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NEWS.md

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News

This package is in early development; minor versions may introduce breaking changes. New features are shown in this news file, but many internal improvements are not.

v0.2.3

v0.2.2

  • Add ability to customise the order in which basis blades are displayed with BasisDisplayStyle on a per-algebra basis. (E.g., so that 3v12 - 2v13 + 1v23 displays as 1𝒆23 + 2𝒆31 + 3𝒆12 or 1𝒊 + 2𝒋 + 3𝒌).

  • Add @symbolicga convenience macro for compiling symbolically evaluated expressions, inspired by serenity4/SymbolicGA.jl.

v0.2.1

  • Support Multivectors with immutable component arrays (in particular, SVectors). Various improvements to type stability throughout.

  • Change BasisBlade constructor argument order to BasisBlade{Sig}(coeff, bits). Matches the convention used throughout where the coefficient is followed by the unit basis blade, agreeing with mathematical notation.

  • Prefer 0:dim:dim over (0, dim) as the grade parameter of scalar-pseudoscalars. This is more consistent with 0:dim and 0:2:dim.

  • Add basis(Multivector{Sig,K}) to generate a multivector basis, and basis(sig, k) for a basis of blades (k is no longer a keyword argument for consistency).

v0.2.0

  • Remove KVector{Sig,K} and Multivector{Sig} types in favour of Multivector{Sig,K}, where the grade K may now be a collection (e.g., range, tuple) in order to represent inhomogeneous multivectors. This simplifies and generalises the types: only one parametric type is needed, and arbitrary grade combinations (e.g., 0:2:dim for even multivectors) may be represented efficiently.

  • Grade promotion between different grades returns the next smallest subalgebra out of

    • 0 for scalars,
    • (0, dim) for scalar-pseudoscalars,
    • 0:2:dim for even multivectors,
    • 0:dim for general multivectors,

    for more efficient representations.

  • Remove vector_repr and make matrix_repr allow subspace representations.

  • Rename poincaredual to rdual and add ldual. These are also known as the right and left complements.

  • Add sandwich product and ‘antiwedge’ product ∨.

v0.1.2

  • Rename Blade, Multivector and MixedMultivector to BasisBlade, KVector and Multivector, respectively, to more closely reflect standard terminology.

    • BasisBlade is appropriate because only basis blades are representable, not all blades.
    • KVector aligns with “k-vector”, common for homogeneous multivectors.
    • Multivector is a general term which includes inhomogeneous multivectors.

  • Use Symbolics.jl to optimise geometric and derived products by performing computations algebraically and reusing the results.

  • Naive implementations of log, sqrt and trig functions using matrix methods.

  • Add duality operations flipdual, hodgedual and poincaredual. Have not defined dual because there doesn’t seem to be a single universal notion of multivector duality.

v0.1.1

  • Add inner and scalar products and left/right contraction products.

  • Add cayleytable for printing multiplication tables, inspired by ATell-SoundTheory/CliffordAlgebras.jl.

  • Add vector_repr and matrix_repr for converting between geometric algebra and matrix algebra. (Only the canonical linear representation is supported.)

  • Add Cl(p, q, r) metric signature, and allow integers for Euclidean spaces.

v0.1.0

  • Initial working version