How close is sage to ready for teaching undergrad/grad combinatorial courses
[http://sage.math.washington.edu/home/burhanud/sd7/teaching/teaching.wav Audio]
Textbooks:
Brualdi - Introductory Combinatorics
Wilf - Zeilberger Generating functionalogy
Stanley - Enumerative Combinatorics
CAGES Combinatorial http://www.math.mtu.edu/~kreher/cages.html
Knuth Graham Pataschnik - Concrete mathematics
van Lint, Wilson: A course in Combinatorics http://www.amazon.com/Course-Combinatorics-J-van-Lint/dp/0521422604
Graphs:
- - Complete, except maybe chromatic number and Hamiltonian paths? - interface with graphviz: There is some functionality to interface NetworkX with graphviz and some algorithms that are implemented directly in Cython (like spring layout). We also have a way to interface with pygraphviz, but it's probably not as natural or as easy as it should be.
- See CombinatoricaCompare for a comparison to the fairly comprehensive graph theory functionality of the Mathematica Combinatorica package.
Trees:
- - spanning trees / ... are there
- maybe they should return a Graph (could be made to return graph by creating an empty graph and adding the returned edges).
- Parts could be taken from MuPAD-Combinat
Posets:
- - TODO: (integrate Stembridge + MuPAD-Combinat)
Linear programming:
- - Should be there ... - Networks?
Coding theory:
- - Link with Guava in GAP: sage.coding.guava
Automata
- - There exist specialized things in pyrex
Classical combinatorial objects
- - Should be complete enough: partitions / ...
Generating functions
- - guess / ... (TODO: port Martin Rubey's implementation in Axiom)