├── .github ├── Dockerfile ├── icons │ ├── blue.ico │ └── orange.ico └── workflows │ ├── create-wsl-image.yml │ ├── update-dockerfile-dev.yml │ └── update-dockerfile-master.yml ├── .gitignore ├── Dockerfile ├── LICENSE ├── README.rst └── notebooks └── Start here.ipynb /.github/Dockerfile: -------------------------------------------------------------------------------- 1 | # Multi-stage Dockerfile for slim Sage 2 | # https://docs.docker.com/build/building/multi-stage 3 | 4 | FROM ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-targets:10.6 AS target 5 | 6 | # Resolve symbolic links to recreate them later 7 | RUN readlink /sage/prefix >> /sage/prefix_link 8 | RUN readlink /sage/venv >> /sage/venv_link 9 | 10 | WORKDIR /sage 11 | 12 | # Strip executables in /sage 13 | RUN LC_ALL=C find local src pkgs -type f -exec strip '{}' ';' 2>&1 | grep -v "file format not recognized" || true 14 | 15 | # Clean up before copying in the next stage 16 | RUN rm -rf local/share/doc local/share/*/doc local/share/*/examples local/share/singular/html 17 | 18 | # Remove all __pycache__ directories 19 | RUN find /sage -type d -name "__pycache__" -exec rm -rf {} + 20 | # Remove all .c .cpp files corresponding to .pyx files 21 | RUN find /sage -name "*.pyx" | sed 's/\(.*\)[.]pyx$/\1.c \1.cpp/' | xargs rm -f + 22 | 23 | FROM ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-system-packages:10.6 24 | 25 | USER root 26 | 27 | # Remove warnings 28 | ENV DEBIAN_FRONTEND noninteractive 29 | ENV DEBCONF_NOWARNINGS="yes" 30 | 31 | # Install JupyterLab to the system 32 | RUN apt-get update 33 | RUN apt-get install -y --no-install-recommends python3-pip 34 | RUN python3 -m pip install --no-warn-script-location --no-cache-dir notebook jupyterlab ipywidgets 35 | 36 | # Disable annoying popup for Jupyter news 37 | RUN jupyter labextension disable "@jupyterlab/apputils-extension:announcements" 38 | 39 | # Install /sage from target 40 | COPY --from=target /sage/local /sage/local 41 | COPY --from=target /sage/src/bin /sage/src/bin 42 | COPY --from=target /sage/src/sage /sage/src/sage 43 | COPY --from=target /sage/sage /sage/sage 44 | COPY --from=target /sage/pkgs/sage-conf /sage/pkgs/sage-conf 45 | 46 | # Recreate symbolic links 47 | COPY --from=target /sage/prefix_link /sage/prefix_link 48 | COPY --from=target /sage/venv_link /sage/venv_link 49 | RUN ln -s $(cat /sage/prefix_link) /sage/prefix && rm /sage/prefix_link 50 | RUN ln -s $(cat /sage/venv_link) /sage/venv && rm /sage/venv_link 51 | 52 | # Configure Sage library 53 | RUN /sage/sage -pip install --root-user-action=ignore /sage/pkgs/sage-conf 54 | 55 | # Remove problematic lines! 56 | RUN sed -i '/^__requires__/d' /sage/venv/bin/sage-venv-config 57 | RUN sed -i '/^__import__/d' /sage/venv/bin/sage-venv-config 58 | -------------------------------------------------------------------------------- /.github/icons/blue.ico: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sagemath/sage-binder-env/0c6ba26c96262f643fedc626c38074fac3fbf60a/.github/icons/blue.ico -------------------------------------------------------------------------------- /.github/icons/orange.ico: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sagemath/sage-binder-env/0c6ba26c96262f643fedc626c38074fac3fbf60a/.github/icons/orange.ico -------------------------------------------------------------------------------- /.github/workflows/create-wsl-image.yml: -------------------------------------------------------------------------------- 1 | name: Build docker image and export for WSL 2 | 3 | on: 4 | schedule: 5 | - cron: '0 2 * * *' # Run every day 6 | workflow_dispatch: 7 | 8 | jobs: 9 | build-and-export: 10 | runs-on: ubuntu-latest 11 | outputs: 12 | upload_url: ${{ steps.create_release.outputs.upload_url }} 13 | version: ${{ steps.extract_version.outputs.version }} 14 | steps: 15 | 16 | # Create WSL export (a tar file) of the minimal Sage install 17 | 18 | - name: Prepare Dockerfile 19 | run: | 20 | curl -o Dockerfile https://raw.githubusercontent.com/sagemath/sage-binder-env/master/Dockerfile 21 | sed -i '/COPY notebooks/d' Dockerfile # remove the line from Dockerfile 22 | 23 | - name: Extract version from Dockerfile 24 | id: extract_version 25 | run: | 26 | VERSION=$(grep '^FROM ghcr.io/sagemath/sage-binder-env:' Dockerfile | sed 's/^FROM ghcr.io\/sagemath\/sage-binder-env://') 27 | echo "VERSION=$VERSION" >> $GITHUB_ENV 28 | echo "version=$VERSION" >> $GITHUB_OUTPUT 29 | 30 | - name: Build and export Docker image 31 | run: | 32 | docker build -t sagemath-container . 33 | export CONTAINER_ID=$(docker create sagemath-container) 34 | docker export $CONTAINER_ID -o sagemath-$VERSION-wsl.tar 35 | 36 | - name: Upload tar file as artifact 37 | id: upload-artifact 38 | uses: actions/upload-artifact@v4 39 | with: 40 | name: sagemath-${{ env.VERSION }}-wsl 41 | path: sagemath-${{ env.VERSION }}-wsl.tar 42 | 43 | # Make a release 44 | 45 | - name: Get latest release version 46 | id: get_latest_release 47 | run: | 48 | LATEST_VERSION=$(curl -s https://api.github.com/repos/${{ github.repository }}/releases/latest | jq -r '.tag_name // "0.0.0"' | sed 's/v//') 49 | echo "LATEST_VERSION=$LATEST_VERSION" >> $GITHUB_ENV 50 | 51 | - name: Zip the tar file 52 | if: ${{ env.VERSION != env.LATEST_VERSION }} 53 | run: | 54 | zip sagemath-${{ env.VERSION }}-wsl.zip sagemath-${{ env.VERSION }}-wsl.tar 55 | 56 | - name: Create GitHub Release 57 | if: ${{ env.VERSION != env.LATEST_VERSION }} 58 | id: create_release 59 | uses: actions/create-release@v1 60 | env: 61 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 62 | with: 63 | tag_name: v${{ env.VERSION }} 64 | release_name: Run SageMath ${{ env.VERSION }} on WSL 65 | body: | 66 | We recommend you check if WSL is enabled before running the installer. 