made signature utilities robust

Project.toml

@@ -1,7 +1,7 @@
 name = "DirectSum"
 uuid = "22fd7b30-a8c0-5bf2-aabe-97783860d07c"
 authors = ["Michael Reed"]
-version = "0.8.11"
+version = "0.8.12"
 
 [deps]
 ComputedFieldTypes = "459fdd68-db75-56b8-8c15-d717a790f88e"

src/DirectSum.jl

@@ -20,7 +20,7 @@ module DirectSum
 export TensorBundle, Signature, DiagonalForm, Manifold, Submanifold, ℝ, ⊕, mdims
 import Base: getindex, convert, @pure, +, *, ∪, ∩, ⊆, ⊇, ==
 import LinearAlgebra, AbstractTensors
-import LinearAlgebra: det, rank
+import LinearAlgebra: det, rank, isdiag
 using Leibniz, ComputedFieldTypes
 
 ## Manifold{N}
@@ -36,7 +36,7 @@ import Leibniz: printlabel, supermanifold, shift_indices, shift_indices!, printi
 import Leibniz: symmetricmask, parityleft, parityright, paritylefthodge, combine
 import Leibniz: parityrighthodge, parityclifford, parityconj, parityreverse, parityinvolute
 import Leibniz: parityrightnull, parityleftnull, parityrightnullpre, parityleftnullpre
-import Leibniz: hasconformal, parval, TensorTerm, mixed, subs, sups, vio
+import Leibniz: hasconformal, parval, TensorTerm, mixed, subs, sups, vio, gdims
 
 import Leibniz: grade, order, options, metric, polymode, dyadmode, diffmode, diffvars
 import Leibniz: pseudograde, hasinf, hasorigin, norm, indices, isbasis, Bits, bits, ≅
@@ -214,6 +214,7 @@ end
 #@pure Submanifold{M}() where M = Submanifold{M isa Int ? Submanifold(M) : M,rank(M)}()
 @pure Submanifold{V,N}() where {V,N} = Submanifold{V,N}(UInt(1)<<N-1)
 @pure Submanifold{M,N}(b::UInt) where {M,N} = Submanifold{M,N,b}()
+@pure Submanifold{M,N}(b::Submanifold{M,N}) where {M,N} = b
 Submanifold{M,N}(b::Values{N}) where {M,N} = Submanifold{M,N}(bit2int(indexbits(mdims(M),b)))
 Submanifold{M}(b::UnitRange) where M = Submanifold{M,length(b)}(Values(b...))
 Submanifold{M}(b::Vector) where M = Submanifold{M,length(b)}(Values(b...))
@@ -243,17 +244,27 @@ for t ∈ (Any,Integer)
  elseif typeof(M)<:Int
  1
  else
- val = M[indices(S)[i]]
- typeof(M)<:Signature ? (val ? -1 : 1) : val
+ ind = indices(S)
+ val = M[ind[i]]
+ if typeof(M)<:Signature
+ val ? -1 : 1
+ else
+ typeof(val)<:Values ? val[Values(ind...)] : val
+ end
  end
  end
 end
 @inline getindex(vs::Submanifold,i::Vector) = [getindex(vs,j) for j ∈ i]
 @inline getindex(vs::Submanifold,i::UnitRange{Int}) = [getindex(vs,j) for j ∈ i]
 @inline function getindex(::Submanifold{M,N,S} where N,i::Colon) where {M,S}
  typeof(M)<:Int && (return ones(Int,M))
- val = M[indices(S)]
- typeof(M)<:Signature ? [v ? -1 : 1 for v ∈ val] : val
+ ind = indices(S)
+ val = M[ind]
+ if typeof(M)<:Signature
+ [v ? -1 : 1 for v ∈ val]
+ else
+ eltype(val) <: Values ? getindex.(val,Ref(Values(ind...))) : val
+ end
 end
 
