added spaces to the sorts of forms and vector fields

src/ThDEC.jl

@@ -7,38 +7,64 @@ struct SortError <: Exception
     message::String
 end
 
+@struct_hash_equal struct Space
+    name::Symbol
+    dim::Int
+end
+
+dim(s::Space) = s.dim
+nameof(s::Space) = s.name
+
+struct SpaceLookup
+    default::Space
+    named::Dict{Symbol,Space}
+end
+
 @data Sort begin
     Scalar()
-    Form(dim::Int, isdual::Bool)
-    VField(isdual::Bool)
+    Form(dim::Int, isdual::Bool, space::Space)
+    VField(isdual::Bool, space::Space)
 end
 export Sort, Scalar, Form, VField
 
-const SORT_LOOKUP = Dict(
-    :Form0 => Form(0, false),
-    :Form1 => Form(1, false),
-    :Form2 => Form(2, false),
-    :DualForm0 => Form(0, true),
-    :DualForm1 => Form(1, true),
-    :DualForm2 => Form(2, true),
-    :Constant => Scalar()
-)
+function fromexpr(lookup::SpaceLookup, e, ::Type{Sort})
+    (name, spacename) = @match e begin
+        name::Symbol => (name, nothing)
+        :(Form0{$})
+    end
+    space = @match spacename begin
+        ::Nothing => lookup.default
+        name::Symbol => lookup.named[name]
+    end
+    @match name begin
+        :Form0 => Form(0, false, space),
+        :Form1 => Form(1, false, space),
+        :Form2 => Form(2, false, space),
+        :DualForm0 => Form(0, true, space),
+        :DualForm1 => Form(1, true, space),
+        :DualForm2 => Form(2, true, space),
+        :Constant => Scalar()
+    end
+end
 
 function Base.nameof(s::Scalar)
     :Constant
 end
 
 function Base.nameof(f::Form)
     dual = isdual(f) ? "Dual" : ""
-    Symbol("$(dual)Form$(dim(f))")
+    formname = Symbol("$(dual)Form$(dim(f))")
+    Expr(:curly, formname, dim(space(f)))
 end
 
 const VF = VField
 
 dim(ω::Form) = ω.dim
 isdual(ω::Form) = ω.isdual
+space(ω::Form) = ω.space
 
 isdual(v::VField) = v.isdual
+space(v::VField) = v.space
 
 # convenience functions
 PrimalForm(i::Int) = Form(i, false)
@@ -60,17 +86,23 @@ function Base.show(io::IO, ω::Form)
     print(io, isdual(ω) ? "DualForm($(dim(ω)))" : "PrimalForm($(dim(ω)))")
 end
 
+# TODO: VField
 @nospecialize
 function +(s1::Sort, s2::Sort)
     @match (s1, s2) begin
         (Scalar(), Scalar()) => Scalar()
-        (Scalar(), Form(i, isdual)) ||
-            (Form(i, isdual), Scalar()) => Form(i, isdual)
-        (Form(i1, isdual1), Form(i2, isdual2)) =>
-            if (i1 == i2) && (isdual1 == isdual2)
+        (Scalar(), Form(i, isdual, space)) ||
+            (Form(i, isdual, space), Scalar()) => Form(i, isdual, space)
+        (Form(i1, isdual1, space2), Form(i2, isdual2, space2)) =>
+            if (i1 == i2) && (isdual1 == isdual2) && (space1 == space2)
                 Form(i1, isdual1)
             else
-                throw(SortError("Cannot add two forms of different dimensions/dualities: $((i1,isdual1)) and $((i2,isdual2))"))
+                throw(SortError(
+                    """
+                    Can not add two forms of different dimensions/dualities/spaces:
+                    $((i1,isdual1,space1)) and $((i2,isdual2,space2))
+                    """)
+                )
             end
     end
 end
@@ -83,13 +115,15 @@ end
 # Negation is always valid
 -(s::Sort) = s
 
