improved interoperability for non-metric algebras

.travis.yml

@@ -16,7 +16,7 @@ jobs:
       julia: 1.5
       os: linux
       script:
-        - julia --project=docs/ -e 'using Pkg; Pkg.add("Documenter"); Pkg.add("DirectSum"); Pkg.add("AbstractTensors"); Pkg.add("Leibniz"); Pkg.add("Adapode"); Pkg.add("StaticArrays"); Pkg.develop(PackageSpec(path=pwd()))'
+        - julia --project=docs/ -e 'using Pkg; Pkg.add("Documenter"); Pkg.add("DirectSum"); Pkg.add("AbstractTensors"); Pkg.add("Leibniz"); Pkg.add("StaticArrays"); Pkg.develop(PackageSpec(path=pwd()))'
         - julia --project=docs/ docs/make.jl
       after_success: skip
 notifications:

docs/make.jl

@@ -1,11 +1,11 @@
 #   This file is part of Grassmann.jl. It is licensed under the GPL license
 #   Grassmann Copyright (C) 2019 Michael Reed
 
-using Documenter, AbstractTensors, DirectSum, Leibniz, Grassmann, Adapode, StaticArrays
+using Documenter, AbstractTensors, DirectSum, Leibniz, Grassmann, StaticArrays
 
 makedocs(
     # options
-    modules = [AbstractTensors,DirectSum,Leibniz,Grassmann,Adapode],
+    modules = [AbstractTensors,DirectSum,Leibniz,Grassmann],#Adapode],
     doctest = false,
     format = Documenter.HTML(prettyurls = get(ENV, "CI", nothing) == "true"),
     sitename = "Grassmann.jl",

