[HN Gopher] Directsum.jl - Abstract tangent bundle vector space ...
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       Directsum.jl - Abstract tangent bundle vector space type operations
        
       Author : DreamScatter
       Score  : 47 points
       Date   : 2020-01-18 18:07 UTC (4 hours ago)
        
 (HTM) web link (github.com)
 (TXT) w3m dump (github.com)
        
       | dan-robertson wrote:
       | I feel like the readme could do with a better introduction. At
       | the moment it seems like weird mix of mathematically technical
       | definitions, code examples (I guess related to api specifics),
       | and some random Julia type-system/size-limit technicalities
       | thrown in too.
       | 
       | But that said, I don't think I know anything about this sort of
       | geometry or algebra so maybe instead I should want a paragraph
       | telling me to give up.
       | 
       | Also is V"++++" the same as S"++++" (or rather, is V the same as
       | S?), this looked like maybe the notation just changed? But like I
       | say, I couldn't really follow the readme so I'm likely wrong
       | here.
        
         | dan-robertson wrote:
         | I found this link which provides a bit of colour and is a bit
         | more readable than the readme:
         | 
         | https://grassmann.crucialflow.com/dev/
        
         | DreamScatter wrote:
         | The difference between V"++++" and S"++++" is that the S"
         | specifically constructs a Signature concrete type, while the V"
         | is for automatically selecting an appropriate type of the
         | VectorBundle category, which is not limited to Signature
         | specifically, making it a more general constructor call.
        
       | DreamScatter wrote:
       | Related: Grassmann.jl - Differential Geometric Algebra -
       | https://news.ycombinator.com/item?id=22076368
        
       | ganzuul wrote:
       | What problem is one solving when this becomes useful? Is it a
       | compressed representation of something?
        
         | DreamScatter wrote:
         | Correct, it is an encoding to represent SubManifold spaces used
         | in the multi-linear Grassmann algebra. It might seem strange on
         | its own, but the advantage it provides in Grassmann.jl is
         | specialized automatic pre-compilation for differential
         | geometric algebras based on a vector bundle manifold. For
         | example, see https://grassmann.crucialflow.com
        
       | aesthesia wrote:
       | I'm not sure I understand how the different types in this library
       | ---Manifold, VectorBundle, SubManifold---correspond to the
       | standard definitions of these mathematical objects. How is a
       | manifold represented here? Can arbitrary manifolds be
       | represented?
        
         | dan-robertson wrote:
         | I think a complication is that there are abstract types and
         | concrete types. The abstract types let you say "give me a
         | tangent bundle where ..." and the concrete types actually
         | implement the thing as eg a vector or a sparse vector or ...
         | 
         | An alternative example would be that in Julia you can talk
         | about abstract vector types of which dense and sparse form
         | disjoint subtypes
        
           | DreamScatter wrote:
           | Indeed, the Manifold{n} type from AbstractTensors.jl
           | (https://github.com/chakravala/AbstractTensors.jl) is defined
           | as an abstract type in Julia. The parameter `n` is used to
           | specify the Manifold dimension, which is locally isomorphic
           | to R^n.
           | 
           | A VectorBundle is another abstract type, which standardizes
           | an encoding format for concrete Signature and DiagonalForm
           | types, or more. SubManifold can select subspaces of a
           | VectorBundle or generally an arbitrary Manifold.
           | 
           | The design of the type system was optimized for algebra
           | interoperability and adaptive subspace precompilation.
        
       | adamnemecek wrote:
       | If this tickles your fancy, check out the bivector.net community.
       | 
       | Check the demo
       | 
       | https://observablehq.com/@enkimute/animated-orbits
       | 
       | Join the discord
       | 
       | https://discord.gg/vGY6pPk
        
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       (page generated 2020-01-18 23:00 UTC)