Changes between Version 58 and Version 59 of SageCombinatRoadMap
 Timestamp:
 05/06/12 17:42:04 (5 years ago)
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SageCombinatRoadMap
v58 v59 45 45 * Hopf algebras, Symmetric functions, and generalizations 46 46 * Symmetric Functions 47 * #11563: Make lrcalc a standard package 47 48 * #12525: SFAHomogeneous does not work with RealField 48 49 * Refactor SymmetricFunctions using «multiple realizations» and deprecate SFASchur and friends … … 63 64 * #6889: Invariant rings of permutation group 64 65 65 * #10305 (prototype): Add rings for the center of the symmetric group algebras 66 Mathieu GuayPaquet, Valentin Feray 67 68 * Root systems 69 66 * Representation theory: 67 * Finite dimensional algebras: 68 * Decomposition of the center, construction of central idempotents (as in MuPADCombinat) 69 * Quiver, Cartan matrix, radical filtration (as in MuPADCombinat) 70 * Depends on: #11111 71 * Finite monoids 72 * #12914 (prototype): Representation theory of finite semigroups 73 * #8360 (finalize) interface to JeanÉric Pin's Semigroupe package 74 * #12915: Interfaces to the GAP packages KBMag (and to Monoids, Citrus, ...) 75 * Group algebras: 76 * #10305 (prototype): Add rings for the center of the symmetric group algebras 77 Mathieu GuayPaquet, Valentin Feray 78 * #6654: new features in group algebra category 79 Valentin Feray 80 * Path algebras: 81 * #9889 (prototype): A new module implementing Monomial Algebras 82 83 * Experiment with KBMAG / PLURAL (see #4539) to implement various 84 algebras like affine nilCoxeter algebra, affine nilTemperley Lieb 85 algebra, affine local plactic algebra), see also patch 86 nilTemperleyas.patch in the sagecombinat queue) (AnneSchilling) 87 This could possibly make use of KBMAG. 88 89 * Root systems: 70 90 * #8906 (needs finalization): Optional package for gap3 71 * Constructing a root/coroot lattice realization from a pair of matrices 72 Work in progress by Christian Stump 91 * Integrate/interface PyCox 92 * Root systems: 93 * Constructing a root/coroot lattice realization from a pair of matrices 94 Work in progress by Christian Stump 95 * Allows a generalized Cartan matrix as input for Dynkin diagrams 96 * Coxeter groups, reflection groups: 97 * Computation of reflection degrees from positive roots (easy) 98 * #8359 (needs finalization): permutation representation of a Coxeter group, using GAP3 99 * Implement general Coxeter groups given by a Coxeter diagram 100 * #12912: Interface to Coxeter 3 from Fokko Ducloux (MikeHansen) 101 * #12774: (needs review): various enhancements for Coxeter and Weyl groups 102 * #11187 (prototype): Implementation of finite reflection groups 103 73 104 * Automatic finite Coxeter/(affine)Weyl type recognition, using graph 74 105 isomorphism with predefined cartan types (complex reflection group is harder) 75 106 (Volunteers?) 76 * Computation of reflection degrees from positive roots (easy)77 * #8359 (needs finalization): permutation representation of a Coxeter group, using GAP378 107 * #8327 (needs review): implement the universal cyclotomic field, using the Zumbroich basis 79 108 Christian Stump 80 * Implement general Coxeter groups given by a Coxeter diagram 81 * #12912: Interface to Coxeter 3 from Fokko Ducloux (MikeHansen) 82 83 * Port over the character tables (depends on 1 to be most useful) 84 * Representations/character tables of the Hecke algebras 85 * #12774: (needs review): various enhancements for Coxeter and Weyl groups 86 * Port Specht (AndrewMathas) 87 * Implement data structures for character tables / use it systematically in Sage (Volunteers? Nicolas has some design notes about this): 88 * of groups in Sage / GAP 89 * of semisimple algebras (in Sage / GAP) 90 * of a coset 91 * See #7555: fix Cayley tables, add operation tables 92 93 * Further improve root systems, Coxeter groups and the like, 94 getting features, inspiration, code, doc, tests, developers from Chevie (...) 