+# TODO: VField
 @nospecialize
 function *(s1::Sort, s2::Sort)
     @match (s1, s2) begin
         (Scalar(), Scalar()) => Scalar()
-        (Scalar(), Form(i, isdual)) ||
-            (Form(i, isdual), Scalar()) => Form(i, isdual)
-        (Form(_, _), Form(_, _)) => throw(SortError("Cannot scalar multiply a form with a form. Maybe try `∧`??"))
+        (Scalar(), Form(i, isdual, space)) ||
+            (Form(i, isdual, space), Scalar()) => Form(i, isdual)
+        (Form(_, _, _), Form(_, _, _)) =>
+            throw(SortError("Cannot scalar multiply a form with a form. Maybe try `∧`??"))
     end
 end
 
@@ -99,17 +133,20 @@ function as_sub(n::Int)
     join(map(d -> SUBSCRIPT_DIGIT_0 + d, digits(n)))
 end
 
+# TODO: VField
 @nospecialize
 function ∧(s1::Sort, s2::Sort)
     @match (s1, s2) begin
-        (Form(i, isdual), Scalar()) || (Scalar(), Form(i, isdual)) => Form(i, isdual)
-        (Form(i1, isdual), Form(i2, isdual)) =>
-            if i1 + i2 <= 2
-                Form(i1 + i2, isdual)
+        (Form(i, isdual, space), Scalar()) || (Scalar(), Form(i, isdual, space)) =>
+            Form(i, isdual, space)
+        (Form(i1, isdual, space), Form(i2, isdual, space)) => begin
+            if i1 + i2 <= dim(space)
+                Form(i1 + i2, isdual, space)
             else
                 throw(SortError("Can only take a wedge product when the dimensions of the forms add to less than 2: tried to wedge product $i1 and $i2"))
             end
-        _ => throw(SortError("Can only take a wedge product of two forms of the same duality"))
+        end
+        _ => throw(SortError("Can only take a wedge product of two forms of the same duality on the same space"))
     end
 end
 
@@ -124,11 +161,11 @@ end
 function d(s::Sort)
     @match s begin
         Scalar() => throw(SortError("Cannot take exterior derivative of a scalar"))
-        Form(i, isdual) =>
-            if i <= 1
-                Form(i + 1, isdual)
+        Form(i, isdual, space) =>
+            if i < dim(space)
+                Form(i + 1, isdual, space)
             else
-                throw(SortError("Cannot take exterior derivative of a n-form for n >= 1"))
+                throw(SortError("Cannot take exterior derivative of a k-form for k >= n, where n = $(dim(space)) is the dimension of its ambient space"))
             end
     end
 end
@@ -141,13 +178,13 @@ end
 function ★(s::Sort)
     @match s begin
         Scalar() => throw(SortError("Cannot take Hodge star of a scalar"))
-        Form(i, isdual) => Form(2 - i, !isdual)
+        Form(i, isdual, space) => Form(dim(space) - i, !isdual, space)
     end
 end
 
 function Base.nameof(::typeof(★), s)
     inv = isdual(s) ? "⁻¹" : ""
-    Symbol("★$(as_sub(isdual(s) ? 2 - dim(s) : dim(s)))$(inv)")
+    Symbol("★$(as_sub(isdual(s) ? dim(space(s)) - dim(s) : dim(s)))$(inv)")
 end
 
 @nospecialize
@@ -183,15 +220,15 @@ end
 
 function ♭♯(s::Sort)
     @match s begin
-        Form(i, isdual) => Form(i, !isdual)
+        Form(i, isdual, space) => Form(i, !isdual, space)
         _ => throw(SortError("♭♯ is only defined on forms."))
     end
 end
 
 # Δ = ★d⋆d, but we check signature here to throw a more helpful error
 function Δ(s::Sort)
     @match s begin
-        Form(0, isdual) => Form(0, isdual)
+        Form(0, isdual, space) => Form(0, isdual, space)
         _ => throw(SortError("Δ is not defined for $s"))
     end
 end