docs/src/library.md

@@ -5,5 +5,5 @@ Pages = ["library.md"]
 ```
 
 ```@autodocs
-Modules = [AbstractTensors, DirectSum, Grassmann, Leibniz, Adapode]
+Modules = [AbstractTensors, DirectSum, Grassmann, Leibniz]
 ```

src/Grassmann.jl

@@ -26,7 +26,7 @@ import AbstractTensors: vector, isvector, bivector, isbivector, volume, isvolume
 import Leibniz: algebra_limit, sparse_limit, cache_limit, fill_limit
 import Leibniz: binomial, binomial_set, binomsum, binomsum_set, lowerbits, expandbits
 import Leibniz: bladeindex, basisindex, indexbasis, indexbasis_set, loworder, intlog
-import Leibniz: promote_type, mvec, svec, intlog, insert_expr
+import Leibniz: promote_type, mvec, svec, intlog, insert_expr, supermanifold
 
 include("multivectors.jl")
 include("parity.jl")
@@ -233,7 +233,7 @@ end
 initpoints(P::T) where T<:AbstractVector = Chain{ℝ2,1}.(1.0,P)
 initpoints(P::T) where T<:AbstractRange = Chain{ℝ2,1}.(1.0,P)
 @generated function initpoints(P,::Val{n}=Val(size(P,1))) where n
-    Expr(:.,:(Chain{$(SubManifold(ℝ^(n+1))),1}),
+    Expr(:.,:(Chain{$(SubManifold(n+1)),1}),
          Expr(:tuple,1.0,[:(P[$k,:]) for k ∈ 1:n]...))
 end
 
@@ -515,6 +515,8 @@ function __init__()
         Chain{V,1,Chain{W,1}}(m::StaticArrays.SMatrix{M,N}) where {V,W,M,N} = Chain{V,1}(Chain{W,1}.(getindex.(Ref(m),:,StaticArrays.SVector{N}(1:N))))
     end
     @require GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" begin
+        GeometryBasics.Point(t::Values) = GeometryBasics.Point(Tuple(t.v))
+        GeometryBasics.Point(t::Variables) = GeometryBasics.Point(Tuple(t.v))
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorTerm{V} where V = GeometryBasics.Point(value(Chain{V,valuetype(t)}(vector(t))))
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorTerm{V,0} where V = GeometryBasics.Point(zeros(valuetype(t),ndims(V))...)
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorAlgebra = GeometryBasics.Point(value(vector(t)))

src/composite.jl

@@ -343,7 +343,7 @@ function Cramer(N::Int,j=0)
 end
 
 @generated function Base.:\(t::SVector{M,<:Chain{V,1}},v::Chain{V,1}) where {M,V}
-    W = M≠mdims(V) ? M : V; N = M-1
+    W = M≠mdims(V) ? SubManifold(M) : V; N = M-1
     if M == 1 && (V === ℝ1 || V == 1)
         return :(Chain{V,1}(Values(v[1]/t[1][1])))
     elseif M == 2 && (V === ℝ2 || V == 2)
@@ -393,7 +393,7 @@ end
 end
 
 @generated function Base.inv(t::Values{M,<:Chain{V,1}}) where {M,V}
-    W = M≠mdims(V) ? SubManifold(Manifold(M)) : V; N = M-1
+    W = M≠mdims(V) ? SubManifold(M) : V; N = M-1
     N<1 && (return :(_transpose(Values(inv(t[1])),$W)))
     M > mdims(V) && (return :(tt = _transpose(t,$W); tt⋅inv(Chain{$W,1}(t)⋅tt)))
     x,y,xy = Grassmann.Cramer(N)
@@ -413,7 +413,7 @@ end
 end
 
 @generated function grad(T::SVector{M,<:Chain{V,1}}) where {M,V}
-    W = M≠mdims(V) ? SubManifold(Manifold(M)) : V; N = mdims(V)-1
+    W = M≠mdims(V) ? SubManifold(M) : V; N = mdims(V)-1
     M < mdims(V) && (return :(ct = Chain{$W,1}(T); map(↓(V),ct⋅inv(_transpose(T,$W)⋅ct))))
     x,y,xy = Grassmann.Cramer(N)
     val = if iseven(N)
@@ -432,7 +432,7 @@ end
 end
 
 @generated function Base.:\(t::SVector{N,<:Chain{M,1}},v::Chain{V,1}) where {N,M,V}
-    W = M≠mdims(V) ? SubManifold(Manifold(N)) : V
+    W = M≠mdims(V) ? SubManifold(N) : V
     if mdims(M) > mdims(V)
         :(ct=Chain{$W,1}(t); ct⋅(inv(_transpose(t,$W)⋅ct)⋅v))
     else # mdims(M) < mdims(V) ? inv(tt⋅t)⋅(tt⋅v) : tt⋅(inv(t⋅tt)⋅v)
@@ -468,8 +468,8 @@ end
 vandermonde(x,y,V) = (length(x)≠mdims(V) ? _vandermonde(x,V) : vandermonde(x,V))\y
 vandermonde(x,V) = transpose(_vandermonde(x,V))
 _vandermonde(x::Chain,V) = _vandermonde(value(x),V)
-@generated _vandermonde(x::SVector{N},V) where N = :(Chain{$(SubManifold(Manifold(N))),1}(polynom.(x,$(Val(mdims(V))))))
-@generated polynom(x,::Val{N}) where N = Expr(:call,:(Chain{$(SubManifold(Manifold(N))),1}),Expr(:call,:SVector,[:(x^$i) for i ∈ 0:N-1]...))
+@generated _vandermonde(x::SVector{N},V) where N = :(Chain{$(SubManifold(N)),1}(polynom.(x,$(Val(mdims(V))))))