95 * Implement the many representations of the Hecke algebra (AndrewMathas, ...) 96 * Implement more models of Crystals (alcove and littlemann path, ...): #8984, ... 97 98 * Modules and vector spaces 99 * Tensor products of morphism 109 * Representations of Coxeter groups and Hecke algebras 110 * Port over the character tables 111 * Representations/character tables of the Hecke algebras 112 * Port Specht (AndrewMathas) 113 * Implement data structures for character tables / use it systematically in Sage (Volunteers? Nicolas has some design notes about this): 114 * of groups in Sage / GAP 115 * of semisimple algebras (in Sage / GAP) 116 * of a coset 117 * See also #7555: fix Cayley tables, add operation tables 118 * Implement the many realizations of the Hecke algebra (AndrewMathas, ...) 119 120 * Further improve root systems, Coxeter groups and the like, 121 getting features, inspiration, code, doc, tests, developers from Chevie (...) 122 123 124 * Crystals: 125 * Implement more models of Crystals? 126 * #11305: Bijection between Rigged Configurations and Crystal Paths 127 * #12251: Implementation of Littelmann path model for crystals 128 129 * Cluster algebras (Christian Stump, ...): 130 * #10819: Implementation of the cluster complex 131 * #10538: Implementation of the classes ClusterSeed and Quiver 132 * #11010: Implementation of the SubwordComplex as defined by Knutson and Miller 133 * #12587: Simplicial complexes lack hash function 134 * #11523: Implementation of CohenMacaulay test for simplicial complexes 135 136 * Modules and vector spaces: 100 137 * Generalized tensor product 101 138 * #10673: Roadmap for (Combinatorial)FreeModule 102 139 * #11111 (needs finalization): More support for finite dimensional free modules and algebras 103 104 * Categories 140 Depends on #8678 141 * #8678: module morphisms (tensor products, inverses, ...) 142 143 * Categories & coercion: 105 144 106 145 * #10963: More functorial constructions (NicolasThiéry) 107 146 * #10668, #10667: Cleanup support for morphisms 147 * (prototype) Implement multiparameter morphisms 148 This could be extracted and finalized without much work 149 * #8900 (prototype): Implement multiparameter overloaded functions, with explicit registration 150 Depends on #7420; #383 is not enough 151 NicolasThiery 152 * #7420 (prototype): Use breathfirstsearch or Dijkstra in Coercion, as discussed in (volunteers?) 153 NicolasThiery 108 154 109 155 * Combinatorics … … 121 167 * #5268: Further cleanup of Enumerated sets 122 168 * #11407: Add normalization to clonable lists 169 * Use ClonableIntArray and friends for all combinatorial object: permutations, partitions, compositions... 170 * Fix everything from: http://wiki.sagemath.org/combinat/Weirdness 123 171 * #10534 (needs review): Optimizations for the generation of subwords, subsets, and set partitions 124 172 VincentDelecroix … … 131 179 * #11529 (needs review): Rooted_trees 132 180 133 134 181 == Former road maps and history == 135 182 136 183 * Todo for/at Sage Days 20.5 (May 2010): 137 * Finalize the basic Cython datasctructure for combinatorial objects (in progress #8702, FlorenHivert)138 * Finalize the cleanup of combinatorial object: permutations, partitions, compositions...139 * #8876: Generalize #7914 (Florent)140  Support for a (partial) inverse function on terms141 (when the indices of the domain do not coincide with those of the codomain)142  Non invertible triangular morphism:143  phi.preimage(y): returns the preimage x of y or None if it does not exists (or raise an exception?)144  phi.reduce(y): returns (x, r) such that y = phi(x) + r, and r contains no leading term of phi(domain)145 (that would be euclidean division if phi was x > x * p where p is some polynomial)146 Better name for that method?147 * (6) Use breathfirstsearch or Dijkstra in Coercion, as discussed in #7420 (volunteers?)148 * (7) Allow for user defined overloaded operators, with signature declarations (#383 is a progress, but not enough) (NicolasThiéry, depends on (6))149 * #7980: Extract basic support for the "concrete representation of150 an abstract algebra" relation out of the ncsf patch (JasonBandlow)151 * (7), #7980 are building blocks for further progress in qsym/ncsf/polynomials with several basis (#6889)152 * (9) is a building block for the representation theory of monoids153 * (10) is the main building block for the representation theory of finite dimensional algebra154 184 * Design and implement framework for computing with representations / modules / character rings 155 * Finalize interface to JeanÉric Pin's Semigroupe package (#8360), and 156 extend further the semigroup/monoid/group algebra code (#6654, ...) 157 * Explore / expose the functionalities of KBMAG for computing with (semi)groups defined by presentations 158 * Discussion about implementation of various algebras (affine nilCoxeter algebra, affine nilTemperley Lieb algebra, affine local plactic algebra), see also patch nilTemperleyas.patch in the sagecombinat queue) (AnneSchilling) This could possibly make use of KBMAG. 159 * Categorification of the crystal code (AnneSchilling) #8911 185 160 186 * Words improvements: 161 187 * #8595, #8618, #8574, #8673 and #8674 (misc defect fixes), … … 174 200 175 201 * 2012: 202 * Optimizations: 203 * #11115: Rewrite cached_method in Cython 176 204 * Symmetric functions and generalizations: 177 * #10333: Interface for lrcalc178 * Categories: #9469, #8119, #12527 205 * #10333: An interface to Anders Buch's LittlewoodRichardson Calculator ``lrcalc`` 206 * Categories: #9469, #8119, #12527, #12877, #11943 179 207 * Coercion: #11250, #11257 180 208 * Enumerated sets: #11118 … … 189 217 190 218 * 2011: 191 * #8702: Datastructure for objects with prototype (clone) design pattern. 219 * #8702: Fast datastructure for (combinatorial) objects with prototype (clone) design pattern. 220 * #11290: Implementation of noncommutative kSchur functions in the nilCoxeter algebra 221 * Documentation: #11251, #11282 222 * Debugging, profiling: #11287 223 * Installation: #11296 224 * Posets: #10065, #11293 225 * Combinatorics: #11300, #11301, #11314 192 226 193 227 * 2010: 194 * #6655: Cleanups and new features about corners and cells in partition and tableau195 228 * Root systems, crystals, ... 196 229 * #8984: Implementation of the LenartPostnikov alcove path crystal 197 230 * #8380: Interface with GAP3 198 * Categories: 231 * #8911: Categorification of Crystals 232 * Categories, parents, elements: 199 233 * #8001: Stronger category tests 200 234 * #7921: Categories for extension types via __getattr___ 235 * #8044: Categories for finite/permutation/symmetric groups 236 * #9138, #9056, #8917, #8913, #8579 237 * #8120: UniqueRepresentation and hash value 238 * #8028: Improvements to element_wrapper 201 239 * Symmetric functions: 202 240 * #8259: Conversion from symmetric polynomials to basis of monomial symmetric functions 203 * #7004: Refactor the graph layout code, and add interface with graphviz for acyclic layout204 241 * Modules and vector spaces: 205 242 * #8876: Triangular morphisms with domain and codomain having different index sets … … 208 245 * #9651: Addition on CombinatorialFreeModule directly on dictionaries (closed: fixed) 209 246 * #9648: ModulesWithBasis allows module_morphism's to a wider class of ... (closed: fixed) 247 248 * Graphs: 249 * #7004: Refactor the graph layout code, and add interface with graphviz for acyclic layout 250 * Enumerated sets: 251 * #8519: NN, NonNegativeIntegers, PositiveIntegers, IntegerRange, ... 252 * #6655: Cleanups and new features about corners and cells in partition and tableau 210 253 211 254 * 2009: