diff --git a/docs/Manifest.toml b/docs/Manifest.toml
index 510a92fac..99b3d09a0 100644
--- a/docs/Manifest.toml
+++ b/docs/Manifest.toml
@@ -1,5 +1,11 @@
 # This file is machine-generated - editing it directly is not advised
 
+[[Adapt]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "3.3.1"
+
 [[ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
@@ -9,18 +15,80 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.8+0"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.1+0"
+
 [[ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
 path = ".."
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 version = "1.11.1"
 
+[[ChangesOfVariables]]
+deps = ["LinearAlgebra", "Test"]
+git-tree-sha1 = "9a1d594397670492219635b35a3d830b04730d62"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.1"
+
+[[ColorSchemes]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
+git-tree-sha1 = "a851fec56cb73cfdf43762999ec72eff5b86882a"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.15.0"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.0"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.8"
+
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
 git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
 version = "3.40.0"
 
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+
+[[Contour]]
+deps = ["StaticArrays"]
+git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.5.7"
+
+[[DataAPI]]
+git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.9.0"
+
+[[DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.10"
+
+[[DataValueInterfaces]]
+git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
+uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
+version = "1.0.0"
+
 [[Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
@@ -55,16 +123,156 @@ version = "0.25.5"
 deps = ["ArgTools", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 
+[[EarCut_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
+uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
+version = "2.2.3+0"
+
+[[Expat_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
+uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
+version = "2.2.10+0"
+
+[[FFMPEG]]
+deps = ["FFMPEG_jll"]
+git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
+uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
+version = "0.4.1"
+
+[[FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.4.0+0"
+
+[[FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.4"
+
+[[Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
+uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
+version = "2.13.93+0"
+
+[[Formatting]]
+deps = ["Printf"]
+git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
+uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
+version = "0.4.2"
+
+[[FreeType2_jll]]
+deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
+uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
+version = "2.10.4+0"
+
+[[FriBidi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
+uuid = "559328eb-81f9-559d-9380-de523a88c83c"
+version = "1.0.10+0"
+
+[[GLFW_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
+git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
+uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
+version = "3.3.5+1"
+
+[[GR]]
+deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
+git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
+uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
+version = "0.62.1"
+
+[[GR_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
+uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
+version = "0.62.0+0"
+
+[[GeometryBasics]]
+deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
+git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
+uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+version = "0.4.1"
+
+[[Gettext_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
+uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
+version = "0.21.0+0"
+
+[[Glib_jll]]
+deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
+uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
+version = "2.68.3+0"
+
+[[Graphite2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
+uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
+version = "1.3.14+0"
+
+[[Grisu]]
+git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
+uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
+version = "1.0.2"
+
+[[HTTP]]
+deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
+git-tree-sha1 = "14eece7a3308b4d8be910e265c724a6ba51a9798"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "0.9.16"
+
+[[HarfBuzz_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
+git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
+uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
+version = "2.8.1+0"
+
 [[IOCapture]]
 deps = ["Logging"]
 git-tree-sha1 = "377252859f740c217b936cebcd918a44f9b53b59"
 uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
 version = "0.1.1"
 
+[[IniFile]]
+deps = ["Test"]
+git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
+uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
+version = "0.5.0"
+
 [[InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
+[[InverseFunctions]]
+deps = ["Test"]
+git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
+uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
+version = "0.1.2"
+
+[[IrrationalConstants]]
+git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
+uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
+version = "0.1.1"
+
+[[IterTools]]
+git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
+uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
+version = "1.3.0"
+
+[[IteratorInterfaceExtensions]]
+git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
+uuid = "82899510-4779-5014-852e-03e436cf321d"
+version = "1.0.0"
+
 [[JLLWrappers]]
 deps = ["Preferences"]
 git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
@@ -77,6 +285,35 @@ git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.2"
 
