--- a/Manifest.toml	Tue Feb 10 22:41:19 2026 +0100
+++ b/Manifest.toml	Sat Feb 14 23:38:32 2026 +0100
@@ -2,13 +2,19 @@
 
 julia_version = "1.12.4"
 manifest_format = "2.0"
-project_hash = "b34dd02a79a0ac02863ec0bc982b7a29ded57ff3"
+project_hash = "09ffd21aba1eada37be92d01708d2df8356cace2"
 
 [[deps.ANSIColoredPrinters]]
 git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c"
 uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9"
 version = "0.0.1"
 
+[[deps.AbstractPlutoDingetjes]]
+deps = ["Pkg"]
+git-tree-sha1 = "6e1d2a35f2f90a4bc7c2ed98079b2ba09c35b83a"
+uuid = "6e696c72-6542-2067-7265-42206c756150"
+version = "1.3.2"
+
 [[deps.AbstractTrees]]
 git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177"
 uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
@@ -50,6 +56,16 @@
 uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
 version = "0.7.8"
 
+[[deps.ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "67e11ee83a43eb71ddc950302c53bf33f0690dfe"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.12.1"
+weakdeps = ["StyledStrings"]
+
+    [deps.ColorTypes.extensions]
+    StyledStringsExt = "StyledStrings"
+
 [[deps.Compat]]
 deps = ["TOML", "UUIDs"]
 git-tree-sha1 = "9d8a54ce4b17aa5bdce0ea5c34bc5e7c340d16ad"
@@ -146,6 +162,12 @@
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 version = "1.11.0"
 
+[[deps.FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.5"
+
 [[deps.Git]]
 deps = ["Git_LFS_jll", "Git_jll", "JLLWrappers", "OpenSSH_jll"]
 git-tree-sha1 = "824a1890086880696fc908fe12a17bcf61738bd8"
@@ -169,6 +191,18 @@
 uuid = "c27321d9-0574-5035-807b-f59d2c89b15c"
 version = "1.4.0"
 
+[[deps.Hyperscript]]
+deps = ["Test"]
+git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
+uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
+version = "0.0.5"
+
+[[deps.HypertextLiteral]]
+deps = ["Tricks"]
+git-tree-sha1 = "d1a86724f81bcd184a38fd284ce183ec067d71a0"
+uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
+version = "1.0.0"
+
 [[deps.IOCapture]]
 deps = ["Logging", "Random"]
 git-tree-sha1 = "0ee181ec08df7d7c911901ea38baf16f755114dc"
@@ -316,6 +350,11 @@
 uuid = "6f1432cf-f94c-5a45-995e-cdbf5db27b0b"
 version = "3.5.0"
 
+[[deps.MIMEs]]
+git-tree-sha1 = "c64d943587f7187e751162b3b84445bbbd79f691"
+uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
+version = "1.1.0"
+
 [[deps.MacroTools]]
 git-tree-sha1 = "1e0228a030642014fe5cfe68c2c0a818f9e3f522"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
@@ -416,6 +455,12 @@
 uuid = "32113eaa-f34f-5b0d-bd6c-c81e245fc73d"
 version = "0.2.15"
 
+[[deps.PlutoUI]]
+deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "Downloads", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
+git-tree-sha1 = "3ac7038a98ef6977d44adeadc73cc6f596c08109"
+uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+version = "0.7.79"
+
 [[deps.PrecompileTools]]
 deps = ["Preferences"]
 git-tree-sha1 = "07a921781cab75691315adc645096ed5e370cb77"
@@ -459,6 +504,11 @@
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 version = "1.11.0"
 
+[[deps.Reexport]]
+git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
+uuid = "189a3867-3050-52da-a836-e630ba90ab69"
+version = "1.2.2"
+
 [[deps.RegistryInstances]]
 deps = ["LazilyInitializedFields", "Pkg", "TOML", "Tar"]
 git-tree-sha1 = "ffd19052caf598b8653b99404058fce14828be51"
@@ -663,6 +713,11 @@
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.11.3"
 
