| 1 | 1 | Currently, the Partition/Diagram Algebra implementations in Sage need to be redone. This problem was identified at Sage Days 38. The documentation is not very clear on how it should be used, and although it is supposed to be an algebra, it does not follow the standard form for algebras in Sage (most likely because these algebras have not been modified since 2007.) [[BR]][[BR]]This attached program seeks to provide an alternate implementation for, and eventually replace once dependencies are resolved, the existing !PartionAlgebra package. More detail about these specific algebras can be found in a 2005 paper by Halverson and Ram titled "Partition Algebras." This new implementation restructures the Partition/Diagram Algebras to use the category structure in Sage, so that they are actually implemented as Algebras_with_basis. The new implementation also provides much more detailed documentation on how to use the Partition Algebras, what they actually are, and provides an easier and more standard usage pattern (inherited from !CombinatorialFreeModule.) |
