upgraded syntax definitions

Author: chakravala

Project.toml

@@ -1,7 +1,7 @@
 name = "DirectSum"
 uuid = "22fd7b30-a8c0-5bf2-aabe-97783860d07c"
 authors = ["Michael Reed"]
-version = "0.8.13"
+version = "0.8.14"
 
 [deps]
 ComputedFieldTypes = "459fdd68-db75-56b8-8c15-d717a790f88e"
@@ -12,7 +12,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [compat]
 julia = "1"
-Leibniz = "0.2"
+Leibniz = "0.2,0.3"
 AbstractTensors = "0.8.3"
 ComputedFieldTypes = "1"
 

src/DirectSum.jl

@@ -39,11 +39,11 @@ import Leibniz: parityrightnull, parityleftnull, parityrightnullpre, parityleftn
 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, ≅
+import Leibniz: pseudograde, hasinf, hasorigin, norm, indices, isbasis, ≅
 import Leibniz: isdyadic, isdual, istangent, involute, basis, alphanumv, alphanumw
 
 import Leibniz: algebra_limit, sparse_limit, cache_limit, fill_limit
-import Leibniz: binomial, binomial_set, binomsum, binomsum_set, lowerbits, expandbits
+import Leibniz: binomial, gdimsall, binomsum, binomcumsum, lowerbits, expandbits
 import Leibniz: bladeindex, basisindex, indexbasis, indexbasis_set, loworder, intlog
 import Leibniz: promote_type, mvec, svec, intlog, insert_expr, indexparity!
 
@@ -52,6 +52,8 @@ import Leibniz: promote_type, mvec, svec, intlog, insert_expr, indexparity!
 """
     TensorBundle{n,ℙ,g,ν,μ} <: Manifold{n}
 
+A manifold representing the space of tensors with a given metric and basis for projection.
+
 Let `n` be the rank of a `Manifold{n}`.
 The type `TensorBundle{n,ℙ,g,ν,μ}` uses *byte-encoded* data available at pre-compilation, where
 `ℙ` specifies the basis for up and down projection,
@@ -62,26 +64,67 @@ Lastly, `ν` is the number of tangent variables.
 abstract type TensorBundle{n,Options,Metrics,Vars,Diff,Name} <: Manifold{n,Int} end
 rank(::TensorBundle{n}) where n = n
 mdims(M::TensorBundle) = rank(M)
+# Return the manifold dimension (i.e., rank) of a tensor bundle.
+
+"""
+    tensorhash(d, o; c=0, C=0) -> Int
 
-@pure doc2m(d,o,c=0,C=0) = (1<<(d-1))|(1<<(2*o-1))|(c<0 ? 8 : (1<<(3*c-1)))|(1<<(5*C-1))
+Compute a unique integer representation for a set of options.
 
-const names_cache = NTuple{4,String}[]
-function names_index(a::NTuple{4,String})
-    if a ∈ names_cache
-        findfirst(x->x==a,names_cache)
-    else
-        push!(names_cache,a)
-        length(names_cache)
+# Arguments:
+- `d`: Number of tangent variables (corresponds to `ν`).
+- `o`: Order of Leibniz-Taylor monomials multiplicity limit (corresponds to `μ`).
+- `c`: Coefficient used to specify the metric (corresponds to `g`). Defaults to 0.
+- `C`: Additional coefficient. Defaults to 0.
+
+# Returns
+A unique integer representation that can be used as a cache key.
+"""
+@pure function tensorhash(d,o,c=0,C=0)
+    (1<<(d-1))|(1<<(2*o-1))|(c<0 ? 8 : (1<<(3*c-1)))|(1<<(5*C-1))
+end
+
+const namecache = NTuple{4,String}[]
+
+"""
+    nameindex(a::NTuple{4, String}) -> Int
+
+Get a unique index for a set of name options, based on a cached result.
+"""
+function nameindex(a::NTuple{4,String})
+    if a ∈ namecache # check if options are in cache
+        findfirst(x->x==a,namecache)
+    else # cache the options and add them to the list
+        push!(namecache,a)
+        length(namecache)
     end
 end
-@pure names_index(V::T) where T<:TensorBundle{N,M,S,F,D,Q} where {N,M,S,F,D} where Q = Q
-@pure names_index(V::T) where T<:Manifold = names_index(supermanifold(V))
-@pure names_index(V::Int) = 1
-@pure namelist(V) = names_cache[names_index(V)]
 
