From 08bb5679ed2006c1713dba35ac2b022431dafaa3 Mon Sep 17 00:00:00 2001
From: Orjan Ameye <orjan.ameye@hotmail.com>
Date: Thu, 6 Aug 2026 15:21:43 +0200
Subject: [PATCH] feat: enhance SLH display with detailed descriptions for S,
 L, and H

---
 src/SLH.jl       | 63 ++++++++++++++++++++++++++++++++++++++++++++++++
 test/test_SLH.jl | 53 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 116 insertions(+)

diff --git a/src/SLH.jl b/src/SLH.jl
index 34bc2d0..78954e2 100644
--- a/src/SLH.jl
+++ b/src/SLH.jl
@@ -202,6 +202,69 @@ Return the Hamiltonian `H` of an SLH object.
 hamiltonian(G::SLH) = G.hamiltonian
 
 
+# ──────────────────────────────────────────────
+# Display
+# ──────────────────────────────────────────────
+
+# `S`, `L` and `H` hold expressions that grow without bound, so they are described
+# rather than printed; the accessors give the operators themselves.
+
+_is_symbolic(x) = x isa SQA.QField || x isa BasicSymbolic || x isa Symbolics.Num
+_is_symbolic(x::Complex) = _is_symbolic(real(x)) || _is_symbolic(imag(x))
+
+function _is_identity(S::AbstractMatrix)
+    for j in axes(S, 2), i in axes(S, 1)
+        x = S[i, j]
+        _is_time_dep(x) && return false
+        (i == j ? _isunit(x) : iszero(x)) || return false
+    end
+    return true
+end
+
+_nterms(x) = x isa SQA.QAdd && hasproperty(x, :arguments) ? length(x.arguments) : 1
+
+_plural(n::Int, noun::AbstractString) = string(n, " ", noun, n == 1 ? "" : "s")
+
+_dims(x) = string(size(x, 1), "×", size(x, 2))
+
+function _describe(x)
+    _is_time_dep(x) && return "time-dependent"
+    iszero(x) && return "0"
+    x isa SQA.QField && return string("symbolic, ", _plural(_nterms(x), "term"))
+    x isa QuantumOpticsBase.AbstractOperator && return string("numeric, ", _dims(x))
+    _is_symbolic(x) && return "symbolic"
+    return sprint(show, x)  # a plain number describes itself
+end
+
+function _describe_scattering(S::AbstractMatrix)
+    _is_identity(S) && return string(_dims(S), " identity")
+    any(_is_time_dep, S) && return string(_dims(S), " time-dependent")
+    return string(_dims(S), " ", _is_symbolic(first(S)) ? "symbolic" : string(eltype(S)))
+end
+
+function _describe_lindblad(L::AbstractVector)
+    n = length(L)
+    any(_is_time_dep, L) && return _plural(n, "time-dependent jump operator")
+    x = first(L)
+    numeric = x isa QuantumOpticsBase.AbstractOperator
+    adjective = numeric ? "numeric " : _is_symbolic(x) ? "symbolic " : ""
+    desc = _plural(n, adjective * "jump operator")
+    notes = numeric ? [_dims(x)] : String[]
+    nzero = count(iszero, L)
+    nzero == 0 || push!(notes, nzero == n ? "all zero" : string(nzero, " zero"))
+    return isempty(notes) ? desc : string(desc, " (", join(notes, ", "), ")")
+end
+
+Base.show(io::IO, ::SLH{N}) where {N} =
+    print(io, "SLH{", N, "} with ", N, N == 1 ? " port" : " ports")
+
+function Base.show(io::IO, ::MIME"text/plain", G::SLH)
+    show(io, G)
+    print(io, "\n  S = ", _describe_scattering(scattering(G)))
+    print(io, "\n  L = ", _describe_lindblad(lindblad(G)))
+    return print(io, "\n  H = ", _describe(hamiltonian(G)))
+end
+
 # ──────────────────────────────────────────────
 # Equality
 # ──────────────────────────────────────────────
diff --git a/test/test_SLH.jl b/test/test_SLH.jl
index b4792b7..ab1105e 100644
--- a/test/test_SLH.jl
+++ b/test/test_SLH.jl
@@ -95,6 +95,59 @@ using Test
         @test iszero(simplify(lindblad(G_cas)[2] - (gv2' * av2)))
     end
 
+    @testset "show" begin
+        @test sprint(show, G_u) == "SLH{1} with 1 port"
+        @test sprint(show, MIME("text/plain"), G_u) ==
+              "SLH{1} with 1 port\n" *
+              "  S = 1×1 identity\n" *
+              "  L = 1 symbolic jump operator\n" *
+              "  H = 0"
+
+        @test sprint(show, MIME("text/plain"), G_u ⊞ G_c) ==
+              "SLH{2} with 2 ports\n" *
+              "  S = 2×2 identity\n" *
+              "  L = 2 symbolic jump operators\n" *
+              "  H = symbolic, 1 term"
+
+        # no equation ever reaches the output, whatever the system size
+        M = 6
+        @variables s[1:M, 1:M]::Complex
+        ops = [gu * au, √(γ) * c, gv * av, gu * au * c' * av, c' * c * av, au * av' * c]
+        G_big = SLH([s[i, j] for i = 1:M, j = 1:M], ops, sum(ops[i]' * ops[i] for i = 1:M))
+        @test sprint(show, MIME("text/plain"), G_big) ==
+              "SLH{6} with 6 ports\n" *
+              "  S = 6×6 symbolic\n" *
+              "  L = 6 symbolic jump operators\n" *
+              "  H = symbolic, 8 terms"
+
+        # passive component: nothing couples to the ports
+        @variables r::Real τ::Real
+        @test sprint(show, MIME("text/plain"), SLH([r τ; τ -r], [0, 0], 0)) ==
+              "SLH{2} with 2 ports\n" *
+              "  S = 2×2 symbolic\n" *
+              "  L = 2 jump operators (all zero)\n" *
+              "  H = 0"
+
+        L_f = FunctionWrapper{typeof(gu' * au),Tuple{Float64}}(t -> gu' * au)
+        @test sprint(show, MIME("text/plain"), SLH(1, L_f, 0 * au)) ==
+              "SLH{1} with 1 port\n" *
+              "  S = 1×1 identity\n" *
+              "  L = 1 time-dependent jump operator\n" *
+              "  H = time-dependent"
+
+        bc = FockBasis(4)
+        a_op = destroy(bc)
+        @test sprint(
+            show,
+            MIME("text/plain"),
+            SLH(1, sparse(a_op), sparse(dagger(a_op) * a_op)),
+        ) ==
+              "SLH{1} with 1 port\n" *
+              "  S = 1×1 identity\n" *
+              "  L = 1 numeric jump operator (5×5)\n" *
+              "  H = numeric, 5×5"
+    end
+
     @testset "numeric type stability" begin
         bc = FockBasis(4)
         a_op = destroy(bc)