Grassmann.jl

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v1 is the standard basis vector

julia> Zygote.gradient(v->0v, v1)
ERROR: cannot convert from ⟨×××⟩ to ⟨+++---⟩*
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] (::SubManifold{⟨+++---⟩*, 6, 0x000000000000003f})(b::SubManifold{⟨×××⟩, 0, 0x0000000000000000})
    @ DirectSum ~/.julia/packages/DirectSum/XQ4T8/src/operations.jl:231
  [3] interop
    @ ~/.julia/packages/AbstractTensors/f9LPE/src/AbstractTensors.jl:151 [inlined]
  [4] *
    @ ~/.julia/packages/AbstractTensors/f9LPE/src/AbstractTensors.jl:186 [inlined]
  [5] (::ChainRules.var"#times_pullback#1182"{Int64, SubManifold{⟨×××⟩, 1, 0x0000000000000001}, ChainRulesCore.ProjectTo{Number, NamedTuple{(), Tuple{}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}})(Ω̇::SubManifold{⟨×××⟩, 0, 0x0000000000000000})
    @ ChainRules ~/.julia/packages/ChainRules/Tj6lu/src/rulesets/Base/fastmath_able.jl:243
  [6] ZBack
    @ ~/.julia/packages/Zygote/rv6db/src/compiler/chainrules.jl:179 [inlined]
  [7] Pullback
    @ ./REPL[18]:1 [inlined]
  [8] (::typeof(∂(#7)))(Δ::SubManifold{⟨×××⟩, 0, 0x0000000000000000})
    @ Zygote ~/.julia/packages/Zygote/rv6db/src/compiler/interface2.jl:0
  [9] (::Zygote.var"#52#53"{typeof(∂(#7))})(Δ::SubManifold{⟨×××⟩, 0, 0x0000000000000000})
    @ Zygote ~/.julia/packages/Zygote/rv6db/src/compiler/interface.jl:41
 [10] gradient(f::Function, args::SubManifold{⟨×××⟩, 1, 0x0000000000000001})
    @ Zygote ~/.julia/packages/Zygote/rv6db/src/compiler/interface.jl:76
 [11] top-level scope
    @ REPL[18]:1

What's this? I have no idea what you're trying to discuss here.

The README mentions applications through automatic differentiation, but there seem to be some issues with it.

Some examples:

using Grassman, Zygote
basis"3" # this defines (⟨×××⟩, v, v₁, v₂, v₃, v₁₂, v₁₃, v₂₃, v₁₂₃)
Zygote.gradient(v->v^2 ,v₁) # this gives (2v₁,)
Zygote.gradient(v -> 1 * v^2, v₁) # similar error as above

The last two calls should be identical but are not. To be fair, the issue seems to be in DirectSum/AbstractTensors, so I can move the issue to there if you like, though iirc both of those are also your packages.

Grassmann.jl has its own experimental automatic differentiation built-in to the tensor algebra. It is not intended to be used with a separate AD package, but is its own experimental AD design from scratch based on tensor algebra. I don't know about Zygote syntax.

If you want to discuss my experimental AD design, we can do that in private. I no longer like to publicly discuss design details, these type of discussions with me are now a premium feature for private discussion.

interesting. are there any examples of its usage?

fwiw, adding zygote support would increase usability of the package a fair bit for several applications, and i'd be willing to chip in some money for it.

Alright, I will email you to discuss this privately for now.

By the way, you can make all your examples above work just by using a Signature instead of an Int

julia> @basis S"++"
(⟨++⟩, v, v₁, v₂, v₁₂)

julia> Zygote.gradient(v -> 1 * v^2, v₁) # similar error as above
(2v₁,)

julia> Zygote.gradient(v->0v, v1)
(0v,)