-# vector and co-vector prefix
-names_index(pre)
-names_index(PRE)
+# initialize vector and co-vector prefix
+nameindex(pre)
+nameindex(PRE)
+
+"""
+    nameindex(V::T) -> Int
+
+Returns the name index for `V` when `V` is a `TensorBundle` or `Manifold`.
+"""
+@pure nameindex(V::T) where T<:TensorBundle{N,M,S,F,D,Q} where {N,M,S,F,D} where Q = Q
+@pure nameindex(V::T) where T<:Manifold = nameindex(supermanifold(V))
+
+"""
+    nameindex(V::Int) -> Int
+
+Returns a default name index for an integer input.
+"""
+@pure nameindex(V::Int) = 1
+
+"""
+    namelist(V) -> String
+
+Get the cached name list for the options specified in `V`.
+"""
+@pure namelist(V) = namecache[nameindex(V)]
 
 ## Signature{N}
 
@@ -92,18 +135,17 @@ end
 @pure Signature{N,M,S,F,D}() where {N,M,S,F,D} = Signature{N,M,S,F,D,1}()
 @pure Signature{N,M,S}() where {N,M,S} = Signature{N,M,S,0,0}()
 @pure Signature{N,M}(b::BitArray{1},f=0,d=0) where {N,M} = Signature{N,M,bit2int(b[1:N]),f,d}()
-@pure Signature{N,M}(b::Array{Bool,1},f=0,d=0) where {N,M} = Signature{N,M}(convert(BitArray{1},b),f,d)
+@pure Signature{N,M}(b::Vector{Bool},f=0,d=0) where {N,M} = Signature{N,M}(convert(BitArray{1},b),f,d)
 @pure Signature{N,M}(s::String) where {N,M} = Signature{N,M}([k=='-' for k∈s])
 @pure Signature(str::String) = Signature{length(str)}(str)
-@pure Signature(n::Int,d::Int=0,o::Int=0,s::UInt=zero(UInt)) = Signature{n,doc2m(d,o),s}()
-
+@pure Signature(n::Int,d::Int=0,o::Int=0,s::UInt=zero(UInt)) = Signature{n,tensorhash(d,o),s}()
 @pure function Signature{N}(s::String) where N
     ms = match(r"[0-9]+",s)
     if ms ≠ nothing && String(ms.match) == s
         length(s) < 4 && (s *= join(zeros(Int,5-length(s))))
         Signature(parse(Int,s[1]),parse(Int,s[2]),parse(Int,s[3]),UInt(parse(Int,s[4:end])))
     else
-        Signature{N,doc2m(Int(vio[1]∈s),Int(vio[2]∈s))}(replace(replace(s,vio[1]=>'+'),vio[2]=>'-'))
+        Signature{N,tensorhash(Int(vio[1]∈s),Int(vio[2]∈s))}(replace(replace(s,vio[1]=>'+'),vio[2]=>'-'))
     end
 end
 
@@ -118,7 +160,9 @@ Base.firstindex(m::TensorBundle) = 1
 Base.lastindex(m::TensorBundle{N}) where N = N
 Base.length(s::TensorBundle{N}) where N = N
 
+# Type promotion to allow using `Int` with `Signature`
 Base.promote_rule(::Type{Int}, ::Type{<:Signature}) = Signature
+#Base.promote_rule(::Type{Int}, ::Type{<:TensorBundle}) = Signature
 
