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FAQ & Tips

How do I install the package?

This package is currently hosted on GitHub. Install with:

import Pkg
Pkg.add(url="https://github.com/ATell-SoundTheory/CliffordAlgebras.jl")

For local development:

import Pkg
Pkg.develop(path="/absolute/path/to/CliffordAlgebras.jl")

Minimum Julia version: 1.6.

How do I type Unicode operators like ∧ ⋅ ⨼ ⨽ ×₋ ≀ ?

Use Julia's LaTeX-style tab completions in the REPL and many editors:

  • \wedge<Tab> → ∧ (exterior)
  • \vee<Tab> → ∨ (regressive)
  • \cdot<Tab> → ⋅ (fat dot)
  • \lrcorner<Tab> → ⨼ (left contraction)
  • \llcorner<Tab> → ⨽ (right contraction)
  • \star<Tab> → ⋆ (scalar)
  • \times<Tab>\_ -<Tab> → ×₋ (commutator)
  • \times<Tab>\_ +<Tab> → ×₊ (anti-commutator)
  • \Vert<Tab> → ≀ (sandwich)

ASCII alternatives (function calls):

  • exteriorprod(a,b) for a ∧ b
  • fatdotprod(a,b) for a ⋅ b
  • leftcontractionprod(a,b) for a ⨼ b
  • rightcontractionprod(a,b) for a ⨽ b
  • scalarprod(a,b) for a ⋆ b
  • commutatorprod(a,b) for a ×₋ b
  • anticommutatorprod(a,b) for a ×₊ b
  • sandwichproduct(a,b) for a ≀ b

What predefined algebras are available?

Common aliases include:

  • :Complex (ℂ), :Quaternions (ℍ)
  • :Spacetime (STA)
  • :PGA2D, :PGA3D
  • :CGA2D, :CGA3D

See the examples on the Home page for usage.

How do I benchmark operations?

This repository includes a small benchmark suite under benchmark/.

  • Quick run:
julia --project=benchmark benchmark/run.jl
  • Full PkgBenchmark run:
julia --project=benchmark -e 'using PkgBenchmark, CliffordAlgebras; benchmarkpkg(CliffordAlgebras)'

Can I use ASCII-only code?

Yes. All Unicode operators have function equivalents (see above). You can also import and call CliffordAlgebras.<name> functions directly.

I get a MethodError mixing different algebras

Operations require both operands to belong to the same algebra. Construct both operands from the same CliffordAlgebra(...) instance.

prune changes the type — is that intended?

Yes. prune removes zero coefficients and may return a different sparse type. Use extend(mv) if you need a full, fixed representation.