Main topic

Matrices and matrix objects in GAP

Originally, matrices in GAP were introduced as lists of lists of equal length with entries in a (usually common) ring. Advantages of this setup are simplicity and flexibility.

But there are also disadvantages, for example:

• it can be expensive to find out if a GAP object is a matrix
• it is easy to fall into efficiency traps related to GAP’s type determination of nested lists
• one cannot store meta-information about a matrix in a list of lists (e.g., a ground ring, or various properties and attributes)
• it is difficult to make functions for matrices work with other matrices which are not implemented as lists of lists (e.g., sparse matrices, wrapped matrices from external programs)
• matrices with zero rows or columns do not work well (useful for programming, an empty list has no information about which type of elements it does not contain)

There exists plans, descriptions and code for matrix objects in the GAP library. Goals of this meeting could be:

• to clarify open points in the usage interface (API) of such objects
• to document this API
• to implement (or finish partial implementations) of some types of matrices according to the API
• to make as much code as possible in the GAP library work with matrix objects instead of list-of-lists matrices (e.g., the creation of and computation with matrix groups where generators are given as matrix objects)

A more detailed account of the current status was given by Max Horn in this github issue.

Another source are old files by Max Neunhöffer: see here. In particular, there is a testing function we might want to look at (and adjust to a final API).