+[[JpegTurbo_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
+uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
+version = "2.1.0+0"
+
+[[LAME_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
+uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
+version = "3.100.1+0"
+
+[[LZO_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
+uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
+version = "2.10.1+0"
+
+[[LaTeXStrings]]
+git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
+uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
+version = "1.3.0"
+
+[[Latexify]]
+deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
+git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
+uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+version = "0.15.9"
+
 [[LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
@@ -96,40 +333,175 @@ uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
 [[Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[Libffi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b"
+uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
+version = "3.2.2+0"
+
+[[Libgcrypt_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
+git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
+uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
+version = "1.8.7+0"
+
+[[Libglvnd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
+git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
+uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
+version = "1.3.0+3"
+
+[[Libgpg_error_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
+uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
+version = "1.42.0+0"
+
+[[Libiconv_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
+uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
+version = "1.16.1+1"
+
+[[Libmount_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
+uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
+version = "2.35.0+0"
+
+[[Libtiff_jll]]
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
+uuid = "89763e89-9b03-5906-acba-b20f662cd828"
+version = "4.3.0+0"
+
+[[Libuuid_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
+uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
+version = "2.36.0+0"
+
 [[LinearAlgebra]]
 deps = ["Libdl"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[[LogExpFunctions]]
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
+uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+version = "0.3.5"
+
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[MacroTools]]
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
+uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
+version = "0.5.9"
+
 [[Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
+git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "1.0.3"
+
 [[MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 
+[[Measures]]
+git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
+uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
+version = "0.3.1"
+
+[[Missings]]
+deps = ["DataAPI"]
+git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
+version = "1.0.2"
+
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
 [[MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 
+[[NaNMath]]
+git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+version = "0.3.5"
+
 [[NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
+[[Ogg_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
+uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
+version = "1.3.5+0"
+
+[[OpenSSL_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
+uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
+version = "1.1.10+0"
+
+[[Opus_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
+uuid = "91d4177d-7536-5919-b921-800302f37372"
+version = "1.3.2+0"
+
+[[OrderedCollections]]
+git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.4.1"
+
+[[PCRE_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
+uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
+version = "8.44.0+0"
+
 [[Parsers]]
 deps = ["Dates"]
 git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "2.1.2"
 
+[[Pixman_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
+uuid = "30392449-352a-5448-841d-b1acce4e97dc"
+version = "0.40.1+0"
+
 [[Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
+[[PlotThemes]]
+deps = ["PlotUtils", "Requires", "Statistics"]
+git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
+uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
+version = "2.0.1"
+
+[[PlotUtils]]
+deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
+git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
+uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
+version = "1.0.15"
+
+[[Plots]]
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
+git-tree-sha1 = "7dc03c2b145168f5854085a16d054429d612b637"
+uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+version = "1.23.5"
+
 [[Preferences]]
 deps = ["TOML"]
 git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
@@ -140,6 +512,12 @@ version = "1.2.2"
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[Qt5Base_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
+git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
+uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
+version = "5.15.3+0"
+
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -148,6 +526,28 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
+[[RecipesBase]]
+git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
+uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+version = "1.1.2"
+
+[[RecipesPipeline]]
+deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
+git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
+uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
+version = "0.4.1"
+
+[[Reexport]]
+git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
+uuid = "189a3867-3050-52da-a836-e630ba90ab69"
+version = "1.2.2"
+
+[[Requires]]
+deps = ["UUIDs"]
+git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
+version = "1.1.3"
+
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
@@ -157,6 +557,12 @@ git-tree-sha1 = "aa841c3738cec78b5dbccd56dda332710f35f6a5"
 uuid = "322a6be2-4ae8-5d68-aaf1-3e960788d1d9"
 version = "0.2.0"
 
+[[Scratch]]
+deps = ["Dates"]
+git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
+uuid = "6c6a2e73-6563-6170-7368-637461726353"
+version = "1.1.0"
+
 [[Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
@@ -164,21 +570,68 @@ uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
+[[Showoff]]
+deps = ["Dates", "Grisu"]
+git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
+uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
+version = "1.0.3"
+
 [[Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
+[[SortingAlgorithms]]
+deps = ["DataStructures"]
+git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "1.0.1"
+
 [[SparseArrays]]
 deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
+[[StaticArrays]]
+deps = ["LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
+uuid = "90137ffa-7385-5640-81b9-e52037218182"
+version = "1.2.13"
+
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
+[[StatsAPI]]
+git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.0.0"
+
+[[StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.33.12"
+
+[[StructArrays]]
+deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
+git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
+uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+version = "0.6.3"
+
 [[TOML]]
 deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 
+[[TableTraits]]
+deps = ["IteratorInterfaceExtensions"]
+git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
+uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
+version = "1.0.1"
+
+[[Tables]]
+deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
+git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
+uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
+version = "1.6.0"
+
 [[Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
@@ -187,6 +640,11 @@ uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[URIs]]
+git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
+uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
+version = "1.3.0"
+
 [[UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
@@ -194,16 +652,202 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 [[Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[UnicodeFun]]
+deps = ["REPL"]
+git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
+uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
+version = "0.4.1"
+
+[[Wayland_jll]]
+deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
+uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
+version = "1.19.0+0"
+
+[[Wayland_protocols_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
+git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
+uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
+version = "1.18.0+4"
+
+[[XML2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
+uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
+version = "2.9.12+0"
+
+[[XSLT_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
+git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
+uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
+version = "1.1.34+0"
+
+[[Xorg_libX11_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
+git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
+uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
+version = "1.6.9+4"
+
+[[Xorg_libXau_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
+uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
+version = "1.0.9+4"
+
+[[Xorg_libXcursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
+uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
+version = "1.2.0+4"
+
+[[Xorg_libXdmcp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
+uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
+version = "1.1.3+4"
+
+[[Xorg_libXext_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
+uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
+version = "1.3.4+4"
+
+[[Xorg_libXfixes_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
+version = "5.0.3+4"
+
+[[Xorg_libXi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
+version = "1.7.10+4"
+
+[[Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
+git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
+version = "1.1.4+4"
+
+[[Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
+version = "1.5.2+4"
+
+[[Xorg_libXrender_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
+uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
+version = "0.9.10+4"
+
+[[Xorg_libpthread_stubs_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
+uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
+version = "0.1.0+3"
+
+[[Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
+git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.13.0+3"
+
+[[Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
+version = "1.1.0+4"
+
+[[Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.2+4"
+
+[[Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.27.0+4"
+
+[[Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.4.0+3"
+
 [[Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 
+[[Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.0+0"
+
+[[libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.1+0"
+
+[[libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+0"
+
 [[libsass_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "663428b7ebaf60c60ee147f0f9466430e9959ad6"
 uuid = "47bcb7c8-5119-555a-9eeb-0afcc36cd728"
 version = "3.5.5+0"
 