67 | 68 | The .ps1 installer downloads the .zip file and imports a minimized SageMath ${{ env.VERSION }} into WSL. 69 | 70 | After downloading the installer, right-click it to open the context menu and run it with PowerShell. 71 | You may also open the installer as a text file, and copy and paste all lines into a PowerShell window. 72 | 73 | The installer should create two shortcuts on your desktop: one for launching SageMath 74 | and another to start the Jupyter server for SageMath. 75 | 76 | The minimized SageMath is the same as the one used in the Binder environment, meaning no bells and whistles. 77 | Notably the Sage build system is not included. 78 | draft: false 79 | prerelease: false 80 | 81 | - name: Upload release asset 82 | if: ${{ env.VERSION != env.LATEST_VERSION }} 83 | uses: actions/upload-release-asset@v1 84 | env: 85 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 86 | with: 87 | upload_url: ${{ steps.create_release.outputs.upload_url }} 88 | asset_path: ./sagemath-${{ env.VERSION }}-wsl.zip 89 | asset_name: sagemath-${{ env.VERSION }}-wsl.zip 90 | asset_content_type: application/zip 91 | 92 | # Generate a Windows PowerShell script 93 | 94 | - name: Checkout repo 95 | uses: actions/checkout@v3 96 | 97 | - name: Generate PowerShell Script 98 | run: | 99 | cat << EOF > download_and_import_sagemath_to_wsl.ps1 100 | # ---------------------------------------------------- 101 | # Copy and paste all lines into the Windows PowerShell 102 | # ---------------------------------------------------- 103 | 104 | [Console]::OutputEncoding = [System.Text.Encoding]::UTF8 105 | try { 106 | Write-Host "Checking WSL installation." 107 | wsl --install --no-distribution 108 | if (\$LASTEXITCODE -ne 0) { 109 | Write-Host "WSL installation failed." 110 | Read-Host -Prompt "Press any key to exit"; exit 111 | } 112 | } catch { 113 | Write-Host "Could not check WSL installation, proceeding with fingers crossed." 114 | } 115 | # Check if SageMath already exists in WSL 116 | \$sagemathWSL = "SageMath-$VERSION" 117 | if ((wsl -l -q) -contains \$sagemathWSL) { 118 | # Ask user if they want to reinstall SageMath 119 | \$response = Read-Host "\$sagemathWSL is already installed. Do you want to reinstall it? (y/n)" 120 | if (\$response -eq "y") { 121 | Write-Host "Uninstalling \$sagemathWSL." 122 | # Unregister the existing SageMath WSL distribution 123 | wsl --unregister \$sagemathWSL 124 | } else { 125 | Read-Host "OK. Press any key to exit"; exit 126 | } 127 | } 128 | \$artifactUrl = "https://github.com/sagemath/sage-binder-env/releases/download/v$VERSION/sagemath-$VERSION-wsl.zip" 129 | \$zipFilePath = "\$PWD\\artifact.zip" 130 | \$dataPath = "\$HOME\\AppData\\Local\\SageMath" 131 | \$tarFilePath = "\$dataPath\\sagemath-$VERSION-wsl.tar" 132 | # Ensure the path exists 133 | if (-Not (Test-Path \$dataPath)) { New-Item -Path \$dataPath -ItemType Directory > \$null } 134 | # Skip downloading and extracting if the tar file already exists 135 | if (-Not (Test-Path \$tarFilePath)) { 136 | Write-Host "Downloading \$sagemathWSL..." 137 | Start-BitsTransfer -Source \$artifactUrl -Destination \$zipFilePath 138 | Write-Host "Extracting..." 139 | Expand-Archive -Path \$zipFilePath -DestinationPath \$dataPath -Force 140 | if (Test-Path \$tarFilePath) { Remove-Item \$zipFilePath } 141 | } else { 142 | Write-Host "\$sagemathWSL was already downloaded." 143 | } 144 | # Import the WSL image 145 | Write-Host "Start importing..." 146 | wsl --import SageMath-$VERSION \$dataPath \$tarFilePath 147 | # Check if importing succeeded 148 | if (-Not ((wsl -l -q) -contains \$sagemathWSL)) { 149 | Write-Host "Importing \$sagemathWSL into WSL failed." 150 | Write-Host "If WSL was freshly installed by this installer, try again after rebooting the computer." 151 | Read-Host "Press any key to exit"; exit 152 | } 153 | Write-Host "Creating shortcults at:" 154 | # Download icons for shortcuts 155 | \$iconUrlOrange = "https://raw.githubusercontent.com/sagemath/sage-binder-env/refs/heads/master/.github/icons/orange.ico" 156 | \$iconUrlBlue = "https://raw.githubusercontent.com/sagemath/sage-binder-env/refs/heads/master/.github/icons/blue.ico" 157 | \$iconPathOrange = "\$dataPath\\orange.ico" 158 | \$iconPathBlue = "\$dataPath\\blue.ico" 159 | # Download the icon if it doesn't exist 160 | if (-Not (Test-Path \$iconPathBlue)) { 161 | Start-BitsTransfer -Source \$iconUrlBlue -Destination \$iconPathBlue 162 | } 163 | if (-Not (Test-Path \$iconPathOrange)) { 164 | Start-BitsTransfer -Source \$iconUrlOrange -Destination \$iconPathOrange 165 | } 166 | # Create shortcuts 167 | \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Sage.lnk" 168 | \$TargetPath = "C:\\Windows\\System32\\wsl.exe" 169 | \$Arguments = "-d \$sagemathWSL --user user --cd ~ /sage/sage" 170 | \$WScriptShell = New-Object -ComObject WScript.Shell 171 | \$Shortcut = \$WScriptShell.CreateShortcut(\$ShortcutFile) 172 | \$Shortcut.TargetPath = \$TargetPath 173 | \$Shortcut.Arguments = \$Arguments 174 | \$Shortcut.IconLocation = \$iconPathBlue 175 | \$Shortcut.Save() 176 | Write-Host "\$ShortcutFile" 177 | # Create a shortcut that starts Jupyter on Desktop 178 | \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Jupyter.lnk" 179 | \$TargetPath = "C:\\Windows\\System32\\wsl.exe" 180 | \$Arguments = "-d \$sagemathWSL --user user --cd ~ jupyter lab --no-browser" 181 | \$WScriptShell = New-Object -ComObject WScript.Shell 182 | \$Shortcut = \$WScriptShell.CreateShortcut(\$ShortcutFile) 183 | \$Shortcut.TargetPath = \$TargetPath 184 | \$Shortcut.Arguments = \$Arguments 185 | \$Shortcut.IconLocation = \$iconPathOrange 186 | \$Shortcut.Save() 187 | Write-Host "\$ShortcutFile" 188 | Read-Host "\`n\$sagemathWSL installation succeeded!\`nPress any key to exit" 189 | EOF 190 | cat << EOF > remove_sagemath_from_wsl.ps1 191 | # ---------------------------------------------------- 192 | # Copy and paste all lines into the Windows PowerShell 193 | # ---------------------------------------------------- 194 | 195 | [Console]::OutputEncoding = [System.Text.Encoding]::UTF8 196 | try { 197 | Write-Host "Checking WSL installation." 198 | wsl --install --no-distribution 199 | if (\$LASTEXITCODE -ne 0) { 200 | Write-Host "WSL installation failed." 201 | Read-Host -Prompt "Press any key to exit"; exit 202 | } 203 | } catch { 204 | Write-Host "Could not check WSL installation, proceeding with fingers crossed." 205 | } 206 | # Check if SageMath already exists in WSL 207 | \$sagemathWSL = "SageMath-$VERSION" 208 | \$dataPath = "\$HOME\\AppData\\Local\\SageMath" 209 | \$iconPathOrange = "\$dataPath\\orange.ico" 210 | \$iconPathBlue = "\$dataPath\\blue.ico" 211 | if ((wsl -l -q) -contains \$sagemathWSL) { 212 | # Ask user if they want to reinstall SageMath 213 | \$response = Read-Host "Do you want to uninstall \$(\$sagemathWSL) from WSL? (y/n)" 214 | if (\$response -eq "y") { 215 | Write-Host "Uninstalling \$sagemathWSL..." 216 | try { 217 | wsl --unregister \$sagemathWSL 218 | } catch { 219 | Write-Host "Failed: wsl --unregister \$sagemathWSL" 220 | } 221 | try { 222 | rm -recurse \$dataPath 223 | } catch { 224 | Write-Host "Failed: rm -recurse \$dataPath" 225 | } 226 | try { 227 | \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Sage.lnk" 228 | rm \$ShortcutFile 229 | } catch { 230 | Write-Host "Failed: rm \$ShortcutFile" 231 | } 232 | try { 233 | \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Jupyter.lnk" 234 | rm \$ShortcutFile 235 | } catch { 236 | Write-Host "Failed: rm \$ShortcutFile" 237 | } 238 | } else { 239 | Read-Host "OK. Press any key to exit"; exit 240 | } 241 | } else { 242 | Write-Host "\$sagemathWSL is not found." 243 | Read-Host -Prompt "Press any key to exit"; exit 244 | } 245 | Read-Host "\`n\$sagemathWSL uninstallation succeeded!\`nPress any key to exit" 246 | EOF 247 | shell: bash 248 | 249 | - name: Upload installation script as artifact 250 | uses: actions/upload-artifact@v4 251 | with: 252 | name: download_and_import_sagemath_to_wsl 253 | path: download_and_import_sagemath_to_wsl.ps1 254 | 255 | - name: Upload uninstallation script as artifact 256 | uses: actions/upload-artifact@v4 257 | with: 258 | name: remove_sagemath_from_wsl 259 | path: remove_sagemath_from_wsl.ps1 260 | 261 | - name: Upload installation script as release asset 262 | if: ${{ env.VERSION != env.LATEST_VERSION }} 263 | uses: actions/upload-release-asset@v1 264 | env: 265 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 266 | with: 267 | upload_url: ${{ steps.create_release.outputs.upload_url }} 268 | asset_path: ./download_and_import_sagemath_to_wsl.ps1 269 | asset_name: sagemath-${{ env.VERSION }}-wsl-installer.ps1 270 | asset_content_type: application/octet-stream 271 | 272 | - name: Upload uninstallation script as release asset 273 | if: ${{ env.VERSION != env.LATEST_VERSION }} 274 | uses: actions/upload-release-asset@v1 275 | env: 276 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 277 | with: 278 | upload_url: ${{ steps.create_release.outputs.upload_url }} 279 | asset_path: ./remove_sagemath_from_wsl.ps1 280 | asset_name: sagemath-${{ env.VERSION }}-wsl-uninstaller.ps1 281 | asset_content_type: application/octet-stream 282 | 283 | # build-exe: 284 | # runs-on: windows-latest 285 | # needs: build-and-export 286 | # if: ${{ contains(needs.build-and-export.outputs.upload_url || '', 'http') }} 287 | # steps: 288 | # - name: Checkout repository 289 | # uses: actions/checkout@v3 290 | # 291 | # - name: Download PowerShell Script artifact 292 | # uses: actions/download-artifact@v4 293 | # with: 294 | # name: download_and_import_sagemath_to_wsl 295 | # 296 | # - name: Install PS2EXE 297 | # run: | 298 | # Install-Module -Name ps2exe -Force 299 | # Import-Module ps2exe 300 | # Invoke-ps2exe -inputFile .\download_and_import_sagemath_to_wsl.ps1 -outputFile .