From 14b37998c4016f8fbe72febfcc2793f402ab8698 Mon Sep 17 00:00:00 2001
From: Marek Kaluba <kalmar@amu.edu.pl>
Date: Tue, 5 Dec 2023 16:32:28 +0100
Subject: [PATCH] first try on coefficients

---
 src/StarAlgebras.jl |  2 ++
 src/coefficients.jl | 55 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 57 insertions(+)
 create mode 100644 src/coefficients.jl

diff --git a/src/StarAlgebras.jl b/src/StarAlgebras.jl
index aaeadad..11f2912 100644
--- a/src/StarAlgebras.jl
+++ b/src/StarAlgebras.jl
@@ -11,6 +11,8 @@ include("bases.jl")
 include("mstructures.jl")
 include("mtables.jl")
 
+include("coefficients.jl")
+
 include("types.jl")
 include("algebra_elts.jl")
 include("arithmetic.jl")
diff --git a/src/coefficients.jl b/src/coefficients.jl
new file mode 100644
index 0000000..92183eb
--- /dev/null
+++ b/src/coefficients.jl
@@ -0,0 +1,55 @@
+"""
+    implements `Base.keys`, `Base.values`
+"""
+abstract type AbstractCoefficients{V,K} end
+
+struct DiracDelta{V,K} <: AbstractCoefficients{V,K}
+    value::V
+    element::K
+end
+DiracDelta(x) = DiracDelta(1, x)
+Base.getindex(δ::DiracDelta{V,K}, i::K) =
+    ifelse(i == δ.element, δ.value, zero(δ.value))
+
+Base.keys(δ::DiracDelta) = (δ.element,)
+Base.values(δ::DiracDelta) = (δ.value,)
+
+struct SparseCoefficients{V,K,Vv<:AbstractVector{V},Vk<:AbstractVector{K}} <: AbstractCoefficients{V,K}
+    values::Vv
+    basis_elements::Vk
+end
+
+Base.keys(sc::SparseCoefficients) = sc.basis_elements
+Base.values(sc::SparseCoefficients) = sc.values
+
+function SparseCoefficients(
+    values::AbstractVector{V},
+    basis_elements::AbstractVector{K}
+) where {K,V}
+    return SparseCoefficients{V,K,typeof(values),typeof(basis)}(values, basis_elements)
+end
+
+function mul!(
+    ms::MultiplicativeStructure,
+    res::SparseCoefficients,
+    v::AbstractCoefficients,
+    w::AbstractCoefficients,
+)
+    for (a, kv) in pairs(v)
+        for (b, kw) in pairs(w)
+            c = ms[kv, kw]
+            unsafe_append!(res, c => a * b)
+        end
+    end
+    __canonicalize!(res)
+    return res
+end
+
+function unsafe_append!(mc::SparseCoefficients, p::Pair{<:SparseCoefficients,T}) where {T}
+    c, val = p
+    append!(mc.basis_elements, keys(c))
+    for v in values(c)
+        push!(mc.values, val * v)
+    end
+    return mc
+end