org/Days9Projects?action=AttachFile&do=view&target=ChristoffelWord.py ChristoffelWord.py] 3. Add gridlines support for show() in sage. Franco Saliola improved *a lot* my initial patch by changing it all (!!) and added many options to make it work like in Matematica. See [http://trac.sagemath.org/sage_trac/ticket/3825 Ticket #3825] * ''Michael Lamoureux'': '''EasyBalls'''. A 2D animation of colliding balls, maybe with gravity, maybe with E&M if I can get the 3D in there. * ''Jakub Marecek'': '''Toy Integer Programming Solver'''. A very limited integer programming solver for instances with 3 variables, but complete with several primal heuristics in use today, and visualising the workings nicely. See [http://wiki.sagemath.org/JakubMarecek here] for more. 
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* ''Yair Go1dberg'': '''3D Graphing in PiScript'''. Plotting 3 dimensional functions in PiScript. * ''Steve Kieffer'': '''Algebra sketches'''. Tools with which to produce sketches of a kind often drawn on blackboards to illustrate algebraic structures. * ''Michael Lamoureux'': '''EasyBalls'''. A 2D animation of colliding balls, maybe with gravity, maybe with E&M if I can get the 3D in there. * ''Ryan Hoban'': '''Hyperbolic Geometry'''. Using sage to draw geometric structures in the Hyperbolic plane. * ''Sébastien Labbé'': '''Combinatorics on words'''. 1. Use colors and @interact of sage to study equations on words. 2. Use jyscript and jython to create a java applet to illustrate Christoffel words [http://wiki.sagemath.org/Days9Projects?action=AttachFile&do=view&target=ChristoffelWord.py ChristoffelWord.py] 
* ''Zhivko Nedev'': '''Encoding/Representing a class of combinatorial structures and making tools for their visualization and analysis'''. The comb. structure is a MINIMAL edge coloring of K_n, the complete graph, with the following properties: 1. No two adjacent edges have the same color. 2. Our coloring splits the set of edges of K_n into color classes; we require that every class has at least two members. 3. The coloring is minimal by inclusion. That is, if we delete any subset of vertices of K_n (and any adjacent edges), then property 2 is violated  there will be at least one color class with one member. * ''Olesya Peshko'': '''Intensitybased Image Segmentation Tool''' A simple segmentation tool which shows regions of the image (represented by a 2D or 3D matrix of pixel/voxel intensity values) in different colours for easy visualization of the structures shown in the image. * ''Ignacio Rozada'': '''Python and PDE's.''' Solving and plotting numerical solutions to reactiondiffusion partial differential equations on growing domains; a comparison between scipymatplotlib and matlab. * ''Véronique SanginGagnon'': '''Triangle Hyperbolic Group''' Graphics that show the representation of a hyperbolic group. * ''Matthew Stamps'': '''Topological Methods for Determining Graph Colourablility''' Graph colouring problems are, in general, very difficult and often require a wide variety of mathematical techniques to solve. A number of topological methods for bounding the chromatic number of a graph have been developed over the last 30 years. I will introduce one such approach with the help of an interactive graph editor I developed in PiScript/JyScript this week. 
Sage days 9 Student Projects
Please add your project to this list. Follow the examples that are already there.
Adrian Belshaw: Unimodular Polynomials. Using Sage to draw unimodualr polynomials on the unit circle in the complex plane.
Arnaud Bergeron: Better adaptive plotting in Sage. At William's request, I am working on better adaptive refinement for Sage's plot() command.
Drew Chorney: Fundamental Domains of Congruence Subgroups and an Animation of a Geodesic :Some Geodesic's on the identification space of a fundamental domain for PSL(2,Z) in jyscript. And visualization of fundamental domains for congruence subgroups using SAGE.
Mclean Edwards, Scott Zhou: BFGS Iterates. Plotting iterates, in an interactive manner, of the celebrated BFGS method for the minimization of nonconvex and convex functions. Comparison of sage, jyscript/piscript, and our own pythonbased solutions.
Adam Getchell: Nonlinear Dynamics in SAGE. Illustrate and solve solutions to nonlinear equations. Add basic cobweb diagrams. Wrap Maxima's CTensor package and compare speed with SAGE's Christoffel symbol calculation in calculus/tests.py.
Yair Go1dberg: 3D Graphing in PiScript. Plotting 3 dimensional functions in PiScript.
Ryan Hoban: Geometric Structures. Using sage to draw geometric structures in the Hyperbolic plane. (Slides available <a href="http://www.math.umd.edu/~rfhoban/GeometricStructures.pdf"> here</a>
Steve Kieffer: Algebra sketches. Tools with which to produce sketches of a kind often drawn on blackboards to illustrate algebraic structures.
Avra Laarakker: Properties of Digit Sets and Dilation Matrices using Sage. Given a dilation matrix A, and a digit set D, want to see visually if a tiling of Z^n is possible.
Sébastien Labbé: Combinatorics on words.
 Use colors and @interact of sage to study equations on words.
[http://wiki.sagemath.org/Days9Projects?action=AttachFile&do=get&target=Equations_on_words_with_color.sws Equations_on_words_with_color.sws] (Next version of [http://code.google.com/p/sagewords/ sagewords package] needed to run it!!)
 Use jyscript and jython to create a java applet to illustrate Christoffel words
Add gridlines support for show() in sage. Franco Saliola improved *a lot* my initial patch by changing it all (!!) and added many options to make it work like in Matematica. See [http://trac.sagemath.org/sage_trac/ticket/3825 Ticket #3825]
 Use colors and @interact of sage to study equations on words.
Michael Lamoureux: EasyBalls. A 2D animation of colliding balls, maybe with gravity, maybe with E&M if I can get the 3D in there.
Jakub Marecek: Toy Integer Programming Solver. A very limited integer programming solver for instances with 3 variables, but complete with several primal heuristics in use today, and visualising the workings nicely. See [http://wiki.sagemath.org/JakubMarecek here] for more.
Aurel Meyer: Symmetry groups of polytopes. Graphics to illustrate that all symmetry groups of regular polytopes are finite Coxeter groups.
Zhivko Nedev: Encoding/Representing a class of combinatorial structures and making tools for their visualization and analysis. The comb. structure is a MINIMAL edge coloring of K_n, the complete graph, with the following properties:
 No two adjacent edges have the same color.
 Our coloring splits the set of edges of K_n into color classes; we require that every class has at least two members.
 The coloring is minimal by inclusion. That is, if we delete any subset of vertices of K_n (and any adjacent edges), then property 2 is violated  there will be at least one color class with one member.
Olesya Peshko: Intensitybased Image Segmentation Tool A simple segmentation tool which shows regions of the image (represented by a 2D or 3D matrix of pixel/voxel intensity values) in different colours for easy visualization of the structures shown in the image.
Ignacio Rozada: Python and PDE's. Solving and plotting numerical solutions to reactiondiffusion partial differential equations on growing domains; a comparison between scipymatplotlib and matlab.
Véronique SanginGagnon: Triangle Hyperbolic Group Graphics that show the representation of a hyperbolic group.
Matthew Stamps: Topological Methods for Determining Graph Colourablility Graph colouring problems are, in general, very difficult and often require a wide variety of mathematical techniques to solve. A number of topological methods for bounding the chromatic number of a graph have been developed over the last 30 years. I will introduce one such approach with the help of an interactive graph editor I developed in PiScript/JyScript this week.