+[[libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+0"
+
 [[nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
@@ -211,3 +855,21 @@ uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
 [[p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+
+[[x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "0.9.1+5"
diff --git a/docs/Project.toml b/docs/Project.toml
index a9c8bac2b..c271f32e1 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -4,7 +4,9 @@ Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 DocThemeIndigo = "8bac0ac5-51bf-41f9-885e-2bf1ac2bec5f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 
 [compat]
 DocThemeIndigo = "0.1.3"
 Documenter = "0.25.2"
+Plots = "1.20"
diff --git a/docs/make.jl b/docs/make.jl
index 72d1cd8cd..e817a8842 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,3 +1,5 @@
+ENV["GKSwstype"] = "100"  # make Plots/GR work on headless machine
+
 using ChainRulesCore
 using Documenter
 using DocThemeIndigo
@@ -69,6 +71,7 @@ makedocs(;
         ],
         "The maths" => [
             "The propagators: pushforward and pullback" => "maths/propagators.md",
+            "Non-differentiable Points" => "maths/nondiff_points.md",
             "Complex numbers" => "maths/complex.md",
             "Deriving array rules" => "maths/arrays.md",
         ],
diff --git a/docs/src/maths/nondiff_points.md b/docs/src/maths/nondiff_points.md
new file mode 100644
index 000000000..4200a1447
--- /dev/null
+++ b/docs/src/maths/nondiff_points.md
@@ -0,0 +1,138 @@
+# What to return for non-differentiable points
+!!! info "What is the short version?"
+    If the function is not-differentiable choose to return something useful rather than erroring.
+    For a branch a function is not differentiable due to e.g. a branch, like `abs`, your rule can reasonably claim the derivative at that point is the value from either branch, *or* any value in-between.
+    In particular for local optima (like in the case of `abs`) claiming the derivative is 0 is a good idea.
+    Similarly, if derivative is from one side is not defined, or is not finite, return the derivative from the other side.
+    Throwing an error, or returning `NaN` is generally the least useful option.
+
+However, contrary to what calculus says most autodiff systems will return an answer for such functions.
+For example for: `abs_left(x) = (x <= 0) ? -x : x`, AD will say the derivative at `x=0` is `-1`.
+Alternatively for:  `abs_right(x) = (x < 0) ? -x : x`, AD will say the derivative at `x=0` is `1`.
+Those two examples are weird since they are equal at all points, but AD claims different derivatives at `x=0`.
+The way to fix autodiff systems being weird is to write custom rules.
+So what rule should we write for this case?
+
+The obvious answer, would be to write a rule that throws an error if input at a point where calculus says the derivative is not defined.
+Another option is to return some error signally value like `NaN`.
+Which you *can* do.
+However, there is no where to go with an error, the user still wants a derivative; so this is not useful.
+
+Let us explore what is useful:
+## Case Studies
+
+```@setup nondiff
+using Plots
+gr(framestyle=:origin, legend=false)
+```
+### Derivative is defined in usual sense
+```@example nondiff
+plot(x->x^3)
+```
+This is the standard case, one can returned the derivative that is defined according to school room calculus.
+Here we would reasonably say that at `x=0` the derivative is `3*0^2=0`. 
+
+
+
+### Local Minima / Maxima
+
+```@example nondiff
+plot(abs)
+```
+
+`abs` is the classic example of a function where the derivative is not defines as the limit from above is not equal to the limit from below
+
+$$\mathrm{abs}'(0) = \lim_{h->0^-} \dfrac{\mathrm{abs}(0)-\mathrm{abs}(0-h)}{0-h} = -1$$
+$$\mathrm{abs}'(0) = \lim_{h->0^+} \dfrac{abs(0)-\mathrm{abs}(0-h)}{0-h} = 1$$
+
+Now, as discussed in the introduction the AD system would on it's own choose either 1 or -1, depending on implementation.
+