 function Base.iterate(r::Submanifold, i::Int=1)
@@ -281,7 +292,13 @@ function Base.show(io::IO,s::Submanifold{V,NN,S}) where {V,NN,S}
  hasorigin(s) && print(io,vio[2])
  ind = indices(S)
  for k ∈ hasinf(s)+hasorigin(s)+1+(d<0 ? abs(d) : 0):NM
- print(io,k ∈ ind ? sig(M,k) : '_')
+ met = if k ∈ ind
+ metr = sig(s,findfirst(x->x==k,ind))
+ typeof(metr)==Bool ? metr ? '-' : '+' : metr
+ else
+ '_'
+ end
+ print(io,met)
  printsep(io,M,k,NM)
  end
  d>0 && print(io,[((C>0)⊻!polymode(s) ? sups : subs)[x-NM] for x ∈ ind[N+1:N+abs(d)]]...)
@@ -393,6 +410,7 @@ Single(v::Complex) = Single{Submanifold(0)}(v)
 @pure Single{V}(b::Submanifold{V,G}) where {V,G} = Single{V,G,b,Int}(1)
 Single{V}(v::T) where {V,T} = Single{V,0,Submanifold{V}(),T}(v)
 Single{V}(v::S) where S<:TensorTerm where V = v
+Single{V}(v::Tuple{UInt,T}) where {V,T} = @inbounds Single{V}(v[2],Submanifold{V}(v[1]))
 Single{V,G,B}(v::T) where {V,G,B,T} = Single{V,G,B,T}(v)
 Single(v,b::S) where S<:TensorTerm{V} where V = Single{V}(v,b)
 Single{V}(v,b::S) where S<:TensorAlgebra where V = v*b
@@ -455,7 +473,10 @@ end
 
 for M ∈ (:Signature,:DiagonalForm,:Submanifold)
  @eval begin
- @inline (V::$M)(s::LinearAlgebra.UniformScaling{T}) where T = Single{V}(T<:Bool ? (s.λ ? 1 : -1) : s.λ,getbasis(V,(one(UInt)<<(mdims(V)-diffvars(V)))-1))
+ @inline function (V::$M)(s::LinearAlgebra.UniformScaling{T}) where T
+ b = getbasis(V,(one(UInt)<<(mdims(V)-diffvars(V)))-1)
+ T<:Bool ? b : Single{V}(s.λ,b)
+ end
  (W::$M)(b::Single) = Single{W}(value(b),W(basis(b)))
  ==(::Type{<:$M}, ::Type{Union{}}) = false
  end
@@ -607,6 +628,6 @@ end
 include("generic.jl")
 include("operations.jl")
 include("basis.jl")
-#include("e.jl")
+include("grade.jl")
 
 end # module

src/basis.jl

@@ -223,9 +223,9 @@ end=#
 const Λ0 = Λ{Submanifold(0)}()
 const Λ0S = Λ{ℝ0}()
 
-for V ∈ (:Int,:Signature,:DiagonalForm)
+for V ∈ (:Int,:Signature,:DiagonalForm,:MetricTensor)
  @eval const $(Symbol(:algebra_cache_,V)) = Vector{Vector{Dict{UInt,Vector{Dict{UInt,Λ}}}}}[]
- @eval @pure getalgebra(V::$V) = getalgebra(Submanifold(V))
+ V≠:MetricTensor && @eval @pure getalgebra(V::$V) = getalgebra(Submanifold(V))
 end
 @eval begin
  @pure function getalgebra(n::Int,m::Int,s,S::UInt,vs::Type,f::Int=0,d::Int=0)
@@ -239,6 +239,8 @@ end
  algebra_cache_Signature
  elseif vs <: DiagonalForm
  algebra_cache_DiagonalForm
+ else
+ algebra_cache_MetricTensor
  end
  for F ∈ length(alc)+1:f1
  push!(alc,Vector{Dict{UInt,Vector{Dict{UInt,Λ}}}}[])
@@ -379,9 +381,9 @@ for (ExtraBasis,extra) ∈ ((SparseBasis,:sparse),(ExtendedBasis,:extended))
  getextra = Symbol(:get,extra)
  getalg = Symbol(getextra,:_Signature)
  extra_cache = Symbol(extra,:_cache)
- for V ∈ (:Int,:Signature,:DiagonalForm)
+ for V ∈ (:Int,:Signature,:DiagonalForm,:MetricTensor)
  @eval const $(Symbol(extra_cache,:_,V)) = Vector{Vector{Dict{UInt,Vector{Dict{UInt,$ExtraBasis}}}}}[]
- V≠:Int && (@eval @pure $getextra(V::$V) = $getextra(Submanifold(V)))
+ V∉(:Int,:MetricTensor) && (@eval @pure $getextra(V::$V) = $getextra(Submanifold(V)))
  end
  @eval begin
  @pure function $getextra(n::Int,m::Int,s,S::UInt,vs,f::Int=0,d::Int=0)
@@ -393,6 +395,8 @@ for (ExtraBasis,extra) ∈ ((SparseBasis,:sparse),(ExtendedBasis,:extended))
  $(Symbol(extra_cache,:_Signature))
  elseif vs <: DiagonalForm
  $(Symbol(extra_cache,:_DiagonalForm))
+ else
+ $(Symbol(extra_cache,:_MetricTensor))
  end
  for F ∈ length(exc)+1:f1
  push!(exc,Vector{Dict{UInt,Vector{Dict{UInt,$ExtraBasis}}}}[])

