AlgebraityfastCD
An efficient C11 library and NumPy-backed Python package for Cayley-Dickson multiplication implementing a novel quasilinear algorithm, matrix-free Cariow–Cariowa, and direct recursive multiplication.
Harrison Lemley
Algebraity
Hello, everypony!
I'm Algebraity, also known as Harrison Lemley. I'm a mathematician, programmer, researcher, mathematical software developer, furry, and otaku.
I'm a mathematics PhD student interested in algebraic complexity, computational algebra, Cayley-Dickson algebras, additive combinatorics, number theory, and more, currently studying at Purdue University.
Projects
Bestiary
A LaTeX-inspired mathematical computing environment that unifies seven animal-themed C libraries behind a GUI, command-line interpreter, and scripting language.
Quaternionic
C library for algebra, arithmetic, and analysis on algebras resulting from the Cayley-Dickson procedure over various fields.
OOKAMI
Python library for computations in additive and multiplicative combinatorics on finite subsets of ℤ.
Research
Cayley–Dickson algebras, additive combinatorics & algebraic cryptography
TANUKI-CD is a research program I founded to promote and facilitate further study into Cayley–Dickson algebras and their properties.
The sum-product conjecture holds for fixed-field lattice product constructions
Harrison Lemley and David Chew
For fixed-field lattice product constructions, any fixed power saving in the product set forces an asymptotically maximal sumset.
Quasilinear multiplication in the Cayley–Dickson tower
A uniform bilinear algorithm for Cayley–Dickson multiplication over unital commutative rings with 2 invertible using O(N log N) ring operations and O(N) auxiliary storage with an MIT-licensed implementation fastCD for the standard real tower.
A Computational Comparison of CSIDH and Constant-Time CSIDH
Implementations and timing benchmarks of CSIDH and its constant-time variant, examining the computational cost of defenses against side-channel attacks.
Interests
Mathematics
algebraic complexity, computational algebra, Cayley-Dickson algebras, additive combinatorics, number theory, and more.
Programming
Algorithms, low-level languages, mathematical programming, C, language design.
Self-hosting, sysadmin, and Linux
Servers, services, GNU/Linux-based infrastructure, self-hosting.
Languages
Japanese, German, Chinese, and what languages have in common and where they differ.
Philosophy and literature
Philosophy, literature, and the human psyche.
Anime, manga, and light novels
Japanese, anime, manga, light novels, music, broader otaku culture.
