Sage Days 30 Coding Sprint Projects

Contents

For the main SD 30 wiki page go here

Below a list of proposed projects.

Combinatorics

* Implement the full collection of d-complete posets and slant product of d-complete posets, and jeu de taquin for them.

* Implement jeu de taquin for increasing tableaux (for d-complete posets or something less general).

* Finalize posets

* Set factories

* Update IntegerVectors internal representation in Sage

Currently IntegerVectors consist of vectors with only positive integer entries. Need a more general object, and to implement various norms. PEOPLE: Eva, Nicolas

* Generate centered digit set for multidimensional radix representation

Prerequisite: updated IntegerVectors. Input: a dilation matrix A (nxn integer matrix, all of whose eigenvalues have modulus > 1). Output: a centered digit set D = {d_1, ..., d_r}; here r = |det A|. The centered digit set is a complete set of coset representatives of Zⁿ/A(Zⁿ), chosen to be the integer vectors contained in the set A((-1/2,1/2]ⁿ).

* Implement Scheicher & Thuswaldner neighbor-finding algorithm

Prerequisite: updated IntegerVectors. Input: a dilation matrix A (nxn integer matrix, all of whose eigenvalues have modulus > 1) and digit set D = {d_1, ..., d_r} (set of integer vectors that comprise a complete set of coset representatives of Zⁿ/A(Zⁿ); here r = |det A|). Output: a list of integer vectors that give the neighbor translates of T(A,D), the set of "decimals" under the multidimensional radix representation with base A and digit set D. See Scheicher and Thuswaldner's paper.

* Visualizing attractors of iterated function systems and other fractal sets

Review/search for graphics packages that are currently usable by Sage, as well as other open-source options for drawing fractals that are available. Find the best one for visualizing fractals, specifically fractals arising from iterated function systems, specifically iterated functions systems arising from multidimensional radix representations (sums of terms of the form Aⁿ d_n, where A is an nxn integer matrix all of whose eigenvalues have modulus > 1, and the d_n are "digit" vectors drawn from a complete set of coset representatives of Zⁿ/A(Zⁿ); for each digit d, we can define a function f_d = A^-1(x+d)). Good qualities in a graphics package include: ability to generate images from batches of examples automatically generated in Sage, ability to focus on areas of interest in the image and zoom in, ability to display both 2D and 3D images, and ability to rotate 3D images for different views.

* Discussion thematic tutorials

* Introduction to Sage book