+[[deps.Tricks]]
+git-tree-sha1 = "311349fd1c93a31f783f977a71e8b062a57d4101"
+uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
+version = "0.1.13"
+
 [[deps.Tullio]]
 deps = ["DiffRules", "LinearAlgebra", "Requires"]
 git-tree-sha1 = "972698b132b9df8791ae74aa547268e977b55f68"
@@ -686,6 +741,11 @@
 uuid = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
 version = "1.6.0"
 
+[[deps.URIs]]
+git-tree-sha1 = "bef26fb046d031353ef97a82e3fdb6afe7f21b1a"
+uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
+version = "1.6.1"
+
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

--- a/Project.toml	Tue Feb 10 22:41:19 2026 +0100
+++ b/Project.toml	Sat Feb 14 23:38:32 2026 +0100
@@ -4,7 +4,7 @@
 version = "0.1.5"
 
 [workspace]
-projects = ["test", "docs", "benchmark"]
+projects = ["test", "docs", "benchmark", "notebooks"]
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/notebooks/Project.toml	Sat Feb 14 23:38:32 2026 +0100
@@ -0,0 +1,4 @@
+[deps]
+Diffinitive = "5a373a26-915f-4769-bcab-bf03835de17b"
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/notebooks/display_examples_nb.jl	Sat Feb 14 23:38:32 2026 +0100
@@ -0,0 +1,377 @@
+### A Pluto.jl notebook ###
+# v0.20.21
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 1f8a7cfa-94cc-41bf-a8c8-2dc5218741e0
+begin
+	using Pkg
+	Pkg.activate(".")
+	
+	using Diffinitive
+	using Diffinitive.Grids
+	using Diffinitive.LazyTensors
+	using Diffinitive.SbpOperators
+	using PlutoUI
+	using StaticArrays
+end
+
+# ╔═╡ 885c60d7-d33c-4741-ae49-6a57510ec7b5
+md"""
+# Display tests
+"""
+
+# ╔═╡ 9ee3372a-e78d-4f74-84ce-e04208d1558d
+repl_show(v) = repr(MIME("text/plain"), v) |> println
+
+# ╔═╡ 51c02ced-f684-417f-83f1-cade4edda43f
+md"""
+Common julia objects to compare with:
+"""
+
+# ╔═╡ 25c90528-22cd-41ca-8572-ccd946928318
+1 |> repl_show
+
+# ╔═╡ e7f3e466-9833-428c-99ad-20bc9d88d951
+[1,1] |> repl_show
+
+# ╔═╡ 2e74f9b5-5b4f-4887-8a30-4655d560a45c
+[1;; 2;;] |> repl_show
+
+# ╔═╡ 365524b5-3182-4691-9817-1bbec1492c14
+[1; 2;;] |> repl_show
+
+# ╔═╡ d5725e1b-bc4f-4a95-975d-179c193908c9
+[1; 2;; 3; 4;;] |> repl_show
+
+# ╔═╡ b824ef8d-5026-4861-9a23-45a7939fd38c
+"hej" |> repl_show
+
+# ╔═╡ fbe365a2-f95e-4297-8326-c18d22932869
+Dict("A" => 1, "B"=> 2) |> repl_show
+
+# ╔═╡ 56670aff-0343-41cb-a653-35a61376dda4
+1//2 |> repl_show
+
+# ╔═╡ b5a6491e-a93e-4058-8ceb-be1dc4d4c100
+BigInt(30) |> repl_show
+
