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  • v1.0.0 c5e79bcb52

    Quaternionic v1.0.0 Stable

    algebraity released this 2026-05-10 17:31:55 -04:00 | 0 commits to main since this release

    Quaternionic - v1.0.0

    This is the first official release of Quaternionic, a mathematics library written from scratch in C offering implementations of the algebra and arithmetic of algebras resulting from the Cayley-Dickson construction. Users may expect v1.0.0 to contain the basic features necessary for serious computational and research use, including Cayley-Dickson algebra arithmetic, quaternion and octonion algebra construction, zero divisor and annihilator computations, ideals and subalgebras, matrix representations of quaternion algebras, and more.

    Quaternionic is designed both as a standalone C library and as a future component of Bestiary. It includes its own supporting implementations of fraction arithmetic, complex arithmetic, matrix and vector operations, and basic field arithmetic, so it does not require external mathematical libraries.

    Features

    Quaternionic v1.0.0 includes:

    • Construction of arbitrary Cayley-Dickson algebras with constructCDAlgebra
    • Dedicated construction functions for quaternion and octonion algebras
    • Construction of Cayley-Dickson, quaternion, and octonion algebra elements
    • Addition, subtraction, multiplication, conjugation, scalar multiplication, inverses, norms, left division, and right division for Cayley-Dickson elements
    • Computation of commutators and associators via cdCommutator and cdAssociator
    • Conversion of Cayley-Dickson elements to and from coordinate vectors over the base field
    • Computation of left multiplication, right multiplication, commutator, and associator matrices
    • Computation of bases for spans, centers, nuclei, generated subalgebras, generated left ideals, generated right ideals, and generated two-sided ideals
    • Detection of left and right zero divisors
    • Computation of bases for left and right annihilators
    • Structured representations of generated ideals and subalgebras through CDIdeal and CDSubalgebra
    • Ideal arithmetic and intersection logic for subalgebras
    • Construction of the standard matrix representation of a quaternion algebra over F(sqrt(a))
    • Basic support for higher Cayley-Dickson algebras, including sedenions, trigintaduonions, and arbitrary Cayley-Dickson algebras

    Building

    Quaternionic is built with a C11 compiler and the C standard library. The library itself has no external dependencies. The only additional system library linked by the test binaries is the standard math library, libm.

    To build Quaternionic from the root of the repository, run:

    make all

    This creates the build/ directory, compiles all source objects from src/, and builds the included test binaries.

    To build and run the full test suite, run:

    make test-all

    License

    Quaternionic and all associated code are licensed under the GPLv3. A copy of this license is included in the main repository as LICENSE.md.

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