+We however have a potentially much nicer answer available to use: 0.
+
+This has a number of advantages.
+- It follows the rule that derivatives are zero at local minima (and maxima).
+- If you leave a gradient decent optimizer running it will eventually actually converge absolutely to the point -- where as with it being 1 or -1 it would never outright converge it would always flee.
+
+Further:
+- It is a perfectly nice member of the [subderivative](https://en.wikipedia.org/wiki/Subderivative).
+- It is the mean of the derivative on each side; which means that it will agree with central finite differencing at the point.
+### Piecewise slope change
+```@example nondiff
+plot(x-> x < 0 ? x : 5x)
+```
+
+Here was have 3 main options, all are good.
+
+We could say there derivative at 0 is:
+ - 1: which agrees with backwards finite differencing
+ - 5: which agrees with forwards finite differencing
+ - 3: which is the mean of `[1, 5]`, and agrees with central finite differencing
+
+All of these options are perfectly nice members of the [subderivative](https://en.wikipedia.org/wiki/Subderivative).
+`3` is the arguably the nicest, but it is also the most expensive to compute.
+In general all are acceptable.
+
+
+### Derivative zero almost everywhere
+
+```@example nondiff
+plot(ceil)
+```
+
+Here it is most useful to say the derivative is zero everywhere.
+The limits are zero from both sides.
+
+The other option for `x->ceil(x)` would be relax the problem into `x->x`, and thus  say it is 1 everywhere
+But that it too weird, if the use wanted a relaxation of the problem then they would provide one.
+We can not be imposing that relaxation on to `ceil` for everyone is not reasonable.
+
+### Not defined on one-side
+```@example nondiff
+plot(x->exp(2log(x)))
+plot!(; xlims=(-10,10), ylims=(-10,10)) #hide
+```
+
+We do not have to worry about what to return for the side where it is not defined.
+As we will never be asked for the derivative at e.g. `x=-2.5` since the primal function errors.
+But we do need to worry about at the boundary -- if that boundary point doesn't error.
+
+Since we will never be asked about the left-hand side (as the primal errors), we can use just the right-hand side derivative.
+In this case giving 0.0.
+`
+Also nice in this case is that it agrees with the symbolic simplification of `x->exp(2log(x))` into `x->x^2`.
+
+
+### Derivative nonfinite and same on both sides
+
+```@example nondiff
+plot(cbrt)
+```
+
+Here we have no real choice but to say the derivative at `0` is `Inf`.
+We could consider as an alternative saying some large but finite value.
+However, if too large it will just overflow rapidly anyway; and if too small it will not dominate over finite terms.
+It is not possible to find a given value that is always large enough.
+Our alternatives  woud be to consider the dederivative at `nextfloat(0.0)` or `prevfloat(0.0)`.
+But this is more or less the same as choosing some large value -- in this case an extremely large value that will rapidly overflow.
+
+
+### Derivative on-finite and different on both sides
+
+```@example nondiff
+plot(x-> sign(x) * cbrt(x))
+```
+
+In this example, the primal is defined and finite, so we would like a derivative to defined.
+We are back in the case of a local minimal like we were for `abs`.
+We can make most of the same arguments as we made there to justify saying the derivative is zero.
+
+## Conclusion
+
+From the case studies a few general rules can be seen for how to choose a value that is _useful_.
+These rough rules are:
+ - Say the derivative is 0 at local optima
+ - If the derivative from one side is defined and the other isn't, say it is the derivative taken from defined side.
+ - If the derivative from one side is finite and the other isn't, say it is the derivative taken from finite side.
+ - When derivative from each side is not equal, strongly consider reporting the average
+
+Our goal as always, is to get a pragmatically useful result for everyone, which must by necessity also avoid a pathological result for anyone.