 @inline sig(s::Bool) = s ? '-' : '+'
 @inline sig(s::Int,k) = '1'
@@ -129,7 +173,7 @@ Base.promote_rule(::Type{Int}, ::Type{<:Signature}) = Signature
 @inline printsep(io,s,k,n) = k≠n && print(io,',')
 
 function Base.show(io::IO,s::Signature)
-    dm = diffmode(s)
+    dm = diffmode(s) # print lead symbols
     print(io,dm>0 ? "T$(sups[dm])⟨" : '⟨')
     C,d = dyadmode(s),diffvars(s)
     N = mdims(s)-(d>0 ? (C<0 ? 2d : d) : 0)
@@ -139,9 +183,9 @@ function Base.show(io::IO,s::Signature)
     print(io,sig.(s[hasinf(s)+hasorigin(s)+1+(d<0 ? abs(d) : 0):N])...)
     d>0 && print(io,[((C>0)⊻!polymode(s) ? sups : subs)[x] for x ∈ 1:abs(d)]...)
     d>0 && C<0 && print(io,[sups[x] for x ∈ 1:abs(d)]...)
-    print(io,'⟩')
+    print(io,'⟩') # print end symbols
     C ≠ 0 ? print(io, C < 0 ? '*' : ''') : nothing
-    names_index(s)>1 && print(io,subs[names_index(s)])
+    nameindex(s)>1 && print(io,subs[nameindex(s)])
 end
 
 ## DiagonalForm{N}
@@ -195,7 +239,7 @@ function Base.show(io::IO,s::DiagonalForm)
     d>0 && C<0 && print(io,[sups[x] for x ∈ 1:abs(d)]...)
     print(io,'⟩')
     C ≠ 0 ? print(io, C < 0 ? '*' : ''') : nothing
-    names_index(s)>1 && print(io,subs[names_index(s)])
+    nameindex(s)>1 && print(io,subs[nameindex(s)])
 end
 
 ## Submanifold{N}
@@ -307,7 +351,7 @@ function Base.show(io::IO,s::Submanifold{V,NN,S}) where {V,NN,S}
     d>0 && C<0 && print(io,[sups[x-NM] for x ∈ ind[N+abs(d)+1:end]]...)
     print(io,'⟩')
     C ≠ 0 ? print(io, C < 0 ? '*' : ''') : nothing
-    names_index(s)>1 && print(io,subs[names_index(s)])
+    nameindex(s)>1 && print(io,subs[nameindex(s)])
     PnV && print(io,'×',length(V))
 end
 

src/basis.jl

@@ -216,7 +216,7 @@ end
     C = V[1]∉('D','C') ? 0 : 1
     length(V) < 5 && (V *= join(zeros(Int,5-length(V))))
     S = UInt(parse(Int,V[5:end]))
-    getalgebra(N,doc2m(parse(Int,V[3]),parse(Int,V[4]),C),C>0 ? flip_sig(N,S) : S)
+    getalgebra(N,tensorhash(parse(Int,V[3]),parse(Int,V[4]),C),C>0 ? flipsign(N,S) : S)
 end=#
 
 # Allocating thread-safe $(2^n)×Submanifold{G,V}
@@ -264,7 +264,7 @@ end
         getalgebra(mdims(M),options(M),metric(M),S,typeof(M),diffvars(M),diffmode(M))
     end
 end
-@pure getalgebra(n::Int,d::Int,o::Int,s,c::Int=0) = getalgebra(n,doc2m(d,o,c),s)
+@pure getalgebra(n::Int,d::Int,o::Int,s,c::Int=0) = getalgebra(n,tensorhash(d,o,c),s)
 @pure getalgebra(n::Int,m::Int,s) = getalgebra(n,m,UInt(s),UInt(1)<<n-1,Signature{n,m,UInt(s),0,0})
 
