# \#geometric-algebra

**URL:** https://discourse.julialang.org/tag/geometric-algebra/787.md

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## [Practical Grassmann.jl examples?](https://discourse.julialang.org/t/practical-grassmann-jl-examples/126439)

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**Author:** [@jada](https://discourse.julialang.org/u/jada)\
**Replies:** 1\
**Last updated:** [March 1, 2025, 12:54am UTC](https://discourse.julialang.org/t/practical-grassmann-jl-examples/126439 "2025-03-01T00:54:33Z")

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I am looking for examples how to work with forms, e.g. how to evaluate a form on a vector field, pull back a form, do external derivatives and so on. I already failed at replicating the tutorial linked below, which give…

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## [\[ANN\] CliffordNumbers.jl: fast, static geometric algebra with multivectors as Number subtypes](https://discourse.julialang.org/t/ann-cliffordnumbers-jl-fast-static-geometric-algebra-with-multivectors-as-number-subtypes/114073)

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**Author:** [@brainandforce](https://discourse.julialang.org/u/brainandforce)\
**Replies:** 11\
**Last updated:** [June 6, 2024, 9:33pm UTC](https://discourse.julialang.org/t/ann-cliffordnumbers-jl-fast-static-geometric-algebra-with-multivectors-as-number-subtypes/114073 "2024-06-06T21:33:01Z")

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CliffordNumbers.jl is a new package for working with Clifford algebras (or geometric algebras) and their elements. Design philosophy AbstractCliffordNumber{Q,T\<:Union{Real,Complex}} type subtypes Number, just as Complex …

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## [Failure to vectorize 8 Int64 multiplies when 8 Float64 multiplies vectorize](https://discourse.julialang.org/t/failure-to-vectorize-8-int64-multiplies-when-8-float64-multiplies-vectorize/114939)

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**Author:** [@brainandforce](https://discourse.julialang.org/u/brainandforce)\
**Replies:** 8\
**Last updated:** [May 31, 2024, 11:52pm UTC](https://discourse.julialang.org/t/failure-to-vectorize-8-int64-multiplies-when-8-float64-multiplies-vectorize/114939 "2024-05-31T23:52:39Z")

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I’ve come across this interesting observation in my package, CliffordNumbers.jl. For context, the multiplication done here is a geometric product (relevant code here) implemented as a grid multiply between blade coeffici…

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## [Essay: Julia and Projective Geometric Algebra](https://discourse.julialang.org/t/essay-julia-and-projective-geometric-algebra/92767)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 9\
**Last updated:** [March 28, 2024, 7:19pm UTC](https://discourse.julialang.org/t/essay-julia-and-projective-geometric-algebra/92767 "2024-03-28T19:19:06Z")

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There appears to be a lot of overlap in the fields of science interested in Julia and the fields of science interested in geometric algebra. Perhaps the two communities would benefit from each other? In an attempt to en…

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## [How to efficiently skip calculating some vector elements?](https://discourse.julialang.org/t/how-to-efficiently-skip-calculating-some-vector-elements/110915)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 4\
**Last updated:** [February 28, 2024, 8:49pm UTC](https://discourse.julialang.org/t/how-to-efficiently-skip-calculating-some-vector-elements/110915 "2024-02-28T20:49:39Z")

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There are significant efficiency gains by implementing Projective Geometric Algebra (PGA) in OpenGL shader hardware as described in Steven De Keninck’s recent paper, “Look, Ma, No Matrices!” Less significant (because it…

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## [Trouble writing custom rule in Enzyme: \`AssertionError: !(overwritten\[end\])\`](https://discourse.julialang.org/t/trouble-writing-custom-rule-in-enzyme-assertionerror-overwritten-end/108939)

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**Author:** [@Gianluca\_Fuwa](https://discourse.julialang.org/u/Gianluca_Fuwa)\
**Replies:** 3\
**Last updated:** [February 20, 2024, 11:25pm UTC](https://discourse.julialang.org/t/trouble-writing-custom-rule-in-enzyme-assertionerror-overwritten-end/108939 "2024-02-20T23:25:57Z")

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Hi, I am currently trying to use Enzyme to get the derivative of a function that takes a multidimensional array of 3x3 matrices and outputs a scalar. The caveat is that these matrices are elements of the Lie-group of sp…

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## [Can a line continue at a '.'?](https://discourse.julialang.org/t/can-a-line-continue-at-a/101364)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 9\
**Last updated:** [July 11, 2023, 5:37pm UTC](https://discourse.julialang.org/t/can-a-line-continue-at-a/101364 "2023-07-11T17:37:40Z")

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Leo Dorst & Steven De Keninck have posted a tutorial and javascript code to animate a hypercube dangling from an elastic string and I’m in the process of porting that code to Julia. The following is their code to genera…

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## [Can the two sides of a mesh have a different color (e.g., origami paper)?](https://discourse.julialang.org/t/can-the-two-sides-of-a-mesh-have-a-different-color-e-g-origami-paper/97118)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 5\
**Last updated:** [April 6, 2023, 5:20pm UTC](https://discourse.julialang.org/t/can-the-two-sides-of-a-mesh-have-a-different-color-e-g-origami-paper/97118 "2023-04-06T17:20:47Z")

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\# fold.jl # MWE of moving mesh # # All the paper test sheet's vertices and faces are defined # according to the wavefront 3D object file format by the # following six lines of text: #= v -2.0 0 2.0 v -2.0 0 -2.0 v 2.…

