On sets of linear forms of maximal complexity

TL;DR

This paper characterizes specific sets of linear forms over rational numbers that require the maximum number of additions, providing a uniform description of their structure and complexity.

Contribution

It offers a novel, uniform characterization of sets of linear forms that achieve maximal computational complexity in terms of additions.

Findings

Identifies sets of linear forms with maximal complexity

Provides a uniform description of these sets

Establishes the exact number of additions needed for computation

Abstract

We present a uniform description of sets of $m$ linear forms in $n$ variables over the field of rational numbers whose computation requires $m(n - 1)$ additions.