src/generic.jl

@@ -57,6 +57,10 @@ end
 
 export isdyadic, isdual, istangent
 
+@pure LinearAlgebra.isdiag(V::Signature) = !hasconformal(V)
+@pure LinearAlgebra.isdiag(::DiagonalForm) = true
+@pure LinearAlgebra.isdiag(::Submanifold{V}) where V = isdiag(V)
+
 @inline value(x::M,T=Int) where M<:TensorBundle = T==Any ? 1 : one(T)
 @inline value(::Submanifold,T=Int) = T==Any ? 1 : one(T)
 @inline value(m::Single,T::DataType=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v

src/grade.jl

@@ -0,0 +1,42 @@
+
+export grade, gdims, Grade
+
+struct Grade{N,G} <: Integer
+ @pure Grade{N,G}() where {N,G} = new{N,G}()
+ @pure Grade{N}(G::Int) where N = new{N,G}()
+ @pure Grade(N::Int,G::Int) = new{N,G}()
+end
+
+Base.show(io::IO,::Grade{N,G}) where {N,G} = print(io,"Λ$G")
+
+Base.convert(::Type{Int},::Grade{N,G}) where {N,G} = G
+Base.convert(::Type{UInt},::Grade{N,G}) where {N,G} = UInt(G)
+
+@pure mdims(::Grade{N}) where N = N
+@pure tdims(::Grade{N}) where N = 1<<N
+@pure grade(::Grade{N,G}) where {N,G} = G
+@pure grades(t::TensorGraded) = Values{1}(Grade(mdims(t),grade(t)))
+
+for fun ∈ (:gdims,:combo,:binomsum,:spinsum,:antisum,:indexbasis)
+ @eval begin
+ @pure $fun(::Grade{N,G}) where {N,G} = $fun(N,G)
+ @pure $fun(::Grade{N,N},::Grade{N,G}) where {N,G} = $fun(N,G)
+ end
+end
+for fun ∈ (:binomial_set,:binomsum_set,:spinsum_set,:antisum_set,:indexbasis_set,:indexeven_set,:indexodd_set,:indexbasis,:indexeven,:indexodd)
+ @eval @pure $fun(::Grade{N,N}) where N = $fun(N)
+end
+
+Base.:+(::Grade{N,G},::Grade{N,F}) where {N,G,F} = Grade{N,G+F}()
+Base.:-(::Grade{N,G},::Grade{N,F}) where {N,G,F} = Grade{N,G-F}()
+
+Base.:+(::Grade{N,G},F::Int) where {N,G} = G+F
+Base.:+(F::Int,::Grade{N,G}) where {N,G} = F+G
+Base.:-(::Grade{N,G},F::Int) where {N,G} = G-F
+Base.:-(F::Int,::Grade{N,G}) where {N,G} = F-G
+
+Base.:(==)(::Grade,::Grade) = false
+Base.:(==)(::Grade{N,G},::Grade{N,G}) where {N,G} = true
+Base.:(==)(::Grade{N,G},F::Int) where {N,G} = G==F
+Base.:(==)(F::Int,::Grade{N,G}) where {N,G} = F==G
+

