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Unexpected behavior may occur. └ @ /tmp/jl_HQMwxJ/Manifest.toml:0  Installed AbstractFFTs ───────── v1.2.1 Installed StaticArrayInterface ─ v1.2.1  Installed LLVMExtra_jll ──────── v0.0.16+2  Installed IRTools ────────────── v0.4.8  Installed Zygote ─────────────── v0.6.55  Installed GPUArrays ──────────── v8.6.3  Installed ChainRules ─────────── v1.48.0  Installed ArrayInterface ─────── v7.2.0  Installed LLVM ───────────────── v4.16.0  Installed VectorizationBase ──── v0.21.60  Installed ForwardDiff ────────── v0.10.35  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_HQMwxJ/Project.toml` [bdcacae8] + LoopVectorization v0.12.171 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_HQMwxJ/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [4fba245c] + ArrayInterface v7.16.0 [d1d4a3ce] + BitFlags v0.1.9 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [fa961155] + CEnum v0.5.0 [2a0fbf3d] + CPUSummary v0.2.6 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [fb6a15b2] + CloseOpenIntervals v0.1.13 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + CommonSubexpressions v0.3.1 [f70d9fcc] + CommonWorldInvalidations v1.0.0 [34da2185] + Compat v4.16.0 [f0e56b4a] + ConcurrentUtilities v2.4.2 [187b0558] + ConstructionBase v1.5.8 [d38c429a] + Contour v0.6.3 [adafc99b] + CpuId v0.3.1 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.20 [e2d170a0] + DataValueInterfaces v1.0.0 [8bb1440f] + DelimitedFiles v1.9.1 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [ffbed154] + DocStringExtensions v0.9.3 [460bff9d] + ExceptionUnwrapping v0.1.10 [c87230d0] + FFMPEG v0.4.2 [1a297f60] + FillArrays v1.13.0 [53c48c17] + FixedPointNumbers v0.8.5 [1fa38f19] + Format v1.3.7 [f6369f11] + ForwardDiff v0.10.36 [0c68f7d7] + GPUArrays v10.3.1 [46192b85] + GPUArraysCore v0.1.6 ⌅ [28b8d3ca] + GR v0.72.10 [42e2da0e] + Grisu v1.0.2 [cd3eb016] + HTTP v1.10.8 [3e5b6fbb] + HostCPUFeatures v0.1.17 [47d2ed2b] + Hyperscript v0.0.5 [ac1192a8] + HypertextLiteral v0.9.5 [b5f81e59] + IOCapture v0.2.5 [7869d1d1] + IRTools v0.4.14 [615f187c] + IfElse v0.1.1 [92d709cd] + IrrationalConstants v0.2.2 [82899510] + IteratorInterfaceExtensions v1.0.0 [1019f520] + JLFzf v0.1.8 [692b3bcd] + JLLWrappers v1.6.1 [682c06a0] + JSON v0.21.4 [929cbde3] + LLVM v9.1.2 [b964fa9f] + LaTeXStrings v1.3.1 [23fbe1c1] + Latexify v0.16.5 [10f19ff3] + LayoutPointers v0.1.17 [2ab3a3ac] + LogExpFunctions v0.3.28 [e6f89c97] + LoggingExtras v1.0.3 [bdcacae8] + LoopVectorization v0.12.171 [6c6e2e6c] + MIMEs v0.1.4 [1914dd2f] + MacroTools v0.5.13 [d125e4d3] + ManualMemory v0.1.8 [739be429] + MbedTLS v1.1.9 [442fdcdd] + Measures v0.3.2 [e1d29d7a] + Missings v1.2.0 [77ba4419] + NaNMath v1.0.2 [6fe1bfb0] + OffsetArrays v1.14.1 [4d8831e6] + OpenSSL v1.4.3 [bac558e1] + OrderedCollections v1.6.3 [69de0a69] + Parsers v2.8.1 [b98c9c47] + Pipe v1.3.0 [ccf2f8ad] + PlotThemes v3.2.0 [995b91a9] + PlotUtils v1.4.1 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [1d0040c9] + PolyesterWeave v0.2.2 [aea7be01] + PrecompileTools v1.2.1 [21216c6a] + Preferences v1.4.3 [c1ae055f] + RealDot v0.1.0 [3cdcf5f2] + RecipesBase v1.3.4 [01d81517] + RecipesPipeline v0.6.12 [189a3867] + Reexport v1.2.2 [05181044] + RelocatableFolders v1.0.1 [ae029012] + Requires v1.3.0 [94e857df] + SIMDTypes v0.1.0 [476501e8] + SLEEFPirates v0.6.43 [6c6a2e73] + Scratch v1.2.1 [992d4aef] + Showoff v1.0.3 [777ac1f9] + SimpleBufferStream v1.2.0 [a2af1166] + SortingAlgorithms v1.2.1 [dc90abb0] + SparseInverseSubset v0.1.2 [276daf66] + SpecialFunctions v2.4.0 [aedffcd0] + Static v1.1.1 [0d7ed370] + StaticArrayInterface v1.8.0 [1e83bf80] + StaticArraysCore v1.4.3 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.7.0 [2913bbd2] + StatsBase v0.34.3 [09ab397b] + StructArrays v0.6.18 [3783bdb8] + TableTraits v1.0.1 [bd369af6] + Tables v1.12.0 [62fd8b95] + TensorCore v0.1.1 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[3fa0cd96] + REPL v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [f489334b] + StyledStrings v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [efcefdf7] + PCRE2_jll v10.42.0+1 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_HQMwxJ` Precompiling project... 847.5 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 787.3 ms ✓ ArrayInterface → ArrayInterfaceChainRulesExt 2 dependencies successfully precompiled in 2 seconds. 258 already precompiled.Șnbpkg_syncÚD Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_HQMwxJ/Manifest.toml:0  Installed AbstractFFTs ───────── v1.2.1 Installed StaticArrayInterface ─ v1.2.1  Installed LLVMExtra_jll ──────── v0.0.16+2  Installed IRTools ────────────── v0.4.8  Installed Zygote ─────────────── v0.6.55  Installed GPUArrays ──────────── v8.6.3  Installed ChainRules ─────────── v1.48.0  Installed ArrayInterface ─────── v7.2.0  Installed LLVM ───────────────── v4.16.0  Installed VectorizationBase ──── v0.21.60  Installed ForwardDiff ────────── v0.10.35  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_HQMwxJ/Project.toml` [bdcacae8] + LoopVectorization v0.12.171 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_HQMwxJ/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [4fba245c] + ArrayInterface v7.16.0 [d1d4a3ce] + BitFlags v0.1.9 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [fa961155] + CEnum v0.5.0 [2a0fbf3d] + CPUSummary v0.2.6 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [fb6a15b2] + CloseOpenIntervals v0.1.13 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + CommonSubexpressions v0.3.1 [f70d9fcc] + CommonWorldInvalidations v1.0.0 [34da2185] + Compat v4.16.0 [f0e56b4a] + ConcurrentUtilities v2.4.2 [187b0558] + ConstructionBase v1.5.8 [d38c429a] + Contour v0.6.3 [adafc99b] + CpuId v0.3.1 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.20 [e2d170a0] + DataValueInterfaces v1.0.0 [8bb1440f] + DelimitedFiles v1.9.1 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [ffbed154] + DocStringExtensions v0.9.3 [460bff9d] + ExceptionUnwrapping v0.1.10 [c87230d0] + FFMPEG v0.4.2 [1a297f60] + FillArrays v1.13.0 [53c48c17] + FixedPointNumbers v0.8.5 [1fa38f19] + Format v1.3.7 [f6369f11] + ForwardDiff v0.10.36 [0c68f7d7] + GPUArrays v10.3.1 [46192b85] + GPUArraysCore v0.1.6 ⌅ [28b8d3ca] + GR v0.72.10 [42e2da0e] + Grisu v1.0.2 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upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_HQMwxJ` Precompiling project... 