+@generated polynom(x,::Val{N}) where N = Expr(:call,:(Chain{$(SubManifold(N)),1}),Expr(:call,:SVector,[:(x^$i) for i ∈ 0:N-1]...))
 
 function vandermondeinterp(x,y,V,grid) # grid=384
     coef = vandermonde(x,y,V) # Vandermonde ((inv(X'*X))*X')*y
@@ -537,7 +537,7 @@ volumes(m,dets) = value.(abs.(.⋆(dets)))
 volumes(m) = mdims(Manifold(m))≠2 ? volumes(m,detsimplex(m)) : edgelength.(value(m))
 detsimplex(m::Vector{<:Chain{V}}) where V = ∧(m)/factorial(mdims(V)-1)
 detsimplex(m::ChainBundle) = detsimplex(value(m))
-mean(m::Vector{<:Chain}) = sum(m)/length(m)
+mean(m::T) where T<:AbstractVector{<:Chain} = sum(m)/length(m)
 mean(m::T) where T<:SVector = sum(m)/length(m)
 mean(m::Chain{V,1,<:Chain} where V) = mean(value(m))
 barycenter(m::SVector{N,<:Chain}) where N = (s=sum(m);s/s[1])

src/forms.jl

@@ -75,6 +75,8 @@
             end
             return Chain{w,G}(out)
         end
+    elseif V == V''
+        return :(w(Chain{$(V''),G}(value(b))))
     else
         :(throw(error("cannot convert from $V to $w")))
     end
@@ -124,6 +126,8 @@ function (W::SubManifold{Q,M,S})(m::MultiVector{V,T}) where {Q,M,V,S,T}
             end
         end
         return MultiVector{W}(out)
+    elseif V == V''
+        return W((V'')(m))
     else
         throw(error("cannot convert from $(V) to $(W)"))
     end

src/multivectors.jl

@@ -43,9 +43,10 @@ end
 end
 
 @generated function Chain(args::𝕂...) where 𝕂
-    V = length(args)
-    ref = SVector{V}([:(args[$i]) for i ∈ 1:V])
-    :(Chain{$V,1}($(Expr(:call,:(SVector{$V,𝕂}),ref...))))
+    N = length(args)
+    V = SubManifold(N)
+    ref = SVector{N}([:(args[$i]) for i ∈ 1:N])
+    :(Chain{$V,1}($(Expr(:call,:(SVector{$N,𝕂}),ref...))))
 end
 
 Chain(v::Chain{V,G,𝕂}) where {V,G,𝕂} = Chain{V,G}(SVector{binomial(mdims(V),G),𝕂}(v.v))
@@ -55,7 +56,7 @@ export Chain
 getindex(m::Chain,i::Int) = m.v[i]
 getindex(m::Chain,i::UnitRange{Int}) = m.v[i]
 getindex(m::Chain,i::T) where T<:AbstractVector = m.v[i]
-getindex(m::Chain{V,G,<:Chain} where {V,G},i::Int,j::Int) = getindex.(m[i],j)
+getindex(m::Chain{V,G,<:Chain} where {V,G},i::Int,j::Int) = m[i][j]
 setindex!(m::Chain{V,G,T} where {V,G},k::T,i::Int) where T = (m.v[i] = k)
 Base.firstindex(m::Chain) = 1
 @pure Base.lastindex(m::Chain{V,G}) where {V,G} = binomial(mdims(V),G)
@@ -66,8 +67,8 @@ Base.zero(::Chain{V,G,T}) where {V,G,T} = Chain{V,G}(zeros(svec(mdims(V),G,T)))
 transpose_row(t::SVector{N,<:Chain{V}},i,W=V) where {N,V} = Chain{W,1}(getindex.(t,i))
 transpose_row(t::FixedVector{N,<:Chain{V}},i,W=V) where {N,V} = Chain{W,1}(getindex.(t,i))
 transpose_row(t::Chain{V,1,<:Chain},i) where V = transpose_row(value(t),i,V)
-@generated _transpose(t::Values{N,<:Chain{V,1}},W=V) where {N,V} = :(Chain{V,1}(transpose_row.(Ref(t),$(Values{mdims(V)}(1:mdims(V))),Ref(W))))
-@generated _transpose(t::FixedVector{N,<:Chain{V,1}},W=V) where {N,V} = :(Chain{V,1}(transpose_row.(Ref(t),$(Values{mdims(V)}(1:mdims(V))),Ref(W))))
+@generated _transpose(t::Values{N,<:Chain{V,1}},W=V) where {N,V} = :(Chain{V,1}(transpose_row.(Ref(t),$(Values{mdims(V)}(1:mdims(V))),W)))
+@generated _transpose(t::FixedVector{N,<:Chain{V,1}},W=V) where {N,V} = :(Chain{V,1}(transpose_row.(Ref(t),$(Values{mdims(V)}(1:mdims(V))),W)))
 Base.transpose(t::Chain{V,1,<:Chain{V,1}}) where V = _transpose(value(t))
 Base.transpose(t::Chain{V,1,<:Chain{W,1}}) where {V,W} = _transpose(value(t),V)
 
@@ -175,8 +176,8 @@ end
 @pure AbstractTensors.mdims(::Vector{<:Chain{V}}) where V = mdims(V)
 @pure Base.parent(::ChainBundle{V}) where V = isbundle(V) ? parent(V) : V
 @pure Base.parent(::Vector{<:Chain{V}}) where V = isbundle(V) ? parent(V) : V
-#@pure DirectSum.supermanifold(m::ChainBundle{V}) where V = V
-#@pure DirectSum.supermanifold(m::Vector{<:Chain{V}}) where V = V
+@pure DirectSum.supermanifold(m::ChainBundle{V}) where V = V
+@pure DirectSum.supermanifold(m::Vector{<:Chain{V}}) where V = V
 @pure points(t::ChainBundle{p}) where p = isbundle(p) ? p : DirectSum.supermanifold(p)
 @pure points(t::Vector{<:Chain{p}}) where p = isbundle(p) ? p : DirectSum.supermanifold(p)
 @pure points(t::Chain{p}) where p = isbundle(p) ? p : DirectSum.supermanifold(p)