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| = Sage Days 30 Coding Sprint Projects = | |
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| <<TableOfContents>> | {{{#!rst Sage Days 38 Coding Sprint Projects =================================== **For the main Sage Days 38 wiki page go** `here`__. __ days38 Below is a list of proposed projects. .. macro:: <<TableOfContents>> Combinatorics ------------- Representation Theory --------------------- * Sage interface to QPA_ (`sourceforge page`__) __ http://www.math.ntnu.no/~oyvinso/QPA/ .. _QPA: http://sourceforge.net/projects/quiverspathalg/ |
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| '''For the main SD 30 wiki page go [[days30|here]]''' | Documentation ------------- |
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| * quick reference card for combinatorics/sage-combinat (see `quickref`_) | |
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| 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). (Hugh, Eric) (Hugh, Eric, Ryan, JP, Florent) * Student project: iterator over LR-tableaux of fixed shape, as in Anders's talk (Hugh) * Student project: implement double Schubert and double Grothendieck polynomials (Hugh) * Finalize posets Christian, Franco, Nicolas, Neil, Carolina * Set factories Jason, Florent, Travis, Nicolas, Anne, Franco * Finalize Mike's permutation group patches Rob, Nicolas * Get the reflection groups / Coxeter groups into a proper state Christian, (Nicolas, Anne ?) * Implementation of energy function of crystals (suitable for an interested student!!!) Anne, Travis * Implementation of cyclic tableaux Anne * Quotient rings of rings of symmetric functions, examples of noncommutative Schur functions, etc. Jason, Anne * Actions on combinatorial free modules Hugh, Anne, Franco, Nicolas, Florent, Chris * Implementation of bijection between crystal paths and rigged configurations Travis, Anne * Polyhedral representation of symmetries Aaron * Partitions related to k-Schur functions Carolina, Jason * (Something with poset partitions?) Holly == Number Theory == * Update IntegerVectors internal representation in Sage [l^p^ norms: norm(p='sage.rings.integer.Integer(2)')]. Eva, Nicolas, Florent, Jordi * Student project: Generate centered digit set for multidimensional radix representation 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 Z^n^/A(Z^n^), chosen to be the integer vectors contained in the set/polytope A((-1/2,1/2]^n^). Josh * Student project: Generate minimum modulus digit set for multidimensional radix representation Input: a dilation matrix A. Output: a digit set D = {d_1, ..., d_r} consisting of the representatives of each coset of Z^n^/A(Z^n^) with minimum l^2^ norm. - Method 1: Use algorithm for centered digit set D_0 to find an initial set of coset representatives. Find the smallest l^2^ norm of any k in Z^n^ that is not in the initial digit set D_0. Search vectors k in Z^n^ of expanding l^2^ norm: check the l^2^ norm of the current representative for the coset that k is in, and replace that representative with k (in the digit list/set D) if k has smaller norm. Note that this is a finite search. - Method 2: Use LLL algorithm to find minimal basis for lattice A(Z^n^). Then take D to be the set of Z^n^ lattice points (integer vectors) in the set/polytope A((-e_1/2,e_1/2] x ... x (-e_n/2,e_n/2]), where e_1, ..., e_n are the LLL basis vectors for A(Z^n^). * Student project: 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 [[https://secure.wikimedia.org/wikipedia/en/wiki/Iterated_function_system|iterated function systems]], specifically iterated functions systems arising from multidimensional radix representations (sums of terms of the form A^n^ 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 Z^n^/A(Z^n^); 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. (Franco to advise) * Potentially suitable as student project?: Implement Scheicher & Thuswaldner neighbor-finding algorithm 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 Z^n^/A(Z^n^); 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 [[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.4331&rep=rep1&type=pdf|Scheicher and Thuswaldner's paper]]. == Documentation == * Discussion thematic tutorials Jason, Anne, Franco, Rob, Nicolas, Florent, Jeff * ``Introduction to Sage'' book Hugh, Rob, Nicolas, Jeff |
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Sage Days 38 Coding Sprint Projects
For the main Sage Days 38 wiki page go here.
Below is a list of proposed projects.
Contents
Combinatorics
Representation Theory
- Sage interface to QPA (sourceforge page)
Documentation
- quick reference card for combinatorics/sage-combinat (see quickref)