An Abstraction-Preserving Block Matrix Implementation in Maple

TL;DR

This paper presents a Maple implementation of partitioned matrices using a recursive block data structure that preserves abstraction across operations, demonstrated through PLU factorization.

Contribution

It introduces a recursive block matrix implementation in Maple that maintains abstraction during various matrix operations, including inversion and factorization.

Findings

Operations preserve block abstraction

Successful PLU factorization demonstration

Implementation enhances Maple's matrix capabilities

Abstract

A Maple implementation of partitioned matrices is described. A recursive block data structure is used, with all operations preserving the block abstraction. These include constructor functions, ring operations such as addition and product, and inversion. The package is demonstrated by calculating the PLU factorization of a block matrix.