847.5 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 787.3 ms ✓ ArrayInterface → ArrayInterfaceChainRulesExt 2 dependencies successfully precompiled in 2 seconds. 258 already precompiled.±LoopVectorizationÚD Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_HQMwxJ/Manifest.toml:0  Installed AbstractFFTs ───────── v1.2.1 Installed StaticArrayInterface ─ v1.2.1  Installed LLVMExtra_jll ──────── v0.0.16+2  Installed IRTools ────────────── v0.4.8  Installed Zygote ─────────────── v0.6.55  Installed GPUArrays ──────────── v8.6.3  Installed ChainRules ─────────── v1.48.0  Installed ArrayInterface ─────── v7.2.0  Installed LLVM ───────────────── v4.16.0  Installed VectorizationBase ──── v0.21.60  Installed ForwardDiff ────────── v0.10.35  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_HQMwxJ/Project.toml` [bdcacae8] + LoopVectorization v0.12.171 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_HQMwxJ/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [4fba245c] + ArrayInterface v7.16.0 [d1d4a3ce] + BitFlags v0.1.9 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [fa961155] + CEnum v0.5.0 [2a0fbf3d] + CPUSummary v0.2.6 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [fb6a15b2] + 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upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_HQMwxJ` Precompiling project... 847.5 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 787.3 ms ✓ ArrayInterface → ArrayInterfaceChainRulesExt 2 dependencies successfully precompiled in 2 seconds. 258 already precompiled.­LinearAlgebraÚD Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_HQMwxJ/Manifest.toml:0  Installed AbstractFFTs ───────── v1.2.1 Installed StaticArrayInterface ─ v1.2.1  Installed LLVMExtra_jll ──────── v0.0.16+2  Installed IRTools ────────────── v0.4.8  Installed Zygote ─────────────── v0.6.55  Installed GPUArrays ──────────── v8.6.3  Installed ChainRules ─────────── v1.48.0  Installed ArrayInterface ─────── v7.2.0  Installed LLVM ───────────────── v4.16.0  Installed VectorizationBase ──── v0.21.60  Installed ForwardDiff ────────── v0.10.35  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_HQMwxJ/Project.toml` [bdcacae8] + LoopVectorization v0.12.171 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_HQMwxJ/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [4fba245c] + ArrayInterface v7.16.0 [d1d4a3ce] + BitFlags v0.1.9 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [fa961155] + CEnum v0.5.0 [2a0fbf3d] + CPUSummary v0.2.6 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [fb6a15b2] + 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[3fa0cd96] + REPL v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [f489334b] + StyledStrings v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [efcefdf7] + PCRE2_jll v10.42.0+1 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_HQMwxJ` Precompiling project... 