Merge branch 'polyinvexample'

.gitignore

@@ -1,3 +1,4 @@
 Manifest.toml
 .ipynb_checkpoints/
 docs/build/
+docs/src/generated/

docs/make.jl

@@ -11,6 +11,7 @@ const OUTPUT_DIR = joinpath(@__DIR__, "src", "generated")
 
 example_scripts = [
     "sine.jl",
+    "polynomial_inversion.jl",
 ]
 
 println("Building examples...")
@@ -27,6 +28,7 @@ println("Finished building examples")
 
 example_pages = [
     "Sine function" => "generated/sine.md",
+    "Polynomial inversion" => "generated/polynomial_inversion.md",
 ]
 
 pages = [

examples/polynomial_inversion.jl

@@ -0,0 +1,57 @@
+# # Polynomial inversion
+#
+# This is a DACE example showing polynomial inversion, demonstrating:
+#
+# - How to load DACE.jl
+# - How to initialise the DACE library
+# - How to create a `DA` object
+# - How to create an `AlgebraicVector`
+# - How to invert a Taylor polynomial
+#
+# ## Install dependencies
+#
+# Make sure the required packages are installed
+
+# ```julia
+# using Pkg
+# Pkg.add("https://github.com/chrisdjscott/DACE_jll.jl.git")
+# Pkg.add("https://github.com/chrisdjscott/DACE.jl.git")
+# ```
+
+# ## Using DACE
+#
+# Write
+
+using DACE
+
+# to load DACE functions and objects into our script.
+#
+# Initialise DACE for 10th-order computations in 1 variable
+
+DACE.init(10, 1)
+
+# Initialise `x` as a `DA` object
+
+x = DACE.DA(1)
+
+# Create `y` as `AlgebraicVector` of type `DA` and size 1
+
+y = AlgebraicVector{DA}(1)
+
+# Store the Taylor expansion of `sin(x)` in the first element of `y`
+
+y[1] = sin(x)
+
+# Invert the Taylor polynomial
+
+inv_y = DACE.invert(y)
+
+# Finally compare the polynomial inversion of `sin(x)`
+
+println("polynomial inversion of sin(x)")
+println(inv_y)
+
+# with `asin(x)`
+
+println("asin(x)")
+println(asin(x))