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## [Can Makie plots be dimension agnostic?](https://discourse.julialang.org/t/can-makie-plots-be-dimension-agnostic/92124)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 16\
**Last updated:** [March 16, 2023, 12:35pm UTC](https://discourse.julialang.org/t/can-makie-plots-be-dimension-agnostic/92124 "2023-03-16T12:35:12Z")

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Makie is new to me and I’m hoping to use it to plot the results of my port of bivector.net’s C++ reference implementation of projective geometric algebra to a Julia reference implementation of projective geometric algebr…

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## [Can an overloaded vector operator be broadcast?](https://discourse.julialang.org/t/can-an-overloaded-vector-operator-be-broadcast/94651)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 15\
**Last updated:** [February 17, 2023, 4:35pm UTC](https://discourse.julialang.org/t/can-an-overloaded-vector-operator-be-broadcast/94651 "2023-02-17T16:35:51Z")

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I’m porting some projective geometric algebra (PGA) applications from ganja.js (JavaScript) to Julia+Makie. In the applications I’m porting (and I suspect in many other PGA applications) it would be convenient to be able…

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## [Does delete! or Observable @view work with Axis3?](https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 2\
**Last updated:** [February 5, 2023, 8:59pm UTC](https://discourse.julialang.org/t/does-delete-or-observable-view-work-with-axis3/94061 "2023-02-05T20:59:10Z")

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As part of an essay (including a listing of the 3D PGA reference implementation ripga3d.jl in the appendix) proposing that Julia + Makie + projective geometric algebra (PGA) are an excellent combination for implementing …

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## [How to scale all the vertices in a GeometryBasics.Mesh?](https://discourse.julialang.org/t/how-to-scale-all-the-vertices-in-a-geometrybasics-mesh/93153)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 5\
**Last updated:** [January 20, 2023, 1:37pm UTC](https://discourse.julialang.org/t/how-to-scale-all-the-vertices-in-a-geometrybasics-mesh/93153 "2023-01-20T13:37:24Z")

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I’m attempting to port Steven De Keninck’s 3D slicer example application (listed here and demonstrated here) from JavaScript to Julia. The example application loads a 3D model of a bunny (from https://enkimute.github.io/…

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## [A macro for pretty geometric algebra equations?](https://discourse.julialang.org/t/a-macro-for-pretty-geometric-algebra-equations/91664)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 15\
**Last updated:** [December 17, 2022, 1:21pm UTC](https://discourse.julialang.org/t/a-macro-for-pretty-geometric-algebra-equations/91664 "2022-12-17T13:21:32Z")

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The following slide is from Steven De Keninck’s presentation at SIBGAPI, an international conference annually promoted by the Special Interest Group on Computer Graphics and Image Processing (CEGRAPI) of the Brazilian Co…

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## [A fast reference implementation of a pretty projective geometric algebra](https://discourse.julialang.org/t/a-fast-reference-implementation-of-a-pretty-projective-geometric-algebra/91451)

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**Author:** [@g2g](https://discourse.julialang.org/u/g2g)\
**Replies:** 18\
**Last updated:** [December 14, 2022, 5:52pm UTC](https://discourse.julialang.org/t/a-fast-reference-implementation-of-a-pretty-projective-geometric-algebra/91451 "2022-12-14T17:52:25Z")

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As shown at the end of this post, I recently ported pga3d.cpp (the bivector.net C++ reference implementation of projective geometric algebra) to Julia because bivector.net does not currently offer a Julia reference imple…

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## [Spherical Cap in Julia](https://discourse.julialang.org/t/spherical-cap-in-julia/78027)

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**Author:** [@OliveiraIgor](https://discourse.julialang.org/u/OliveiraIgor)\
**Replies:** 3\
**Last updated:** [March 18, 2022, 4:31pm UTC](https://discourse.julialang.org/t/spherical-cap-in-julia/78027 "2022-03-18T16:31:53Z")

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I need to use a set of points from a spherical cap to apply KPCA in Julia, but I don’t know how to create these caps, which idea should I use for this application?

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## [\[ANN\] CliffordAlgebras.jl](https://discourse.julialang.org/t/ann-cliffordalgebras-jl/71955)

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**Author:** [@atell\_soundtheory](https://discourse.julialang.org/u/atell_soundtheory)\
**Replies:** 19\
**Last updated:** [November 30, 2021, 1:07am UTC](https://discourse.julialang.org/t/ann-cliffordalgebras-jl/71955 "2021-11-30T01:07:35Z")

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I’m pleased to announce the first release of CliffordAlgebras.jl, a package for performing calculations in generic Clifford algebras / geometric algebras. Package registration is still pending. https://github.com/ATell-…

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## [How do I simply express a canonical basis for G4 using Symbolics.jl](https://discourse.julialang.org/t/how-do-i-simply-express-a-canonical-basis-for-g4-using-symbolics-jl/67540)

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**Author:** [@banksiaboy](https://discourse.julialang.org/u/banksiaboy)\
**Replies:** 2\
**Last updated:** [September 3, 2021, 4:48am UTC](https://discourse.julialang.org/t/how-do-i-simply-express-a-canonical-basis-for-g4-using-symbolics-jl/67540 "2021-09-03T04:48:05Z")

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I am fumbling my way through learning basic Geometric Algebra. I want to bootstrap my understanding of using Symbolics.jl at the same time. I have some dumb questions about the mathematics, and usage of the Symbolics pac…