\sagemath_installer.exe 301 | # shell: powershell 302 | # 303 | # - name: Upload EXE to GitHub Release 304 | # uses: actions/upload-release-asset@v1 305 | # env: 306 | # GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 307 | # with: 308 | # upload_url: ${{ needs.build-and-export.outputs.upload_url }} 309 | # asset_path: ./sagemath_installer.exe 310 | # asset_name: sagemath-${{ needs.build-and-export.outputs.version }}-wsl-installer.exe 311 | # asset_content_type: application/octet-stream 312 | -------------------------------------------------------------------------------- /.github/workflows/update-dockerfile-dev.yml: -------------------------------------------------------------------------------- 1 | name: Update dev image 2 | 3 | on: 4 | schedule: 5 | - cron: '0 1 * * *' # Run every day 6 | workflow_dispatch: 7 | 8 | env: 9 | SAGE_TARGET: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-targets 10 | SAGE_SYSTEM: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-system-packages 11 | TAG: dev 12 | BRANCH: dev 13 | 14 | jobs: 15 | build: 16 | runs-on: ubuntu-latest 17 | permissions: 18 | contents: write 19 | packages: write 20 | steps: 21 | 22 | # Prepare .github/Dockerfile for slim Sage image 23 | 24 | - name: Checkout code 25 | uses: actions/checkout@v4 26 | with: 27 | ref: ${{ env.BRANCH }} 28 | - name: Prepare .github/Dockerfile 29 | run: | 30 | SAGE_VERSION=$(docker run --rm ${SAGE_TARGET}:$TAG /sage/sage --version | grep -oP 'SageMath version \K[0-9.]+(?:beta\d+)?(?:rc\d+)?') 31 | SAGE_TARGET_ESCAPED=$(echo "${SAGE_TARGET}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 32 | SAGE_TARGET_VERSION_ESCAPED=$(echo "${SAGE_TARGET}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 33 | sed -i "s/FROM ${SAGE_TARGET_ESCAPED}:\S*/FROM ${SAGE_TARGET_VERSION_ESCAPED}/g" .github/Dockerfile 34 | SAGE_SYSTEM_ESCAPED=$(echo "${SAGE_SYSTEM}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 35 | SAGE_SYSTEM_VERSION_ESCAPED=$(echo "${SAGE_SYSTEM}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 36 | sed -i "s/FROM ${SAGE_SYSTEM_ESCAPED}:\S*/FROM ${SAGE_SYSTEM_VERSION_ESCAPED}/g" .github/Dockerfile 37 | PACKAGE_NAME=ghcr.io/${{ github.repository }}:${SAGE_VERSION} 38 | echo "PACKAGE_NAME=$PACKAGE_NAME" >> $GITHUB_ENV 39 | git config --global user.email alice@wonderland 40 | git config --global user.name alice 41 | git commit -a --amend -m "Dockerfile for Sage ${SAGE_VERSION}" 42 | git push -f origin $BRANCH 43 | 44 | # Build and publish the slim Sage image to github package registry (ghpr) 45 | 46 | - name: Log in to the Container registry 47 | uses: docker/login-action@v3 48 | with: 49 | registry: ghcr.io 50 | username: ${{ github.actor }} 51 | password: ${{ secrets.GITHUB_TOKEN }} 52 | - name: Build and push Docker image 53 | uses: docker/build-push-action@v5 54 | with: 55 | context: .github 56 | push: true 57 | tags: ${{ env.PACKAGE_NAME }} 58 | 59 | # Update files for Binder 60 | 61 | - name: Checkout code 62 | uses: actions/checkout@v4 63 | with: 64 | ref: ${{ env.BRANCH }} 65 | - name: Update files for Binder 66 | run: | 67 | PACKAGE_NAME=${{ env.PACKAGE_NAME }} 68 | PACKAGE_NAME_ESCAPED=$(echo "${PACKAGE_NAME}" | sed 's/\//\\\//g') 69 | sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" Dockerfile 70 | sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" README.rst 71 | git config --global user.email alice@wonderland 72 | git config --global user.name alice 73 | git commit -a --amend -m "Update files for Binder" 74 | git push -f origin $BRANCH 75 | 76 | # Build docker image for Binder from Dockerfile at root 77 | 78 | - name: Binder build 79 | timeout-minutes: 30 80 | continue-on-error: true 81 | run: | 82 | curl --keepalive-time 600 -L https://mybinder.org/build/gh/sagemath/sage-binder-env/$BRANCH 83 | -------------------------------------------------------------------------------- /.github/workflows/update-dockerfile-master.yml: -------------------------------------------------------------------------------- 1 | name: Update master image 2 | 3 | on: 4 | schedule: 5 | - cron: '0 0 * * *' # Run every day 6 | workflow_dispatch: 7 | 8 | env: 9 | SAGE_TARGET: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-targets 10 | SAGE_SYSTEM: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-system-packages 11 | TAG: latest 12 | BRANCH: master 13 | 14 | jobs: 15 | build: 16 | runs-on: ubuntu-latest 17 | permissions: 18 | contents: write 19 | packages: write 20 | steps: 21 | 22 | # Prepare .github/Dockerfile for slim Sage image 23 | 24 | - name: Checkout code 25 | uses: actions/checkout@v4 26 | with: 27 | ref: ${{ env.BRANCH }} 28 | - name: Prepare .github/Dockerfile 29 | run: | 30 | SAGE_VERSION=$(docker run --rm ${SAGE_TARGET}:$TAG /sage/sage --version | grep -oP 'SageMath version \K[0-9.]+(?:beta\d+)?(?:rc\d+)?') 