847.5 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 787.3 ms ✓ ArrayInterface → ArrayInterfaceChainRulesExt 2 dependencies successfully precompiled in 2 seconds. 258 already precompiled.„PlotsÚD Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_HQMwxJ/Manifest.toml:0  Installed AbstractFFTs ───────── v1.2.1 Installed StaticArrayInterface ─ v1.2.1  Installed LLVMExtra_jll ──────── v0.0.16+2  Installed IRTools ────────────── v0.4.8  Installed Zygote ─────────────── v0.6.55  Installed GPUArrays ──────────── v8.6.3  Installed ChainRules ─────────── v1.48.0  Installed ArrayInterface ─────── v7.2.0  Installed LLVM ───────────────── v4.16.0  Installed VectorizationBase ──── v0.21.60  Installed ForwardDiff ────────── v0.10.35  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_HQMwxJ/Project.toml` [bdcacae8] + LoopVectorization v0.12.171 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_HQMwxJ/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [4fba245c] + ArrayInterface v7.16.0 [d1d4a3ce] + BitFlags v0.1.9 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [fa961155] + CEnum v0.5.0 [2a0fbf3d] + CPUSummary v0.2.6 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [fb6a15b2] + CloseOpenIntervals v0.1.13 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + CommonSubexpressions v0.3.1 [f70d9fcc] + CommonWorldInvalidations v1.0.0 [34da2185] + Compat v4.16.0 [f0e56b4a] + ConcurrentUtilities v2.4.2 [187b0558] + ConstructionBase v1.5.8 [d38c429a] + Contour v0.6.3 [adafc99b] + CpuId v0.3.1 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.20 [e2d170a0] + DataValueInterfaces v1.0.0 [8bb1440f] + DelimitedFiles v1.9.1 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [ffbed154] + DocStringExtensions v0.9.3 [460bff9d] + ExceptionUnwrapping v0.1.10 [c87230d0] + FFMPEG v0.4.2 [1a297f60] + FillArrays v1.13.0 [53c48c17] + FixedPointNumbers v0.8.5 [1fa38f19] + Format v1.3.7 [f6369f11] + ForwardDiff v0.10.36 [0c68f7d7] + GPUArrays v10.3.1 [46192b85] + GPUArraysCore v0.1.6 ⌅ [28b8d3ca] + GR v0.72.10 [42e2da0e] + Grisu v1.0.2 [cd3eb016] + HTTP v1.10.8 [3e5b6fbb] + HostCPUFeatures v0.1.17 [47d2ed2b] + Hyperscript v0.0.5 [ac1192a8] + HypertextLiteral v0.9.5 [b5f81e59] + IOCapture v0.2.5 [7869d1d1] + IRTools v0.4.14 [615f187c] + IfElse v0.1.1 [92d709cd] + IrrationalConstants v0.2.2 [82899510] + IteratorInterfaceExtensions v1.0.0 [1019f520] + JLFzf v0.1.8 [692b3bcd] + JLLWrappers v1.6.1 [682c06a0] + JSON v0.21.4 [929cbde3] + LLVM v9.1.2 [b964fa9f] + LaTeXStrings v1.3.1 [23fbe1c1] + Latexify v0.16.5 [10f19ff3] + LayoutPointers v0.1.17 [2ab3a3ac] + LogExpFunctions v0.3.28 [e6f89c97] + LoggingExtras v1.0.3 [bdcacae8] + LoopVectorization v0.12.171 [6c6e2e6c] + MIMEs v0.1.4 [1914dd2f] + MacroTools v0.5.13 [d125e4d3] + ManualMemory v0.1.8 [739be429] + MbedTLS v1.1.9 [442fdcdd] + Measures