| 65 | | * #10305 (prototype): Add rings for the center of the symmetric group algebras |
| 66 | | Mathieu Guay-Paquet, 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 MuPAD-Combinat) |
| | 69 | * Quiver, Cartan matrix, radical filtration (as in MuPAD-Combinat) |
| | 70 | * Depends on: #11111 |
| | 71 | * Finite monoids |
| | 72 | * #12914 (prototype): Representation theory of finite semigroups |
| | 73 | * #8360 (finalize) interface to Jean-Éric 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 Guay-Paquet, 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 | nilTemperley-as.patch in the sage-combinat queue) (AnneSchilling) |
| | 87 | This could possibly make use of KBMAG. |
| | 88 | |
| | 89 | * Root systems: |
| 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 | |
| 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 semi-simple 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 semi-simple 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 Cohen-Macaulay test for simplicial complexes |
| | 135 | |
| | 136 | * Modules and vector spaces: |
| 137 | | * Finalize the basic Cython data-sctructure 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 terms |
| 141 | | (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 breath-first-search 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 of |
| 150 | | 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 monoids |
| 153 | | * (10) is the main building block for the representation theory of finite dimensional algebra |
