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Implement octonions and split octonions #32940

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slel opened this issue Nov 27, 2021 · 0 comments · Fixed by #35629 or #35630
Closed

Implement octonions and split octonions #32940

slel opened this issue Nov 27, 2021 · 0 comments · Fixed by #35629 or #35630
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c: algebra p: major / 3 t: enhancement
Milestone
sage-10.1

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@slel
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slel commented Nov 27, 2021

CC: @slel

Component: algebra

Keywords: octonions

Issue created by migration from https://trac.sagemath.org/ticket/32940
@slel slel added this to the sage-9.5 milestone Nov 27, 2021
@mkoeppe mkoeppe modified the milestones: sage-9.5, sage-9.6 Dec 18, 2021
@mkoeppe mkoeppe modified the milestones: sage-9.6, sage-9.7 Apr 1, 2022
@mkoeppe mkoeppe modified the milestones: sage-9.7, sage-9.8 Aug 31, 2022
@mkoeppe mkoeppe removed this from the sage-9.8 milestone Jan 29, 2023
This was referenced May 9, 2023
Merged
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vbraun pushed a commit that referenced this issue May 28, 2023
gh-35630: Implement the octonions
82a4509 
    
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### 📚 Description

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The octonions are a nonassociative normed division algebra, one of only
4 over the reals, and used to create the 7 dimensional cross product. We
implement a slight generalization with 3 parameters over an arbitrary
commutative ring of characteristic not equal to 2, which allows us to
also define the split-octonions as another special case.

Fixes #32940.

### 📝 Checklist

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]`. -->

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- [x] The description explains in detail what this PR is about.
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### ⌛ Dependencies

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- #34567: ...
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URL: #35630
Reported by: Travis Scrimshaw
Reviewer(s): Frédéric Chapoton, Matthias Köppe
@mkoeppe mkoeppe added this to the sage-10.1 milestone May 28, 2023
vbraun pushed a commit that referenced this issue Jun 21, 2023
gh-35629: Implement the exceptional Jordan algebra
b0af318 
    
<!-- Please provide a concise, informative and self-explanatory title.
-->
<!-- Don't put issue numbers in the title. Put it in the Description
below. -->
<!-- For example, instead of "Fixes #12345", use "Add a new method to
multiply two integers" -->

### 📚 Description

<!-- Describe your changes here in detail. -->
<!-- Why is this change required? What problem does it solve? -->
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example "Fixes #12345". -->
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appropriately. -->

"The" exceptional Jordan algebra is a 27 dimensional algebra defined as
the $3 \times 3$ self-adjoint matrices over the octonions. This is an
important Jordan algebra as it is used to construct the simple Lie
group/algebra of type $F_4$.

Fixes #32940.

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x
]`. -->

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation accordingly.

### ⌛ Dependencies

- #35630 used in the construction

<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
    
URL: #35629
Reported by: Travis Scrimshaw
Reviewer(s): Frédéric Chapoton, Matthias Köppe, Travis Scrimshaw
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Implement the exceptional Jordan algebra tscrim/sage
Implement the octonions tscrim/sage
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