v0.3.2 [e1d29d7a] + Missings v1.2.0 [77ba4419] + NaNMath v1.0.2 [6fe1bfb0] + OffsetArrays v1.14.1 [4d8831e6] + OpenSSL v1.4.3 [bac558e1] + OrderedCollections v1.6.3 [69de0a69] + Parsers v2.8.1 [b98c9c47] + Pipe v1.3.0 [ccf2f8ad] + 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v1.0.11+0 [935fb764] + Xorg_libXcursor_jll v1.2.0+4 [a3789734] + Xorg_libXdmcp_jll v1.1.4+0 [1082639a] + Xorg_libXext_jll v1.3.6+0 [d091e8ba] + Xorg_libXfixes_jll v5.0.3+4 [a51aa0fd] + Xorg_libXi_jll v1.7.10+4 [d1454406] + Xorg_libXinerama_jll v1.1.4+4 [ec84b674] + Xorg_libXrandr_jll v1.5.2+4 [ea2f1a96] + Xorg_libXrender_jll v0.9.11+0 [14d82f49] + Xorg_libpthread_stubs_jll v0.1.1+0 [c7cfdc94] + Xorg_libxcb_jll v1.17.0+0 [cc61e674] + Xorg_libxkbfile_jll v1.1.2+0 [e920d4aa] + Xorg_xcb_util_cursor_jll v0.1.4+0 [12413925] + Xorg_xcb_util_image_jll v0.4.0+1 [2def613f] + Xorg_xcb_util_jll v0.4.0+1 [975044d2] + Xorg_xcb_util_keysyms_jll v0.4.0+1 [0d47668e] + Xorg_xcb_util_renderutil_jll v0.3.9+1 [c22f9ab0] + Xorg_xcb_util_wm_jll v0.4.1+1 [35661453] + Xorg_xkbcomp_jll v1.4.6+0 [33bec58e] + Xorg_xkeyboard_config_jll v2.39.0+0 [c5fb5394] + Xorg_xtrans_jll v1.5.0+0 [3161d3a3] + Zstd_jll v1.5.6+1 [35ca27e7] + eudev_jll v3.2.9+0 [214eeab7] + fzf_jll v0.53.0+0 [1a1c6b14] + gperf_jll v3.1.1+0 [a4ae2306] + libaom_jll v3.9.0+0 [0ac62f75] + libass_jll v0.15.2+0 [1183f4f0] + libdecor_jll v0.2.2+0 [2db6ffa8] + libevdev_jll v1.11.0+0 [f638f0a6] + libfdk_aac_jll v2.0.3+0 [36db933b] + libinput_jll v1.18.0+0 [b53b4c65] + libpng_jll v1.6.44+0 [f27f6e37] + libvorbis_jll v1.3.7+2 [009596ad] + mtdev_jll v1.1.6+0 ⌅ [1270edf5] + x264_jll v2021.5.5+0 ⌅ [dfaa095f] + x265_jll v3.5.0+0 [d8fb68d0] + xkbcommon_jll v1.4.1+1 [0dad84c5] + ArgTools v1.1.2 [56f22d72] + Artifacts v1.11.0 [2a0f44e3] + Base64 v1.11.0 [ade2ca70] + Dates v1.11.0 [8ba89e20] + Distributed v1.11.0 [f43a241f] + Downloads v1.6.0 [7b1f6079] + FileWatching v1.11.0 [b77e0a4c] + InteractiveUtils v1.11.0 [4af54fe1] + LazyArtifacts v1.11.0 [b27032c2] + LibCURL v0.6.4 [76f85450] + LibGit2 v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.11.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [a63ad114] + Mmap v1.11.0 [ca575930] + NetworkOptions v1.2.0 [44cfe95a] + Pkg v1.11.0 [de0858da] + Printf v1.11.0 [3fa0cd96] + REPL v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [f489334b] + StyledStrings v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [efcefdf7] + PCRE2_jll v10.42.0+1 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_HQMwxJ` Precompiling project... 847.5 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 787.3 ms ✓ ArrayInterface → ArrayInterfaceChainRulesExt 2 dependencies successfully precompiled in 2 seconds. 258 already precompiled.