 
@@ -419,7 +419,7 @@ for (ExtraBasis,extra) ∈ ((SparseBasis,:sparse),(ExtendedBasis,:extended))
         @pure $getextra(V::Int) = $getextra(mdims(V),options(V),metric(V),metric(V),typeof(V),diffvars(V),diffmode(V))
     end
     @eval begin
-        @pure $getextra(n::Int,d::Int,o::Int,s,c::Int=0) = $getalg(n,doc2m(d,o,c),s)
+        @pure $getextra(n::Int,d::Int,o::Int,s,c::Int=0) = $getalg(n,tensorhash(d,o,c),s)
         @pure $getextra(n::Int,m::Int,s) = $getalg(n,m,UInt(s),UInt(1)<<n-1,Signature{n,m,UInt(s),0,0})
     end
 end

src/generic.jl

@@ -12,9 +12,13 @@
 #   https://github.com/chakravala
 #   https://crucialflow.com
 
-export basis, grade, order, options, metric, polymode, dyadmode, diffmode, diffvars
+export basis, grade, order, options, metrichash, polymode, dyadmode, diffmode, diffvars
 export valuetype, value, hasinf, hasorigin, isorigin, norm, indices, tangent, isbasis, ≅
-export pseudograde, pseudoreverse, pseudoinvolute, pseudoclifford
+export pseudograde, pseudoreverse, pseudoinvolute, pseudoclifford, metric
+
+# deprecate
+@pure metric(::T) where T<:TensorBundle{N,M,S} where {N,M} where S = S
+@pure metric(V::Signature,b::UInt) = isodd(count_ones(metric(V)&b)) ? -1 : 1
 
 (M::Signature)(b::Int...) = Submanifold{M}(b)
 (M::DiagonalForm)(b::Int...) = Submanifold{M}(b)
@@ -41,8 +45,10 @@ export pseudograde, pseudoreverse, pseudoinvolute, pseudoclifford
 @pure order(m::Single) = order(basis(m))+order(value(m))
 @pure options(::T) where T<:TensorBundle{N,M} where N where M = M
 @pure options_list(V::M) where M<:Manifold = hasinf(V),hasorigin(V),dyadmode(V),polymode(V)
-@pure metric(::T) where T<:TensorBundle{N,M,S} where {N,M} where S = S
-@pure metric(V::Signature,b::UInt) = isodd(count_ones(metric(V)&b)) ? -1 : 1
+@pure metrichash(::Int) = zero(UInt)
+@pure metrichash(::T) where T<:TensorBundle{N,M,S} where {N,M} where S = S
+@pure metrichash(V::M,b::UInt) where M<:Manifold = PROD(V[indices(b)])
+@pure metrichash(V::Signature,b::UInt) = isodd(count_ones(metric(V)&b)) ? -1 : 1
 @pure polymode(::T) where T<:TensorBundle{N,M} where N where M = _polymode(M)
 @pure dyadmode(::T) where T<:TensorBundle{N,M} where N where M = _dyadmode(M)
 @pure diffmode(::T) where T<:TensorBundle{N,M,S,F,D} where {N,M,S,F} where D = D
@@ -132,21 +138,21 @@ end
 
 # dual involution
 
-@pure flip_sig(N,S::UInt) = UInt(2^N-1) & (~S)
+@pure flipsign(N,S::UInt) = UInt(2^N-1) & (~S)
 
 @pure dual(V::T) where T<:Manifold = isdyadic(V) ? V : V'
 @pure dual(V::T,B,M=Int(rank(V)/2)) where T<:Manifold = ((B<<M)&((1<<rank(V))-1))|(B>>M)
 
 @pure function Base.adjoint(V::Signature{N,M,S,F,D}) where {N,M,S,F,D}
     C = dyadmode(V)
     C < 0 && throw(error("$V is the direct sum of a vector space and its dual space"))
-    Signature{N,doc2m(hasinf(V),hasorigin(V),Int(!Bool(C))),flip_sig(N,S),F,D}()
+    Signature{N,tensorhash(hasinf(V),hasorigin(V),Int(!Bool(C))),flipsign(N,S),F,D}()
 end
 
