0

Constructing an algebra from combinatorial objects

AlgcCombinatorics

asked 2025-10-07 18:25:29 +0200

Jeremy Martin
65 ●2 ●3 ●9

updated 2025-10-08 19:01:56 +0200

I want to construct an algebra by first constructing a free module with basis a set of combinatorial objects (permutations, ordered set compositions, parking functions, whatever...) and then specifying a product. How do I do that? The CombinatorialFreeModule class is not sufficient. There used to be a CombinatorialFreeAlgebra class but that may be long deprecated.

edit retag flag offensive close merge delete

Comments

What do you mean under "not sufficient"? Please provide a code illustrating the issue.

Max Alekseyev ( 2025-10-07 20:37:47 +0200 )edit

The CombinatorialFreeModule class lacks a way to specify a product, unless I am missing something.

Jeremy Martin ( 2025-10-08 16:46:32 +0200 )edit

Is this what you want? https://ask.sagemath.org/question/32064/

Max Alekseyev ( 2025-10-09 02:18:09 +0200 )edit

1 Answer

Sort by » oldest newest most voted

2

answered 2025-10-09 23:05:27 +0200

flag of United States of America

8961 ●20 ●74 ●194 http://www.math.washin...

When you initialize a CombinatorialFreeModule, you can specify a category, and if you specify a category of algebras, then defining a method product_on_basis will give you an algebra structure. Some examples in the Sage library:

Indeed, many of the algebras in Sage inherit from CombinatorialFreeModule.

edit flag offensive delete link

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Question Tools

1 follower

Stats

Asked: 2025-10-07 18:25:29 +0200

Seen: 49 times

Last updated: Oct 09

Related questions

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

Powered by Askbot version 0.7.59