§PlutoUIÚD Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_HQMwxJ/Manifest.toml:0  Installed AbstractFFTs ───────── v1.2.1 Installed StaticArrayInterface ─ v1.2.1  Installed LLVMExtra_jll ──────── v0.0.16+2  Installed IRTools ────────────── v0.4.8  Installed Zygote ─────────────── v0.6.55  Installed GPUArrays ──────────── v8.6.3  Installed ChainRules ─────────── v1.48.0  Installed ArrayInterface ─────── v7.2.0  Installed LLVM ───────────────── v4.16.0  Installed VectorizationBase ──── v0.21.60  Installed ForwardDiff ────────── v0.10.35  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_HQMwxJ/Project.toml` [bdcacae8] + LoopVectorization v0.12.171 ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_HQMwxJ/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [4fba245c] + ArrayInterface v7.16.0 [d1d4a3ce] + BitFlags v0.1.9 [62783981] + BitTwiddlingConvenienceFunctions v0.1.6 [fa961155] + CEnum v0.5.0 [2a0fbf3d] + CPUSummary v0.2.6 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [fb6a15b2] + 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upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_HQMwxJ` Precompiling project... 847.5 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 787.3 ms ✓ ArrayInterface → ArrayInterfaceChainRulesExt 2 dependencies successfully precompiled in 2 seconds. 258 already precompiled.§enabledĂ·restart_recommended_msgÀŽrestart_required_msgÀ­busy_packages¶waiting_for_permissionÂÙ,waiting_for_permission_but_probably_disabled«cell_inputsȚ!Ù$84a5abc6-68a3-4ab2-992e-dbf3e96ab96f„§cell_idÙ$84a5abc6-68a3-4ab2-992e-dbf3e96ab96f€code­md""" --- """šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedĂÙ$a62c6371-39b6-434e-8a39-56cf93454e3e„§cell_idÙ$a62c6371-39b6-434e-8a39-56cf93454e3e€codeÙ`function log₀(ball, y) c = ball.c atanh(√(c) * norm(y)) * y / (√(c) * norm(y)) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$f9aa6c7f-5cde-4b92-829a-1b6b7dc093a9„§cell_idÙ$f9aa6c7f-5cde-4b92-829a-1b6b7dc093a9€codeÙ{function d(ball, x, y) c = curvature(ball) sc = √(c) (2 / sc) * atanh(sc * norm(mobius_add(ball, -x, y))) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$b353c6cb-ccfc-4ed7-b000-4eb0792a9af0„§cell_idÙ$b353c6cb-ccfc-4ed7-b000-4eb0792a9af0€codeًfunction mobius_mul(ball, x, r::Real) c = curvature(ball) nx = norm(x) (1 / √(c)) * tanh(r * atanh(√(c) * nx)) * x / nx endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$185ea194-fc2a-4bc3-9049-af1217f39149„§cell_idÙ$185ea194-fc2a-4bc3-9049-af1217f39149€code šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$4ea42f8e-af75-4bb9-b111-c4ee2d62992d„§cell_idÙ$4ea42f8e-af75-4bb9-b111-c4ee2d62992d€codeÙ%function ℓÂČ(x) sum(abs2, x) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$29bdf881-55b1-4488-8d9b-f6de418c7eb2„§cell_idÙ$29bdf881-55b1-4488-8d9b-f6de418c7eb2€codeÙ_function exp₀(ball, v) c = ball.c tanh(√(c) * norm(v)) * v / (√(c) * norm(v)) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$f3250d44-d070-4269-a1e6-d5d5a78eda94„§cell_idÙ$f3250d44-d070-4269-a1e6-d5d5a78eda94€codeÙmfunction expₚ(ball, p, v) nv = norm(v) mobius_add(ball, p, tanh(λ(ball, p) * nv / 2) * v / nv) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$a6eb8eb8-a56a-4513-9297-6bcd2d5a4461„§cell_idÙ$a6eb8eb8-a56a-4513-9297-6bcd2d5a4461€code­md""" --- """šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedĂÙ$e23ef86b-ba37-4119-91cb-c73fefd951c2„§cell_idÙ$e23ef86b-ba37-4119-91cb-c73fefd951c2€code šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$2154c663-732c-41df-b67f-3043f5252e2e„§cell_idÙ$2154c663-732c-41df-b67f-3043f5252e2e€codeÙKfunction exp₀(::UnitCurvatureBall, v) tanh(norm(v)) * v / norm(v) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$6f2c94ac-56c7-40ae-b71c-9353fecc7e19„§cell_idÙ$6f2c94ac-56c7-40ae-b71c-9353fecc7e19€codeÙ>struct UnitCurvatureBall{F<:AbstractFloat} <: AbstractBall endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$024d72e3-4cf7-4959-804a-68ad846959d5„§cell_idÙ$024d72e3-4cf7-4959-804a-68ad846959d5€codeÚIlet η = .01 r = .9 ΞP = 0 ΞQ = π / 5 rP = r rQ = r-.2 P = [rP*cos(ΞP), rP*sin(ΞP)] Q = [rQ*cos(ΞQ), rQ*sin(ΞQ)] circleshape() = let Ξ = LinRange(0, 2π, 100) cos.(Ξ), sin.(Ξ) end points = [] @gif for epoch in 1:20 plot(circleshape(), size=(500,500), label=nothing) ylims!(-1, 1) xlims!(-1, 1) xaxis!(false) yaxis!(false) show_point!(Q; label="Q") show_point!(P; label="P") ∇P, = Zygote.gradient(P) do X d(UnitCurvatureBall{Float64}(), X, Q) end P = P - η * ∇P plot_grad!(Q, P, η) title!("Gradient d(p, x)") end endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$dbc766f7-5c9c-40f3-ab9a-fd6fbc15bed7„§cell_idÙ$dbc766f7-5c9c-40f3-ab9a-fd6fbc15bed7€codeŸcurvature(ball::Ball) = ball.cšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$73b1969a-556b-43d9-8ee6-4688e41737bc„§cell_idÙ$73b1969a-556b-43d9-8ee6-4688e41737bc€codeÙ.λ(::UnitCurvatureBall, x) = 1 / (2 - norm(x))šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$5a167073-8ca6-4ea6-b0d6-2a524bb83f1d„§cell_idÙ$5a167073-8ca6-4ea6-b0d6-2a524bb83f1d€codeÙBshow_point!((x, y); kwargs...) = scatter!( [x], [y]; kwargs...);šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$e0316d72-b81b-11ed-27ca-6d97f8237ef9„§cell_idÙ$e0316d72-b81b-11ed-27ca-6d97f8237ef9€codeÙ+using Plots, PlutoUI, LinearAlgebra, Zygotešmetadataƒ©show_logsšdisabledÂźskip_as_script«code_foldedÂÙ$e8bf1a30-56b3-4f10-8c7c-e53a4f78dcd5„§cell_idÙ$e8bf1a30-56b3-4f10-8c7c-e53a4f78dcd5€codeÙ0mobius_sub(ball, x, y) = mobius_add(ball, x, -y)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$84b85868-9d3e-4150-9ba5-7eaf22e230ae„§cell_idÙ$84b85868-9d3e-4150-9ba5-7eaf22e230ae€codeÙ"## Utils norm(x) = sqrt(ℓÂČ(x))šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$3d35a821-8b72-4c67-902d-95f276e9e5f6„§cell_idÙ$3d35a821-8b72-4c67-902d-95f276e9e5f6€codeÙćfunction mobius_add(::UnitCurvatureBall, x, y) ℓÂČx = ℓÂČ(x) ℓÂČy = ℓÂČ(y) two_xdoty = 2 * (x ⋅ y) ((1 + two_xdoty + ℓÂČy) * x + (1 - ℓÂČx) * y) / ( 1 + two_xdoty + ℓÂČx * ℓÂČy ) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$a5a3dec8-0844-4671-9551-664a570696aa„§cell_idÙ$a5a3dec8-0844-4671-9551-664a570696aa€codeÙÓfunction plot_grad!(Q, X, η) ∇X, = Zygote.gradient(X) do X d(UnitCurvatureBall{Float64}(), X, Q) end quiver!