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https://github.com/chakravala/leibniz.jl

Tensor algebra utility library

https://github.com/chakravala/leibniz.jl

Science Score: 54.0%

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    Low similarity (7.9%) to scientific vocabulary

Keywords

calculus derivation laplacian math tensor-algebra

Keywords from Contributors

tensor
Last synced: 4 months ago · JSON representation ·

Repository

Tensor algebra utility library

Basic Info
Statistics
  • Stars: 19
  • Watchers: 3
  • Forks: 5
  • Open Issues: 0
  • Releases: 18
Topics
calculus derivation laplacian math tensor-algebra
Created over 6 years ago · Last pushed 5 months ago
Metadata Files
Readme Funding License Citation

README.md

Leibniz.jl

Bit entanglements for tensor algebra derivations and hypergraphs

Build Status Build status Coverage Status codecov.io Gitter Liberapay patrons

Although intended for compatibility use with the Grassmann.jl package for multivariable differential operators and tensor field operations, Leibniz can be used independently.

Extended dual index printing with full alphanumeric characters #62'

To help provide a commonly shared and readable indexing to the user, some print methods are provided: ```julia julia> Leibniz.printindices(stdout,Leibniz.indices(UInt(2^62-1)),false,"v") v₁₂₃₄₅₆₇₈₉₀abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ

julia> Leibniz.printindices(stdout,Leibniz.indices(UInt(2^62-1)),false,"w") w¹²³⁴⁵⁶⁷⁸⁹⁰ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz `` An application of this is inGrassmannandDirectSum`, where dual indexing is used.

Derivation

Generates the tensor algebra of multivariable symmetric Leibniz differentials and interfaces using Reduce, Grassmann to provide the ∇,Δ vector field operators, enabling mixed-symmetry tensors with arbitrary multivariate Grassmann manifolds.

```Julia julia> using Leibniz, Grassmann

julia> V = tangent(ℝ^3,4,3) ⟨+++⟩

julia> V(∇) ∂₁v₁ + ∂₂v₂ + ∂₃v₃

julia> V(∇^2) 0 + 1∂₁∂₁ + 1∂₂∂₂ + 1∂₃∂₃

julia> V(∇^3) 0 + 1∂₁∂₁∂₁v₁ + 1∂₂∂₂∂₂v₂ + 1∂₃∂₃∂₃v₃ + 1∂₂∂₁₂v₁ + 1∂₃∂₁₃v₁ + 1∂₁∂₁₂v₂ + 1∂₃∂₂₃v₂ + 1∂₁∂₁₃v₃ + 1∂₂∂₂₃v₃

julia> V(∇^4) 0.0 + 1∂₁∂₁∂₁∂₁ + 1∂₂∂₂∂₂∂₂ + 1∂₃∂₃∂₃∂₃ + 2∂₁₂∂₁₂ + 2∂₁₃∂₁₃ + 2∂₂₃∂₂₃

julia> ∇^2 == Δ true

julia> ∇, Δ (∂ₖvₖ, ∂ₖ²v) ```

This is an initial undocumented pre-release registration for testing with other packages.

Owner

  • Name: Dream Scatter
  • Login: chakravala
  • Kind: user

computational language algeber 🧐 abstract research mathematician

Citation (CITATION.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Reed"
  given-names: "Michael"
  orcid: "https://orcid.org/0000-0002-8006-7816"
title: "Leibniz.jl"
version: 0.2.9
doi: 10.5281/zenodo.13879405
date-released: 2024-10-02
url: "https://github.com/chakravala/Leibniz.jl"
preferred-citation:
  type: article
  authors:
  - family-names: "Reed"
    given-names: "Michael"
    orcid: "https://orcid.org/0000-0002-8006-7816"
  doi: "10.5281/zenodo.101519786"
  journal: "JuliaCon"
  month: 1
  start: 1 # First page number
  end: 6 # Last page number
  title: "Differential geometric algebra with Leibniz and Grassmann"
  issue: 1
  volume: 1
  year: 2019

GitHub Events

Total
  • Create event: 2
  • Commit comment event: 4
  • Release event: 2
  • Push event: 2
Last Year
  • Create event: 2
  • Commit comment event: 4
  • Release event: 2
  • Push event: 2

Committers

Last synced: almost 2 years ago

All Time
  • Total Commits: 22
  • Total Committers: 2
  • Avg Commits per committer: 11.0
  • Development Distribution Score (DDS): 0.045
Past Year
  • Commits: 0
  • Committers: 0
  • Avg Commits per committer: 0.0
  • Development Distribution Score (DDS): 0.0
Top Committers
Name Email Commits
Michael Reed 1****a 21
Kristoffer Carlsson k****n@c****e 1
Committer Domains (Top 20 + Academic)
chalmers.se: 1

Issues and Pull Requests

Last synced: 5 months ago

All Time
  • Total issues: 0
  • Total pull requests: 2
  • Average time to close issues: N/A
  • Average time to close pull requests: 23 days
  • Total issue authors: 0
  • Total pull request authors: 2
  • Average comments per issue: 0
  • Average comments per pull request: 2.0
  • Merged pull requests: 1
  • Bot issues: 0
  • Bot pull requests: 0
Past Year
  • Issues: 0
  • Pull requests: 0
  • Average time to close issues: N/A
  • Average time to close pull requests: N/A
  • Issue authors: 0
  • Pull request authors: 0
  • Average comments per issue: 0
  • Average comments per pull request: 0
  • Merged pull requests: 0
  • Bot issues: 0
  • Bot pull requests: 0
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Top Authors
Issue Authors
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  • colemanbroad (1)
  • KristofferC (1)
Top Labels
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bug (1) enhancement (1)

Packages

  • Total packages: 1
  • Total downloads:
    • julia 37 total
  • Total dependent packages: 2
  • Total dependent repositories: 0
  • Total versions: 24
juliahub.com: Leibniz

Tensor algebra utility library

  • Versions: 24
  • Dependent Packages: 2
  • Dependent Repositories: 0
  • Downloads: 37 Total
Rankings
Dependent repos count: 9.9%
Dependent packages count: 16.6%
Average: 18.8%
Stargazers count: 24.1%
Forks count: 24.5%
Last synced: 5 months ago