+# ╔═╡ 828d57a1-ee58-4204-8050-78127821a4c6
+1:10 |> repl_show
+
+# ╔═╡ 127d34f6-69f7-4082-a74b-0be86942f153
+range(0,1,10) |> repl_show
+
+# ╔═╡ c46a278e-a102-4544-82d8-7df816440410
+rand(2,2,2,2) |> repl_show
+
+# ╔═╡ 5aa7079c-8005-47f1-bb82-c35f3aa54b42
+md"""
+## Parameter spaces
+"""
+
+# ╔═╡ 08f493ed-189c-43f3-86f2-95fc475ec0e7
+Interval(1,2) |> repl_show
+
+# ╔═╡ f7244bf7-8266-469f-b07f-30c203d9af48
+md"""
+## Grids
+"""
+
+# ╔═╡ 0e14bd28-5dd1-44c4-abf4-23b70546bd49
+equidistant_grid(0,1,11) |> repl_show
+
+# ╔═╡ fcb74341-6b03-4ada-8f5d-bc245c23679b
+equidistant_grid((0,0),(1,1),10,20) |> repl_show
+
+# ╔═╡ 8dec053b-eaae-463d-800b-b8d89d5d550b
+ZeroDimGrid(@SVector[1,2]) |> repl_show
+
+# ╔═╡ c1172a36-c5d7-47dc-bc79-af0d43a8f6ee
+let
+	x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
+    J((ξ, η)) = @SMatrix[
+        2       1-2η;
+        (2+η)*ξ 3+1/2*ξ^2;
+    ]
+
+	mapped_grid(x̄, J, 10,10) |> repl_show
+end
+
+# ╔═╡ 9c889176-865b-402d-81b5-71957d2878f7
+md"""
+## LazyArrays
+"""
+
+# ╔═╡ 85e8e748-e575-4a29-80c7-22d110578343
+LazyTensors.LazyConstantArray(10, (5,)) |> repl_show
+
+# ╔═╡ 804ad722-9081-4d1d-b0d2-c536a26fe20d
+LazyTensors.LazyFunctionArray((i,j)->10*i+j, (3,4)) |> repl_show
+
+# ╔═╡ a70c689d-0851-497f-938a-e5c92ce59ddb
+md"""
+## LazyTensors
+"""
+
+# ╔═╡ 68c7a1d8-729e-4f38-abf2-26deb7a90cb1
+md"""
+### Basic tensors
+"""
+
+# ╔═╡ 2afde3fe-96ed-4d7e-a79b-fc880e0da268
+LazyTensors.IdentityTensor(5) |> repl_show
+
+# ╔═╡ 5451a071-14ae-47ae-99c5-4d65508d280f
+LazyTensors.IdentityTensor(4,3) |> repl_show
+
+# ╔═╡ b6b06fe9-de16-41ca-ad45-eef6dd038485
+LazyTensors.ScalingTensor(2., (4,3)) |> repl_show
+
+# ╔═╡ d1c8c3a0-76ec-4c32-853e-0471d71e5cf0
+LazyTensors.DiagonalTensor([1,2,3,4]) |> repl_show
+
+# ╔═╡ 6051c144-9982-4bd9-92f9-d0aaf3961872
+LazyTensors.DenseTensor(rand(2,2,2,2), (1,2), (3,4)) |> repl_show
+
+# ╔═╡ 83ed7f7e-c88d-4ee4-a53a-1b91e775ff52
+md"""
+### Simple SBP-operators
+"""
+
+# ╔═╡ 12a9f430-f96b-43f2-bf63-149b5a028fd7
+begin
+	g1 = equidistant_grid(0,1,10)
+	g2 = equidistant_grid((0,0),(1,1),10, 11)
+	x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
+    J((ξ, η)) = @SMatrix[
+        2       1-2η;
+        (2+η)*ξ 3+1/2*ξ^2;
+    ]
+	mg = mapped_grid(x̄, J, 10,10) 
+	stencil_set2 = stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
+	stencil_set4 = stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4)
+end;
+
