From d90aa897931d1b8f048dafe91448223f49c46b85 Mon Sep 17 00:00:00 2001
From: Bumblebee00 <mikamatto03@gmail.com>
Date: Fri, 21 Mar 2025 09:05:18 +0100
Subject: [PATCH 1/2] added complex sum to the function _linear_expansion

---
 src/linear_algebra.jl | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/src/linear_algebra.jl b/src/linear_algebra.jl
index f2e1783ef..af24341cd 100644
--- a/src/linear_algebra.jl
+++ b/src/linear_algebra.jl
@@ -262,6 +262,13 @@ function _linear_expansion(t::Equation, x)
     # t.rhs - t.lhs = 0
     return (a₂ - a₁, b₂ - b₁, islinear)
 end
+
+"""
+works with t of two types:
+x (variable, type Num)
+or
+b (constant)
+"""
 trivial_linear_expansion(t, x) = isequal(t, x) ? (1, 0, true) : (0, t, true)
 
 is_expansion_leaf(t) = !iscall(t) || (operation(t) isa Operator)
@@ -294,6 +301,12 @@ function _linear_expansion(t, x)
             b₁ += b₂
         end
         return (a₁, b₁, true)
+    elseif op === Complex{Real}
+        # x+2im is interpreted as Complex{Real}(x, 2)
+        real_part, im_part = arguments(t)
+        a_real, b_real, islinear_real = linear_expansion(real_part, x)
+        a_im, b_im, islinear_im = linear_expansion(im_part, x)
+        return (a_real + a_im * im, b_real + b_im * im, islinear_real && islinear_im)
     elseif op === (-)
         @assert length(args) == 1
         a, b, islinear = linear_expansion(args[1], x)

From 1da658767f013d75ccef498fb9d4cb613a104f85 Mon Sep 17 00:00:00 2001
From: Bumblebee00 <mikamatto03@gmail.com>
Date: Sat, 22 Mar 2025 15:57:15 +0100
Subject: [PATCH 2/2] added tests for linear_expansion for input with complex
 numbers

---
 test/linear_solver.jl | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/test/linear_solver.jl b/test/linear_solver.jl
index 684934d20..ec0d5810b 100644
--- a/test/linear_solver.jl
+++ b/test/linear_solver.jl
@@ -85,3 +85,22 @@ a, b, islinear = Symbolics.linear_expansion(D(x) - x, x)
     @variables x y
     @test !Symbolics.linear_expansion(x + z([x, y]), y)[3]
 end
+
+@testset "linear_expansion with imaginary numbers" begin
+    @variables x y
+
+    a, b, islin = Symbolics.linear_expansion(1im*x^2 + 1im*x, x)
+    @test !islin
+    a, b, islin = Symbolics.linear_expansion(2im*x + 1im, x)
+    @test islin && isequal(a, 2im) && isequal(b, 1im)
+    a, b, islin = Symbolics.linear_expansion(1im*x + 1im*y, x)
+    @test islin && isequal(a, 1im) #&& isequal(b, 1im*y)
+    a, b, islin = Symbolics.linear_expansion(1im*x - y,x)
+    @test islin && isequal(a, 1im) && isequal(b, -y)
+
+    @variables xx[1:2] yy[1:2] zz(..)
+    a, b, islin = Symbolics.linear_expansion(zz(1im * xx[2]) + 1im*xx[1], xx[1])
+    @test islin && isequal(a, im) && isequal(b, zz(1im * xx[2]))
+    a, b, islin = Symbolics.linear_expansion(1im * yy[1], xx[1])
+    @test islin && isequal(a, 0) # && isequal(b, yy[1])
+end
\ No newline at end of file