fixed #51 fixed #68 fixed #69

Project.toml

@@ -18,7 +18,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 julia = "1"
 Leibniz = "0.0.5"
 DirectSum = "0.5.8"
-AbstractTensors = "0.4.3"
+AbstractTensors = "0.4.8"
 ComputedFieldTypes = "0.1"
 StaticArrays = "0"
 Requires = "1"

paper/paper.tex

@@ -210,7 +210,7 @@ \section{Geometric algebraic product structure}
 	Let $v_\pm^2 = \pm1$ be a basis with $v_\infty = v_++v_-$ and $v_\emptyset = (v_--v_+)/2$
 An embedding space $\mb R^{p+1,q+1}$ carrying the action from the group $O(p+1,q+1)$ then has
 $v_\infty^2 =0$, $v_\emptyset^2 =0$,
-$v_\infty \cdot v_\emptyset = 1$,  and $v_{\infty\emptyset}^2 = 1$ with
+$v_\infty \cdot v_\emptyset = -1$,  and $v_{\infty\emptyset}^2 = 1$ with
 Minkowski plane $v_{\infty\emptyset}$ having the Hestenes-Dirac-Clifford product properties
 \begin{align*}
 	v_{\infty\emptyset}\ominus v_\infty &= -v_\infty, &  v_{\infty\emptyset}\ominus v_\emptyset &= v_\emptyset, \\

src/algebra.jl

@@ -352,6 +352,8 @@ Exterior product as defined by the anti-symmetric quotient Λ≡⊗/~
 
 export ∧, ∨, ⊗
 
+@inline ∧(t) = t
+
 @pure function ∧(a::SubManifold{V},b::SubManifold{V}) where V
     ba,bb = bits(a),bits(b)
     A,B,Q,Z = symmetricmask(V,ba,bb)
@@ -378,7 +380,7 @@ end
 #∧(a::SubManifold{V},b::MultiGrade{V}) where V = MultiGrade{V}(b.v,a*basis(b))
 #∧(a::MultiGrade{V},b::MultiGrade{V}) where V = MultiGrade{V}(a.v*b.v,basis(a)*basis(b))
 
-⊗(a::TensorAlgebra{V},b::TensorAlgebra{V}) where V = a∧b
+⊗(a::A,b::B) where {A<:TensorAlgebra,B<:TensorAlgebra} = a∧b
 
 ## regressive product: (L = grade(a) + grade(b); (-1)^(L*(L-ndims(V)))*⋆(⋆(a)∧⋆(b)))
 
@@ -804,14 +806,16 @@ for (op,eop) ∈ ((:+,:(+=)),(:-,:(-=)))
     end
 end
 
+const FieldsBig = (Fields...,BigFloat,BigInt,Complex{BigFloat},Complex{BigInt},Rational{BigInt})
+
 function generate_sums(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CONJ=:conj,PAR=false)
     if Field == Grassmann.Field
         generate_mutators(:(MArray{Tuple{M},T,1,M}),Number,Expr,SUB,MUL)
     elseif Field ∈ (SymField,:(SymPy.Sym))
         generate_mutators(:(SizedArray{Tuple{M},T,1,1}),Field,set_val,SUB,MUL)
     end
     PAR && (DirectSum.extend_field(eval(Field)); global parsym = (parsym...,eval(Field)))
-    TF = Field ∉ Fields ? :Any : :T
+    TF = Field ∉ FieldsBig ? :Any : :T
     EF = Field ≠ Any ? Field : ExprField
     Field ∉ Fields && @eval begin
         Base.:*(a::F,b::SubManifold{V}) where {F<:$EF,V} = Simplex{V}(a,b)

src/products.jl

@@ -46,7 +46,7 @@ end
 insert_t(x) = Expr(:block,:(t=promote_type(valuetype(a),valuetype(b))),x)
 
 function generate_products(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CONJ=:conj,PAR=false)
-    TF = Field ∉ Fields ? :Any : :T
+    TF = Field ∉ FieldsBig ? :Any : :T
     EF = Field ≠ Any ? Field : ExprField
     generate_sums(Field,VEC,MUL,ADD,SUB,CONJ,PAR)
     @eval begin