+# ╔═╡ e44f8d91-1cbf-44be-bef1-40e60c4a777f
+first_derivative(g1, stencil_set2) |> repl_show
+
+# ╔═╡ c378b88a-1d74-44a2-bdc1-b371da478de8
+first_derivative(g1, stencil_set4) |> repl_show
+
+# ╔═╡ 9614cda7-b48c-4925-89b5-113cf514f20f
+first_derivative(g2, stencil_set2, 1) |> repl_show
+
+# ╔═╡ 725e9430-4821-4939-bfef-6c186d2dc500
+first_derivative(g2, stencil_set4, 2) |> repl_show
+
+# ╔═╡ e8ca54a1-a6db-40a1-b44a-73e175894df4
+second_derivative(g1, stencil_set2) |> repl_show
+
+# ╔═╡ 5d1f10fe-f620-469c-822c-55955a5541ad
+second_derivative(g1, stencil_set4) |> repl_show
+
+# ╔═╡ fdc531d4-9d27-41dc-ba79-6febefde223a
+second_derivative(g2, stencil_set2, 1) |> repl_show
+
+# ╔═╡ fff2e04a-357f-4254-996e-d5ccd9ff31f8
+second_derivative(g2, stencil_set4, 2) |> repl_show
+
+# ╔═╡ 959b071e-1ef6-4f29-aa8b-d88bfef80c00
+second_derivative_variable(g1, map(x->2x, g1), stencil_set2) |> repl_show
+
+# ╔═╡ 0a0f7e77-a789-4fb3-a4c2-7853b67788ec
+second_derivative_variable(g1, map(x->2x, g1), stencil_set4) |> repl_show
+
+# ╔═╡ 177e0893-fbb1-4bb5-a108-e5990e943ab7
+ second_derivative_variable(g2, map(x->x[1]+x[2], g2), stencil_set2, 1) |> repl_show
+
+# ╔═╡ f1b6bd54-baf6-4360-aec0-bd8d52497894
+second_derivative_variable(g2, map(x->x[1]+x[2], g2), stencil_set4, 2) |> repl_show
+
+# ╔═╡ a8f8343e-cd6f-451d-a2b3-e5f0f561f8af
+undivided_skewed04(g1,4)[1] |> repl_show
+
+# ╔═╡ 50291998-7194-4a0d-9c19-eacc48b3f5da
+undivided_skewed04(g1,4)[2] |> repl_show
+
+# ╔═╡ 1720af08-85e4-4502-b37e-9fa73008e221
+undivided_skewed04(g2,4,1)[1] |> repl_show
+
+# ╔═╡ 4a72f217-2423-4bc1-8452-eb28dde36689
+undivided_skewed04(g2,4,2)[2] |> repl_show
+
+# ╔═╡ d51b6bd7-0235-4a51-a989-4f7858363d02
+md"""
+### Inner products
+"""
+
+# ╔═╡ 48a28ade-73bb-461d-ab96-82f92ed199c8
+inner_product(g1, stencil_set2) |> repl_show
+
+# ╔═╡ 3c681a63-94a6-4677-aef7-df903c463896
+inner_product(g1, stencil_set4) |> repl_show
+
+# ╔═╡ db735370-153a-40f9-b77f-9f60e30a35c4
+inner_product(g2, stencil_set2) |> repl_show
+
+# ╔═╡ 613ebac7-50bc-424c-8fa2-064b64c93319
+inner_product(g2, stencil_set4) |> repl_show
+
+# ╔═╡ 9e7d7667-960e-491f-8b83-e3b01a0db5b0
+inverse_inner_product(g2, stencil_set4) |> repl_show
+
+# ╔═╡ 29488e48-1d42-4232-9d49-1ee77fb869d8
+md"""
+### Boundary operators
+"""
+
+# ╔═╡ c3005e74-5b96-4b0c-9c57-b7d02968ed94
+boundary_restriction(g1, stencil_set, LowerBoundary()) |> repl_show
+
+# ╔═╡ fd019973-0d54-4e31-b43b-f53a704cb01c
