From 8c97e5b3f13e01aee4cf46aebe580c010e59bb96 Mon Sep 17 00:00:00 2001
From: Herman Sletmoen <hermansletmoen@gmail.com>
Date: Wed, 9 Oct 2024 22:49:33 +0200
Subject: [PATCH] Taylor expand systems of equations

---
 src/taylor.jl  | 4 +++-
 test/taylor.jl | 3 +++
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/src/taylor.jl b/src/taylor.jl
index eb7c33735..dc3ecd8d1 100644
--- a/src/taylor.jl
+++ b/src/taylor.jl
@@ -104,7 +104,9 @@ true
 ```
 """
 function taylor(f, x, ns; kwargs...)
-    if f isa Equation
+    if f isa AbstractArray
+        return taylor.(f, Ref(x), Ref(ns); kwargs...)
+    elseif f isa Equation
         return taylor(f.lhs, x, ns; kwargs...) ~ taylor(f.rhs, x, ns; kwargs...)
     end
 
diff --git a/test/taylor.jl b/test/taylor.jl
index 3d6363e66..6f995dda2 100644
--- a/test/taylor.jl
+++ b/test/taylor.jl
@@ -43,3 +43,6 @@ eqs = taylor_coeff(substitute(eq, x => x_series), ϵ, 0:3)
 sol = x_coeffs .=> [1, -1//5, -1//25, -1//125] # e.g. https://ekamperi.github.io/mathematics/2020/06/21/perturbation-theory.html#MathJax-Element-39-Frame
 eqs = substitute(eqs, Dict(sol))
 @test all(isequal(eq.lhs, eq.rhs) for eq in eqs)
+
+# system of equations
+@test taylor(exp(im*x) ~ 0, x, 0:5) == taylor([cos(x) ~ 0, sin(x) ~ 0], x, 0:5)