# Overview

## A Sage Library of Combinatorial Hopf algebras

This repository contains implementations in Sage of several combinatorial Hopf algebras:

• FQSym,
• WQSym,
• PQSym,
• FSym (and dual),
• PBT,
• CQSym

The code of those implementations is in the process of being integrated in Sage; see ticket #13793: Library of Combinatorial Hopf algebras. It is recommended to use the more recent implementation from the branch attached to this ticket rather than this library.

Nevertheless, for example in case you have difficulty with the above branch, here is how to use this repository:

DIR=<where you want to put the chasage library>
cd $DIR hg clone https://bitbucket.org/nborie/cha export SAGE_PATH=$DIR/cha:

sage
┌────────────────────────────────────────────────────────────────────┐
│ Sage Version 6.5.beta4, Release Date: 2014-12-21                   │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: from chasage.all import *
sage: F = FQSym(QQ).F()
sage: F[2,1]^2
F[2, 1, 4, 3] + F[2, 4, 1, 3] + F[2, 4, 3, 1] + F[4, 2, 1, 3] + F[4, 2, 3, 1] + F[4, 3, 2, 1]