( [X[1]], [X[2]], quiver=( [-η * ∇X[1]], [-η * ∇X[2]], ), c=:gray ) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$ec653efa-2261-412e-923a-56aebfbc5544„§cell_idÙ$ec653efa-2261-412e-923a-56aebfbc5544€codeÙBfunction parallel_transport0(ball, x, v) v ./ 2λ(ball, x) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$2e4ce682-6c01-485b-a59f-cf7f9fc3d0b3„§cell_idÙ$2e4ce682-6c01-485b-a59f-cf7f9fc3d0b3€code·using LoopVectorizationšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$f37818d0-e0ac-4953-a1e8-7a749868e76f„§cell_idÙ$f37818d0-e0ac-4953-a1e8-7a749868e76f€codeÙ5mobius_mul(ball, r::Real, x) = mobius_mul(ball, x, r)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$08e8681e-174f-488c-be8e-0deea80be550„§cell_idÙ$08e8681e-174f-488c-be8e-0deea80be550€codeÙ4curvature(::UnitCurvatureBall{T}) where {T} = one(T)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$64f63b3c-302e-485b-8808-3285947f836b„§cell_idÙ$64f63b3c-302e-485b-8808-3285947f836b€codeُfunction unit_speed_geodesic(ball, x, v) minus_xv = mobius_add(ball, -x, v) t -> mobius_add(ball, x, mobius_mul(ball, minus_xv, t)) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$a4aa2ad7-19fd-4388-9139-1875bd4d3780„§cell_idÙ$a4aa2ad7-19fd-4388-9139-1875bd4d3780€codeÚfunction mobius_add(ball, x, y) c = curvature(ball) cℓÂČx = c * ℓÂČ(x) cℓÂČy = c * ℓÂČ(y) twoc_xdoty = 2c * (x ⋅ y) ((1 + twoc_xdoty + cℓÂČy) * x + (1 - cℓÂČx) * y) / ( 1 + twoc_xdoty + cℓÂČx * cℓÂČy ) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$65ff893d-37a1-4b84-86ae-a79f65422038„§cell_idÙ$65ff893d-37a1-4b84-86ae-a79f65422038€codeÙLfunction log₀(::UnitCurvatureBall, y) atanh(norm(y)) * y / norm(y) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$47371bd5-8238-4b96-8de4-14b194a5d544„§cell_idÙ$47371bd5-8238-4b96-8de4-14b194a5d544€codeÙSfunction parallel_transport(ball, x, y, v) v .* (λ(ball, x) / λ(ball, y)) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$160851ec-5f78-4077-8ccd-26a0b3d5c8a0„§cell_idÙ$160851ec-5f78-4077-8ccd-26a0b3d5c8a0€codeŸabstract type AbstractBall endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$fb32f12d-059f-4c25-a07b-5b224f675daf„§cell_idÙ$fb32f12d-059f-4c25-a07b-5b224f675daf€codeÚÍlet η = .01 P = [0.4, 0.3] Q = [0.3, 0.8] circleshape() = let Ξ = LinRange(0, 2π, 100) cos.(Ξ), sin.(Ξ) end plot(circleshape(), size=(500,500), label=nothing) ylims!(-1, 1) xlims!(-1, 1) xaxis!(false) yaxis!(false) show_point!(Q; label="Q") for Ξ in π:-0.1:-π for r in -.2:0.09:0.96 X = [r * cos(Ξ), r * sin(Ξ)] # scatter!([X[1]],[X[2]], label=nothing) plot_grad!(Q, X, η) end end title!("Gradient d(p, x)") endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$73718205-3563-4cd2-9012-c83737e074d3„§cell_idÙ$73718205-3563-4cd2-9012-c83737e074d3€codeÙ7function λ(ball, x) 1 / (2 - ball.c * norm(x)) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$4eb8ee63-511e-4841-b903-f2cfaf974f1f„§cell_idÙ$4eb8ee63-511e-4841-b903-f2cfaf974f1f€codeÙŰstruct Ball{F<:AbstractFloat} <: AbstractBall c::F function Ball(c::T=1.0) where {T<:AbstractFloat} if c == one(T) return UnitCurvatureBall{T}() end Ball{T}(c) end endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_folded«notebook_idÙ$010e34b6-8a3d-11ef-23a8-8f2534cbb32a«in_temp_diršmetadata€