31 | SAGE_TARGET_ESCAPED=$(echo "${SAGE_TARGET}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 32 | SAGE_TARGET_VERSION_ESCAPED=$(echo "${SAGE_TARGET}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 33 | sed -i "s/FROM ${SAGE_TARGET_ESCAPED}:\S*/FROM ${SAGE_TARGET_VERSION_ESCAPED}/g" .github/Dockerfile 34 | SAGE_SYSTEM_ESCAPED=$(echo "${SAGE_SYSTEM}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 35 | SAGE_SYSTEM_VERSION_ESCAPED=$(echo "${SAGE_SYSTEM}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') 36 | sed -i "s/FROM ${SAGE_SYSTEM_ESCAPED}:\S*/FROM ${SAGE_SYSTEM_VERSION_ESCAPED}/g" .github/Dockerfile 37 | PACKAGE_NAME=ghcr.io/${{ github.repository }}:${SAGE_VERSION} 38 | echo "PACKAGE_NAME=$PACKAGE_NAME" >> $GITHUB_ENV 39 | git config --global user.email alice@wonderland 40 | git config --global user.name alice 41 | git commit -a --amend -m "Dockerfile for Sage ${SAGE_VERSION}" 42 | git push -f origin $BRANCH 43 | 44 | # Build and publish the slim Sage image to github package registry (ghpr) 45 | 46 | - name: Log in to the Container registry 47 | uses: docker/login-action@v3 48 | with: 49 | registry: ghcr.io 50 | username: ${{ github.actor }} 51 | password: ${{ secrets.GITHUB_TOKEN }} 52 | 53 | - name: Build and push Docker image 54 | uses: docker/build-push-action@v5 55 | with: 56 | context: .github 57 | push: true 58 | tags: ${{ env.PACKAGE_NAME }} 59 | 60 | # Update files for Binder 61 | 62 | - name: Checkout code 63 | uses: actions/checkout@v4 64 | with: 65 | ref: ${{ env.BRANCH }} 66 | - name: Update files for Binder 67 | run: | 68 | PACKAGE_NAME=${{ env.PACKAGE_NAME }} 69 | PACKAGE_NAME_ESCAPED=$(echo "${PACKAGE_NAME}" | sed 's/\//\\\//g') 70 | sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" Dockerfile 71 | sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" README.rst 72 | git config --global user.email alice@wonderland 73 | git config --global user.name alice 74 | git commit -a --amend -m "Update files for Binder" 75 | git push -f origin $BRANCH 76 | 77 | # Build docker image for Binder from Dockerfile at root 78 | 79 | - name: Binder build 80 | timeout-minutes: 30 81 | continue-on-error: true 82 | run: | 83 | curl --keepalive-time 600 -L https://mybinder.org/build/gh/sagemath/sage-binder-env/$BRANCH 84 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sagemath/sage-binder-env/0c6ba26c96262f643fedc626c38074fac3fbf60a/.gitignore -------------------------------------------------------------------------------- /Dockerfile: -------------------------------------------------------------------------------- 1 | # Dockerfile for binder 2 | # Reference: https://mybinder.readthedocs.io/en/latest/tutorials/dockerfile.html 3 | 4 | FROM ghcr.io/sagemath/sage-binder-env:10.6 5 | 6 | USER root 7 | 8 | # Create user with uid 1000 9 | ARG NB_USER=user 10 | ARG NB_UID=1000 11 | ENV NB_USER user 12 | ENV NB_UID 1000 13 | ENV HOME /home/${NB_USER} 14 | RUN adduser --disabled-password --gecos "Default user" --uid ${NB_UID} ${NB_USER} 15 | 16 | # Make sure the contents of the notebooks directory are in ${HOME} 17 | COPY notebooks/* ${HOME}/ 18 | RUN chown -R ${NB_USER}:${NB_USER} ${HOME} 19 | 20 | # Switch to the user 21 | USER ${NB_USER} 22 | 23 | # Install Sage kernel to Jupyter 24 | RUN mkdir -p $(jupyter --data-dir)/kernels 25 | RUN ln -s /sage/venv/share/jupyter/kernels/sagemath $(jupyter --data-dir)/kernels 26 | 27 | # Make Sage accessible from anywhere 28 | ENV PATH="/sage:$PATH" 29 | 30 | # Start in the home directory of the user 31 | WORKDIR /home/${NB_USER} 32 | 33 | # Create the jupyter_lab_config.py file with a custom logging filter to 34 | # suppress the perpetual nodejs warning 35 | RUN mkdir -p /home/${NB_USER}/.jupyter 36 | RUN echo "\ 37 | import logging\n\ 38 | \n\ 39 | class NoNodeJSWarningFilter(logging.Filter):\n\ 40 | def filter(self, record):\n\ 41 | return 'Could not determine jupyterlab build status without nodejs' not in record.getMessage()\n\ 42 | \n\ 43 | logging.getLogger('LabApp').addFilter(NoNodeJSWarningFilter())\n\ 44 | " > /home/${NB_USER}/.jupyter/jupyter_lab_config.py 45 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.rst: -------------------------------------------------------------------------------- 1 | A Binder repo for SageMath computing environment 2 | ================================================ 3 | 4 | This repository is a Binder repo based on `SageMath `_. To 5 | access a computing environment created by `Binder `_ using 6 | SageMath kernel, click on this badge 7 | 8 | .. image:: https://mybinder.org/badge_logo.svg 9 | :target: https://mybinder.org/v2/gh/sagemath/sage-binder-env/master 10 | 11 | 12 | An example Binder repo for SageMath 13 | ----------------------------------- 14 | 15 | Have a repository full of Jupyter notebooks using SageMath? It's easy to set up 16 | Binder to let anyone run them. Just fork this repo, put your notebooks in the 17 | `notebooks` directory, and modify this `README.rst` to your needs. In 18 | particular, you probably want to modify this line:: 19 | 20 | :target: https://mybinder.org/v2/gh/... 21 | 22 | with `...` filled with the name of your forked repo. This makes the Binder badge use your 23 | repo to create the computing environment. 24 | 25 | 26 | Extending the Dockerfile 27 | ------------------------ 28 | 29 | The `Dockerfile` is based on the Docker image:: 30 | 31 | FROM ghcr.io/sagemath/sage-binder-env:10.6 32 | 33 | which contains the latest stable version of Sage. 34 | 35 | It includes Sage itself, and all the software packages typically 36 | included in a standard Sage installation, though not *everything*. In 37 | particular not optional Sage SPKGs, or other system software packages. 38 | 39 | 40 | Authors 41 | ------- 42 | 43 | Nicolas M. Thiéry, E. Madison Bray, and Kwankyu Lee 44 | -------------------------------------------------------------------------------- /notebooks/Start here.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# About SageMath\n", 8 | "\n", 9 | "[SageMath](https://www.sagemath.org) (Sage for short) is a general purpose computational mathematics system developed by a worldwide community of hundreds of researchers, teachers and engineers. It’s based on the Python programming language and includes GAP, PARI/GP, Singular, and dozens of other specialized libraries.\n", 10 | "\n", 11 | "This live document will guide you through the first steps of using Sage, and provide pointers to explore and learn further. In the following, we will be assuming that you are reading this document as a Jupyter notebook (Jupyter is the primary user interface\n", 12 | "for Sage).\n", 13 | "$\\def\\NN{\\mathbb{N}}\\def\\ZZ{\\mathbb{Z}}\\def\\QQ{\\mathbb{Q}}\\def\\RR{\\mathbb{R}}\\def\\CC{\\mathbb{C}}$\n", 14 | "" 15 | ] 16 | }, 17 | { 18 | "cell_type": "markdown", 19 | "metadata": {}, 20 | "source": [ 21 | "## A first calculation\n", 22 | "\n", 23 | "Sage can be used as a pocket calculator: you type in some expression to be calculated, Sage evaluates it, and prints the result; and repeat. This is called the *Read-Eval-Print-Loop*. In the Jupyter notebook, you type the expression in an **input cell**, or **code cell**. This is the rectangle below this paragraph containing $1+1$. Click on the cell to select it, and press shift-enter to evaluate it. You may instead click the Run button (right triangle) in the toolbar." 24 | ] 25 | }, 26 | { 27 | "cell_type": "code", 28 | "execution_count": null, 29 | "metadata": {}, 30 | "outputs": [], 31 | "source": [ 32 | "1 + 1" 33 | ] 34 | }, 35 | { 36 | "cell_type": "markdown", 37 | "metadata": {}, 38 | "source": [ 39 | "Sage prints out its response in an **output cell** just below the input cell (that’s 2, so Sage confirms that 1 plus 1 is 2). Click again in the cell, replace $1+1$ by $2+2$, and evaluate it. Notice how much quicker it is now. That’s because a Sage process had to be started the first time, and then stayed ready.\n", 40 | "\n", 41 | "Congratulations, you have done your first calculations with Sage." 42 | ] 43 | }, 44 | { 45 | "cell_type": "markdown", 46 | "metadata": {}, 47 | "source": [ 48 | "## Using the Jupyter notebook\n", 49 | "\n", 50 | "Now take some time to explore the Help menu. You find abundant information on Jupyter, Sage, and friends. \n", 51 | "For now we just review the basics of Jupyter notebook. Use the plus button in the toolbar to create a new input cell below this paragraph (you may need to first click this paragraph to focus), then calculate any simple expression of your liking.\n", 52 | "\n", 53 | "You can move around and edit any cell by clicking in it. Go back and change your $2+2$ above to $3+3$ and evaluate it once again.\n", 54 | "\n", 55 | "You can also edit any **text cell** by double clicking on it. Try it now! The text you see is using the [Markdown](https://jupyter-notebook.readthedocs.io/en/latest/examples/Notebook/Working%20With%20Markdown%20Cells.html) markup language. Do some changes to the text, and evaluate it again to rerender it. Markdown supports a fair amount of basic formatting, such as bold, underline, basic lists, and so forth. Thanks to the LaTeX rendering engine [MathJax](https://www.mathjax.org/), you may embed mathematical formulae such as $\\sin x - y^3$ just like with LaTeX. It can be fun to type in fairly complicated math, like this:\n", 56 | "\n", 57 | "$$\n", 58 | " \\zeta(s)=\\sum_{n=1}^{\\infty}\\frac{1}{n^s}=\\prod_p \\left(\\frac{1}{1-p^{-s}}\\right)\n", 59 | "$$\n", 60 | "\n", 61 | "If you *mess everything up*, you can use the menu Kernel > Restart Kernel to restart Sage. You can also use the menu File > Save Notebook to save notebook, and File > Revert Notebook to Checkpoint to reset to any previously saved version." 62 | ] 63 | }, 64 | { 65 | "cell_type": "markdown", 66 | "metadata": {}, 67 | "source": [ 68 | "## More interactions\n", 69 | "\n", 70 | "We are now done with basic interaction with Sage. Much richer interactions are possible thanks to Jupyter’s *interactive widgets*. Evaluate the next code cell, and try clicking on the sliders to illustrate multiplication below. " 71 | ] 72 | }, 73 | { 74 | "cell_type": "code", 75 | "execution_count": null, 76 | "metadata": {}, 77 | "outputs": [], 78 | "source": [ 79 | "@interact\n", 80 | "def f(n=(1..15), m=(1..15)):\n", 81 | " print(\"n * m = {} = {}\".format(n * m, factor(n * m)))\n", 82 | " P = polygon([(0, 0), (0, n), (m, n), (m, 0)])\n", 83 | " P.show(aspect_ratio=1, gridlines='minor', figsize=[3, 3], xmax=14, ymax=14)" 84 | ] 85 | }, 86 | { 87 | "cell_type": "markdown", 88 | "metadata": {}, 89 | "source": [ 90 | "Also, you can try changing the slider ranges to something different by editing the input cell (make sure to also change `xmax`, `ymax`)." 91 | ] 92 | }, 93 | { 94 | "cell_type": "markdown", 95 | "metadata": {}, 96 | "source": [ 97 | "## A brief tour\n", 98 | "\n", 99 | "We start showcasing the different areas of mathematics covered by Sage.\n", 100 | "" 101 | ] 102 | }, 103 | { 104 | "cell_type": "markdown", 105 | "metadata": {}, 106 | "source": [ 107 | "This should output a rational number. If you know Python, notice the difference; Sage knows fractions!" 