Null geometric algebra with geometric interpretation
Abstract
Null geometric algebra (NGA) refers to a basis-free version of Clifford algebra where the base vector space is spanned by vectors whose inner product with itself equals zero. It provides powerful tools for manipulating expressions in conformal geometric algebra (CGA) when making symbolic reasoning in classical geometry. This paper develops several new techniques in NGA and uses them to explore the geometric interpretations of basic algebraic objects in NGA-null monomials, their scalar parts and pseudo-scalar parts, centred null binomials-and illustrates how these objects are used in making geometric reasoning for problems in classical geometry. This article is part of the theme issue 'Modern applications of geometric algebra'.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Homotopy and Cohomology in Algebraic Topology
Polynomial and algebraic computation
Publication details
- Journal / source
- Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
- Publisher
- The Royal Society
- Volume
- 384
- Issue
- 2326
- Publication date
- 13 August 2026
- Language
- EN