# 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 python-based solutions.*Adam Getchell*:**Nonlinear Dynamics in SAGE**. Illustrate and solve solutions to non-linear 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 here)*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.
Equations_on_words_with_color.sws (Next version of sage-words 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 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 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*:**Intensity-based 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 reaction-diffusion partial differential equations on growing domains; a comparison between scipy-matplotlib and matlab.*Véronique Sangin-Gagnon*:**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.