src/operations.jl

@@ -188,6 +188,7 @@ end
  @inbounds (bi[1], bi[2]>M ? bi[2]-M : bi[2])
 end
 
+@pure (W::Submanifold{Q,M})(b::Zero{V}) where {Q,M,V} = Zero(W)
 @pure function (W::Submanifold{Q,M})(b::Submanifold{V,G,R}) where {Q,M,V,G,R}
  if isbasis(W) && !isbasis(b)
  RS = R&UInt(W)
@@ -297,7 +298,8 @@ for side ∈ (:left,:right)
  end
  @pure function $pg(V::$Q,B,G=count_ones(B))
  ind = indices(B&(UInt(1)<<(mdims(V)-diffvars(V))-1),mdims(V))
- g,c = prod(V[ind]), hasconformal(V) && (B&UInt(3) == UInt(2))
+ gg,c = V[ind], hasconformal(V) && (B&UInt(3) == UInt(2))
+ g = isempty(gg) ? 1 : prod(signbool.(gg))
  $p(0,sum(ind),G,mdims(V)-diffvars(V))⊻c ? -(g) : g
  end
  end
@@ -310,7 +312,8 @@ end
 for Q ∈ (:DiagonalForm,:Submanifold)
  @eval begin
  @pure function paritymetric(V::$Q,B,G=count_ones(B))
- prod(V[indices(B&(UInt(1)<<(mdims(V)-diffvars(V))-1),mdims(V))])
+ g = V[indices(B&(UInt(1)<<(mdims(V)-diffvars(V))-1),mdims(V))]
+ isempty(g) ? 1 : prod(signbool.(g))
  end
  @pure function parityanti(V::$Q,B)
  paritymetric(V,complement(mdims(V),B,diffvars(V),hasinf(V)+hasorigin(V)))
@@ -330,16 +333,20 @@ export complementleftanti, complementrightanti
 @inline complementrightanti(t) = complementright(antimetric(t))
 @inline complementleftanti(t) = complementleft(antimetric(t))
 
+signbool(t::Bool) = t ? -1 : 1
+signbool(t) = t
+
 for side ∈ (:left,:right)
  s,p = Symbol(:complement,side),Symbol(:parity,side)
  h,pg,pn = Symbol(s,:hodge),Symbol(p,:hodge),Symbol(p,:null)
  for (c,p) ∈ ((s,p),(h,pg))
  @eval begin
  @pure function $c(b::Submanifold{V,G,B}) where {V,G,B}
+ $(c≠h ? nothing : side≠:right ? :((!isdiag(V) && !hasconformal(V)) && (return $s(metric(b)))) : :((!isdiag(V) && !hasconformal(V)) && (return reverse(b)*V(LinearAlgebra.I))) )
  d = getbasis(V,complement(mdims(V),B,diffvars(V),$(c≠h ? 0 : :(hasinf(V)+hasorigin(V)))))
  isdyadic(V) && throw(error("Complement for mixed tensors is undefined"))
  v = $(c≠h ? :($pn(V,B,value(d))) : :(value(d)))
- typeof(V)<:Signature ? ($p(b) ? Single{V}(-v,d) : isone(v) ? d : Single{V}(v,d)) : Single{V}($p(b)*v,d)
+ typeof(V)<:Signature ? ($p(b) ? Single{V}(-v,d) : isone(v) ? d : Single{V}(v,d)) : Single{V}(signbool($p(b))*v,d)
  end
  $c(b::Single) = conj(value(b))*$c(basis(b))
  end
@@ -349,15 +356,21 @@ end
 @eval begin
  @pure function metric(b::Submanifold{V,G,B}) where {V,G,B}
  !isbasis(b) && (return metric(V))
+ (!isdiag(V) || hasconformal(V)) && (return complementleft(complementrighthodge(b)))
  isdyadic(V) && throw(error("Complement for mixed tensors is undefined"))
+ hasorigin(b) && !hasinf(b) && (return Zero(V))
+ hasinf(b) && !hasorigin(b) && (return Zero(V))
  p = paritymetric(b)
- typeof(V)<:Signature ? (p ? -b : b ) : Single{V}(p,b)
+ typeof(p)==Bool ? (p ? -b : b ) : Single{V}(p,b)
  end
  metric(b::Single) = value(b)*metric(basis(b))
  @pure function antimetric(b::Submanifold{V,G,B}) where {V,G,B}
+ (!isdiag(V) || hasconformal(V)) && (return antimetric_term(b))
  isdyadic(V) && throw(error("Complement for mixed tensors is undefined"))
+ hasorigin(b) && !hasinf(b) && (return Zero(V))
+ hasinf(b) && !hasorigin(b) && (return Zero(V))
  p = parityanti(b)
- typeof(V)<:Signature ? (p ? -b : b ) : Single{V}(p,b)
+ typeof(p)==Bool ? (p ? -b : b ) : Single{V}(p,b)
  end
  antimetric(b::Single) = value(b)*antimetric(basis(b))
 end