+boundary_restriction(g1, stencil_set, UpperBoundary()) |> repl_show
+
+# ╔═╡ df2e8af0-9ca5-4972-8771-f8bea1591f85
+boundary_restriction(g2, stencil_set, CartesianBoundary{1,LowerBoundary}()) |> repl_show
+
+# ╔═╡ 8e538109-16a1-4af7-a986-9dc1455b7de7
+boundary_restriction(g2, stencil_set, CartesianBoundary{2,UpperBoundary}()) |> repl_show
+
+# ╔═╡ 5f3744a4-72d8-4448-820f-a928bfaaf825
+normal_derivative(g1, stencil_set, LowerBoundary()) |> repl_show
+
+# ╔═╡ 4529b5c4-4905-4fd3-9aaa-5f88faa841c8
+normal_derivative(g1, stencil_set, UpperBoundary()) |> repl_show
+
+# ╔═╡ c3bb0450-a7d5-44c1-9ca9-9e1ecf2db9f8
+normal_derivative(g2, stencil_set, CartesianBoundary{1,LowerBoundary}()) |> repl_show
+
+# ╔═╡ da63e57a-0794-4cd8-9941-ada0e5c1c40e
+normal_derivative(g2, stencil_set, CartesianBoundary{2,UpperBoundary}()) |> repl_show
+
+# ╔═╡ 0b951425-979c-4ac9-8581-f690b729bab4
+md"""
+## Tensor operations
+"""
+
+# ╔═╡ a39bb6e2-f1fe-4206-8ee3-88ff0c075233
+begin
+	Dx = first_derivative(g2, stencil_set2, 1)
+	Dy = first_derivative(g2, stencil_set4, 2)
+
+	v = map(x->sin(x[1]^2+x[2]^2), g2)
+end;
+
+# ╔═╡ 8cd052d9-f40e-4796-aeef-52c02b3bf156
+Dx+Dy |> repl_show
+
+# ╔═╡ 1b1b7d12-50ef-4c4e-9376-a353a56540c3
+Dx∘Dy |> repl_show
+
+# ╔═╡ 57e48b4c-eef6-433e-98a1-1006e844b368
+Dx*v |> repl_show
+
+# ╔═╡ e2bf2649-4770-4f52-9752-b61ce03c6f82
+(Dx+Dy)*v |> repl_show
+
+# ╔═╡ d163d363-853d-4d83-a2d3-f8dd6e8f552d
+(Dx∘Dy)*v |> repl_show
+
+# ╔═╡ 1c38d3f9-1839-468c-a368-4ef101bd4f18
+laplace(g2, stencil_set2) |> repl_show
+
+# ╔═╡ cf84cefb-2dbd-4b8d-880b-47cc350a7c43
+laplace(g2, stencil_set4) |> repl_show
+
+# ╔═╡ 67c73667-1f41-47b5-b59a-459787767f29
+# laplace(mg, stencil_set2) |> repl_show
+
+# ╔═╡ 4634c1a6-0520-4b0f-8d32-a1fdf2ebaea5
+md"""
+## Appendix
+"""
+
+# ╔═╡ 24788161-b29a-450a-bd35-f9c29e7ded9a
+PlutoUI.TableOfContents()
+
+# ╔═╡ Cell order:
+# ╟─885c60d7-d33c-4741-ae49-6a57510ec7b5
+# ╠═9ee3372a-e78d-4f74-84ce-e04208d1558d
+# ╟─51c02ced-f684-417f-83f1-cade4edda43f
+# ╠═25c90528-22cd-41ca-8572-ccd946928318
+# ╠═e7f3e466-9833-428c-99ad-20bc9d88d951
+# ╠═2e74f9b5-5b4f-4887-8a30-4655d560a45c
+# ╠═365524b5-3182-4691-9817-1bbec1492c14
+# ╠═d5725e1b-bc4f-4a95-975d-179c193908c9
+# ╠═b824ef8d-5026-4861-9a23-45a7939fd38c
+# ╠═fbe365a2-f95e-4297-8326-c18d22932869
+# ╠═56670aff-0343-41cb-a653-35a61376dda4
+# ╠═b5a6491e-a93e-4058-8ceb-be1dc4d4c100
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