 @pure function Base.adjoint(V::DiagonalForm{N,M,S,F,D}) where {N,M,S,F,D}
     C = dyadmode(V)
     C < 0 && throw(error("$V is the direct sum of a vector space and its dual space"))
-    DiagonalForm{N,doc2m(hasinf(V),hasorigin(V),Int(!Bool(C))),S,F,D}()
+    DiagonalForm{N,tensorhash(hasinf(V),hasorigin(V),Int(!Bool(C))),S,F,D}()
 end
 
 @pure function Base.adjoint(V::Submanifold{M,N,S}) where {N,M,S}

src/grade.jl

@@ -23,8 +23,8 @@ for fun ∈ (:gdims,:combo,:binomsum,:spinsum,:antisum,:indexbasis)
         @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 = $fun(N)
+for fun ∈ (:gdimsall,:binomcumsum,:spincumsum,:anticumsum,:indexbasis_set,:indexeven_set,:indexodd_set,:indexbasis,:indexeven,:indexodd)
+    @eval @pure Leibniz.$fun(::Grade{N,N}) where N = Leibniz.$fun(N)
 end
 
 Base.:+(::Grade{N,G},::Grade{N,F}) where {N,G,F} = Grade{N,G+F}()

src/operations.jl

@@ -21,13 +21,13 @@ export ⊕, χ, gdims
     D2,O2,C2 = options_list(b)
     ds = (N == M) && (A == B)
     if (D1,O1,C1,D2,O2,C2) == (0,0,0,0,0,0)
-        doc2m(0,0,0)
+        tensorhash(0,0,0)
     elseif (D1,O1,C1,D2,O2,C2) == (0,0,1,0,0,1)
-        doc2m(0,0,1)
+        tensorhash(0,0,1)
     elseif (D1,O1,C1,D2,O2,C2) == (0,0,0,0,0,1)
-        doc2m(0,0,ds ? -1 : 0)
+        tensorhash(0,0,ds ? -1 : 0)
     elseif (D1,O1,C1,D2,O2,C2) == (0,0,1,0,0,0)
-        doc2m(0,0,ds ? -1 : 0)
+        tensorhash(0,0,ds ? -1 : 0)
     else
         throw(error("arbitrary TensorBundle direct-sums not yet implemented"))
     end
@@ -40,13 +40,13 @@ for op ∈ (:+,:⊕)
             D2,O2,C2 = options_list(b)
             NM = N == M
             opt = if (D1,O1,C1,D2,O2,C2) == (0,0,0,0,0,0)
-                doc2m(0,0,0)
+                tensorhash(0,0,0)
             elseif (D1,O1,C1,D2,O2,C2) == (0,0,1,0,0,1)
-                doc2m(0,0,1)
+                tensorhash(0,0,1)
             elseif (D1,O1,C1,D2,O2,C2) == (0,0,0,0,0,1)
-                doc2m(0,0,NM ? (B ≠ flip_sig(N,A) ? 0 : -1) : 0)
+                tensorhash(0,0,NM ? (B ≠ flipsign(N,A) ? 0 : -1) : 0)
             elseif (D1,O1,C1,D2,O2,C2) == (0,0,1,0,0,0)
-                doc2m(0,0,NM ? (A ≠ flip_sig(N,B) ? 0 : -1) : 0)
+                tensorhash(0,0,NM ? (A ≠ flipsign(N,B) ? 0 : -1) : 0)
             else
                 throw(error("arbitrary TensorBundle direct-sums not yet implemented"))
             end
@@ -358,7 +358,7 @@ for field ∈ (false,true)
     args = field ? (:g,) : ()
     @eval begin
         @pure function metric(b::Submanifold{V,G,B},$(args...)) where {V,G,B}
-            !isbasis(b) && (return metric(V))
+            !isbasis(b) && (return metrichash(V)) # can be deprecated
             (!isdiag(V) || hasconformal(V) || $field) && (return complementleft(complementrighthodge(b,$(args...))))
             isdyadic(V) && throw(error("Complement for mixed tensors is undefined"))
             hasorigin(b) && !hasinf(b) && (return Zero(V))