# Projects for Sage Days 60

## Tutorials

* Version control with GIT: 2

* Quick categories intro: 3

* Overview of Graph theory feature

* Intro to Algebraic Number Theory

Here are useful links for Number Theory in Sage:

Here are some lecture notes using Sage on Elementary Number Theory by Karl-Dieter.

Sage reference manual for number fields.

Here is a book by William Stein on Algebraic Number Theory.

Kn: Here is my Sage Worksheet. This is heavily bases on the references (2) and (3) above.

* Contributing to Sage

* Tutorial: Using GAP from Sage

* Explore: polytopes

* Tutorial: optimized code with Cython

* Tutorial: commutative algebra

* Tutorial: Homological algebra

* Creating sage packages

* Tutorial: SageTeX

## Knot theory

Review the existing features in Sage (anything) and elsewhere, and create some tickets of achievable features in the mid-run

As we see here, http://ask.sagemath.org/question/8255/knot-theory-and-sage/ there is demand for this.

Older ideas for many topological things are here http://wiki.sagemath.org/topology

Here is someone using braid group implementation to do basic knot things https://quantumtetrahedron.wordpress.com/tag/knot-theory/

Here is someone who even did some thinking about how to organize it: https://github.com/amitjamadagni/Knots/wiki/Knot-theory-implementation

Here is where braid groups were implemented: http://trac.sagemath.org/ticket/12339

## Representation Zeta functions

## Expose more features from Symmetrica

#15555 Amri

## Quadratic forms over ch=2

## Class for bilinear and sesquilinear forms

## Error estimates for differential difference equations

Approximation of solution of a general equation. To solve the equation at a given point with value and error. (Reference http://www.ams.org/journals/mcom/1969-23-106/S0025-5718-1969-0247789-3/S0025-5718-1969-0247789-3.pdf, http://en.wikipedia.org/wiki/Dickman_function ) #16601 Kamalakshya

## Rational points on elliptic curves

## Play with finite dimensional Hopf algebras

Implement a couple, look for dimensions of comodules (by duality)

Mamta

## Review of tutorials from the Sage-Combinat queue

#3624 coding theory -- A trivial review, now done!

Kamalakshya, Kannappan

## Reorganize the combinatorics documentation indexes into src/sage/combinat

#16256

Anne, Karl, Nicolas, Travis

## Conditional expectations of multivariate random variables

## Dimer model

Implement, import or interface existing soft

Counting, sampling, ...

Arvind

## Lie algebras

More work on the ticket, review, play with, split, ...

Travis, ...

## Categories and Morphisms for crystals

Anne, Nicolas, Travis

## Ticket #16126 on Coxeter Groups

Kannappan: I am interested in this ticket. I guess a minimal implementation should not take extremely long...