# Sage days 9 Student Projects

• 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.

• 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: Hyperbolic Geometry. Using sage to draw geometric structures in the Hyperbolic plane.

• 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.

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
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.

• 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:

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.
• 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.

• 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.

• 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.