108 | ] 109 | }, 110 | { 111 | "cell_type": "code", 112 | "execution_count": null, 113 | "metadata": {}, 114 | "outputs": [], 115 | "source": [ 116 | "4/6" 117 | ] 118 | }, 119 | { 120 | "cell_type": "markdown", 121 | "metadata": {}, 122 | "source": [ 123 | "### Math display\n", 124 | "\n", 125 | "`%display latex` turns on math typesetting using MathJax. Type `%display plain` to turn it off." 126 | ] 127 | }, 128 | { 129 | "cell_type": "code", 130 | "execution_count": null, 131 | "metadata": {}, 132 | "outputs": [], 133 | "source": [ 134 | "%display latex" 135 | ] 136 | }, 137 | { 138 | "cell_type": "code", 139 | "execution_count": null, 140 | "metadata": {}, 141 | "outputs": [], 142 | "source": [ 143 | "factor(x^10 - 1)" 144 | ] 145 | }, 146 | { 147 | "cell_type": "code", 148 | "execution_count": null, 149 | "metadata": {}, 150 | "outputs": [], 151 | "source": [ 152 | "%display plain\n", 153 | "factor(x^10 - 1)" 154 | ] 155 | }, 156 | { 157 | "cell_type": "markdown", 158 | "metadata": {}, 159 | "source": [ 160 | "### Plots" 161 | ] 162 | }, 163 | { 164 | "cell_type": "code", 165 | "execution_count": null, 166 | "metadata": {}, 167 | "outputs": [], 168 | "source": [ 169 | "plot(sin(10*x))" 170 | ] 171 | }, 172 | { 173 | "cell_type": "markdown", 174 | "metadata": {}, 175 | "source": [ 176 | "### Interactive widgets" 177 | ] 178 | }, 179 | { 180 | "cell_type": "code", 181 | "execution_count": null, 182 | "metadata": {}, 183 | "outputs": [], 184 | "source": [ 185 | "@interact\n", 186 | "def plt(n=5, f=[sin, cos, tan]):\n", 187 | " return plot(f(n*x))" 188 | ] 189 | }, 190 | { 191 | "cell_type": "markdown", 192 | "metadata": {}, 193 | "source": [ 194 | "### 3D plots" 195 | ] 196 | }, 197 | { 198 | "cell_type": "code", 199 | "execution_count": null, 200 | "metadata": {}, 201 | "outputs": [], 202 | "source": [ 203 | "plot3d(lambda x, y: x^2 + y^2, (-2,2), (-2,2))" 204 | ] 205 | }, 206 | { 207 | "cell_type": "markdown", 208 | "metadata": {}, 209 | "source": [ 210 | "### Calculus" 211 | ] 212 | }, 213 | { 214 | "cell_type": "code", 215 | "execution_count": null, 216 | "metadata": {}, 217 | "outputs": [], 218 | "source": [ 219 | "%display latex\n", 220 | "var('x,y')\n", 221 | "f = (cos(pi/4 - x) - tan(x)) / (1 - sin(pi/4 + x))\n", 222 | "limit(f, x = pi/4, dir='minus')" 223 | ] 224 | }, 225 | { 226 | "cell_type": "code", 227 | "execution_count": null, 228 | "metadata": {}, 229 | "outputs": [], 230 | "source": [ 231 | "solve([x^2+y^2 == 1, y^2 == x^3 + x + 1], x, y)" 232 | ] 233 | }, 234 | { 235 | "cell_type": "code", 236 | "execution_count": null, 237 | "metadata": {}, 238 | "outputs": [], 239 | "source": [ 240 | "plot3d(sin(pi*sqrt(x^2 + y^2)) / sqrt(x^2 + y^2), (x, -5, 5), (y, -5, 5))" 241 | ] 242 | }, 243 | { 244 | "cell_type": "code", 245 | "execution_count": null, 246 | "metadata": {}, 247 | "outputs": [], 248 | "source": [ 249 | "contour_plot(y^2 + 1 - x^3 - x, (x,-pi,pi), (y,-pi,pi),\n", 250 | " contours=[-8,-4,0,4,8], colorbar=True)" 251 | ] 252 | }, 253 | { 254 | "cell_type": "markdown", 255 | "metadata": {}, 256 | "source": [ 257 | "### Algebra" 258 | ] 259 | }, 260 | { 261 | "cell_type": "code", 262 | "execution_count": null, 263 | "metadata": {}, 264 | "outputs": [], 265 | "source": [ 266 | "factor(x^100 - 1)" 267 | ] 268 | }, 269 | { 270 | "cell_type": "code", 271 | "execution_count": null, 272 | "metadata": {}, 273 | "outputs": [], 274 | "source": [ 275 | "p = 54 * x^4 + 36*x^3 - 102*x^2 - 72*x - 12\n", 276 | "p.factor()" 277 | ] 278 | }, 279 | { 280 | "cell_type": "code", 281 | "execution_count": null, 282 | "metadata": {}, 283 | "outputs": [], 284 | "source": [ 285 | "for K in [ZZ, QQ, ComplexField(16), QQ[sqrt(2)], GF(5)]:\n", 286 | " print(K, \":\"); print(K['x'](p).factor())" 287 | ] 288 | }, 289 | { 290 | "cell_type": "code", 291 | "execution_count": null, 292 | "metadata": {}, 293 | "outputs": [], 294 | "source": [ 295 | "ZZ.category()" 296 | ] 297 | }, 298 | { 299 | "cell_type": "code", 300 | "execution_count": null, 301 | "metadata": {}, 302 | "outputs": [], 303 | "source": [ 304 | "sorted( ZZ.category().axioms() )" 305 | ] 306 | }, 307 | { 308 | "cell_type": "markdown", 309 | "metadata": {}, 310 | "source": [ 311 | "### Linear algebra" 312 | ] 313 | }, 314 | { 315 | "cell_type": "code", 316 | "execution_count": null, 317 | "metadata": {}, 318 | "outputs": [], 319 | "source": [ 320 | "A = matrix(GF(7), 4, [5,5,4,3,0,3,3,4,0,1,5,4,6,0,6,3]); A" 321 | ] 322 | }, 323 | { 324 | "cell_type": "code", 325 | "execution_count": null, 326 | "metadata": {}, 327 | "outputs": [], 328 | "source": [ 329 | "P = A.characteristic_polynomial(); P" 330 | ] 331 | }, 332 | { 333 | "cell_type": "code", 334 | "execution_count": null, 335 | "metadata": {}, 336 | "outputs": [], 337 | "source": [ 338 | "P(A) # Cayley-Hamilton" 339 | ] 340 | }, 341 | { 342 | "cell_type": "code", 343 | "execution_count": null, 344 | "metadata": {}, 345 | "outputs": [], 346 | "source": [ 347 | "A.eigenspaces_left()" 348 | ] 349 | }, 350 | { 351 | "cell_type": "markdown", 352 | "metadata": {}, 353 | "source": [ 354 | "Computing the rank of a large sparse matrix:" 355 | ] 356 | }, 357 | { 358 | "cell_type": "code", 359 | "execution_count": null, 360 | "metadata": {}, 361 | "outputs": [], 362 | "source": [ 363 | "M = random_matrix(GF(7), 10000, sparse=True, density=3/10000)\n", 364 | "M.rank()" 365 | ] 366 | }, 367 | { 368 | "cell_type": "markdown", 369 | "metadata": {}, 370 | "source": [ 371 | "### Geometry" 372 | ] 373 | }, 374 | { 375 | "cell_type": "code", 376 | "execution_count": null, 377 | "metadata": {}, 378 | "outputs": [], 379 | "source": [ 380 | "polytopes.truncated_icosidodecahedron().plot()" 381 | ] 382 | }, 383 | { 384 | "cell_type": "markdown", 385 | "metadata": {}, 386 | "source": [ 387 | "### Programming and plotting" 388 | ] 389 | }, 390 | { 391 | "cell_type": "code", 392 | "execution_count": null, 393 | "metadata": {}, 394 | "outputs": [], 395 | "source": [ 396 | "n, l, x, y = 10000, 1, 0, 0\n", 397 | "p = [[0, 0]]\n", 398 | "for k in range(n):\n", 399 | " theta = (2 * pi * random()).n(digits=5)\n", 400 | " x, y = x + l * cos(theta), y + l * sin(theta)\n", 401 | " p.append([x, y])\n", 402 | "g = line(p, thickness=.4) + line([p[n], [0, 0]], color='red', thickness=2)\n", 403 | "g.show(aspect_ratio=1)" 404 | ] 405 | }, 406 | { 407 | "cell_type": "markdown", 408 | "metadata": {}, 409 | "source": [ 410 | "### Interactive plots" 411 | ] 412 | }, 413 | { 414 | "cell_type": "code", 415 | "execution_count": null, 416 | "metadata": {}, 417 | "outputs": [], 418 | "source": [ 419 | "var('x')\n", 420 | "@interact\n", 421 | "def g(f='x*sin(1/x)',\n", 422 | " c=slider(-1, 1, .01, default=-.5),\n", 423 | " n=(1..30),\n", 424 | " xinterval=range_slider(-1, 1, .1, default=(-8,8), label=\"x-interval\"),\n", 425 | " yinterval=range_slider(-1, 1, .1, default=(-3,3), label=\"y-interval\")):\n", 426 | " f = eval(f)\n", 427 | " x0 = c\n", 428 | " degree = n\n", 429 | " xmin,xmax = xinterval\n", 430 | " ymin,ymax = yinterval\n", 431 | " p = plot(f, xmin, xmax, thickness=4)\n", 432 | " dot = point((x0,f(x=x0)),pointsize=80,rgbcolor=(1,0,0))\n", 433 | " ft = f.taylor(x,x0,degree)\n", 434 | " pt = plot(ft, xmin, xmax, color='red', thickness=2, fill=f)\n", 435 | " show(dot + p + pt, ymin=ymin, ymax=ymax, xmin=xmin, xmax=xmax)\n", 436 | " html(r'$f(x)\\;=\\;%s$' % latex(f))\n", 437 | " html(r'$P_{%s}(x)\\;=\\;%s+R_{%s}(x)$' % (degree,latex(ft),degree))" 438 | ] 439 | }, 440 | { 441 | "cell_type": "markdown", 442 | "metadata": {}, 443 | "source": [ 444 | "### Graph Theory\n", 445 | "\n", 446 | "Coloring graphs:" 447 | ] 448 | }, 449 | { 450 | "cell_type": "code", 451 | "execution_count": null, 452 | "metadata": {}, 453 | "outputs": [], 454 | "source": [ 455 | "g = graphs.PetersenGraph(); g\n", 456 | "g.plot(partition=g.coloring())" 457 | ] 458 | }, 459 | { 460 | "cell_type": "markdown", 461 | "metadata": {}, 462 | "source": [ 463 | "### Combinatorics\n", 464 | "\n", 465 | "Fast counting:" 466 | ] 467 | }, 468 | { 469 | "cell_type": "code", 470 | "execution_count": null, 471 | "metadata": {}, 472 | "outputs": [], 473 | "source": [ 474 | "Partitions(100000).cardinality()" 475 | ] 476 | }, 477 | { 478 | "cell_type": "markdown", 479 | "metadata": {}, 480 | "source": [ 481 | "Playing poker:" 482 | ] 483 | }, 484 | { 485 | "cell_type": "code", 486 | "execution_count": null, 487 | "metadata": {}, 488 | "outputs": [], 489 | "source": [ 490 | "Suits = Set([\"Hearts\", \"Diamonds\", \"Spades\", \"Clubs\"])\n", 491 | "Values = Set([2, 3, 4, 5, 6, 7, 8, 9, 10, \"Jack\", \"Queen\", \"King\", \"Ace\"])\n", 492 | "Cards = cartesian_product([Values, Suits])\n", 493 | "Hands = Subsets(Cards, 5)\n", 494 | "Hands.random_element()" 495 | ] 496 | }, 497 | { 498 | "cell_type": "code", 499 | "execution_count": null, 500 | "metadata": {}, 501 | "outputs": [], 502 | "source": [ 503 | "Hands.cardinality()" 504 | ] 505 | }, 506 | { 507 | "cell_type": "markdown", 508 | "metadata": {}, 509 | "source": [ 510 | "### Algebraic Combinatorics\n", 511 | "\n", 512 | "Drawing an affine root systems:" 513 | ] 514 | }, 515 | { 516 | "cell_type": "code", 517 | "execution_count": null, 518 | "metadata": {}, 519 | "outputs": [], 520 | "source": [ 521 | "L = RootSystem([\"G\", 2, 1]).ambient_space()\n", 522 | "p = L.plot(affine=False, level=1)\n", 523 | "p.show(aspect_ratio=[1, 1, 2], frame=False)" 524 | ] 525 | }, 526 | { 527 | "cell_type": "markdown", 528 | "metadata": {}, 529 | "source": [ 530 | "### Number Theory" 531 | ] 532 | }, 533 | { 534 | "cell_type": "code", 535 | "execution_count": null, 536 | "metadata": {}, 537 | "outputs": [], 538 | "source": [ 539 | "E = EllipticCurve('389a')\n", 540 | "plot(E, thickness=3)" 541 | ] 542 | }, 543 | { 544 | "cell_type": "markdown", 545 | "metadata": {}, 546 | "source": [ 547 | "### Games\n", 548 | "\n", 549 | "Sudoku solver:" 550 | ] 551 | }, 552 | { 553 | "cell_type": "code", 554 | "execution_count": null, 555 | "metadata": {}, 556 | "outputs": [], 557 | "source": [ 558 | "S = Sudoku('5...8..49...5...3..673....115..........2.8..........187....415..3...2...49..5...3'); S" 559 | ] 560 | }, 561 | { 562 | "cell_type": "code", 563 | "execution_count": null, 564 | "metadata": {}, 565 | "outputs": [], 566 | "source": [ 567 | "list(S.solve())" 568 | ] 569 | }, 570 | { 571 | "cell_type": "markdown", 572 | "metadata": {}, 573 | "source": [ 574 | "## Help system\n", 575 | "\n", 576 | "We review the three main ways to get help in Sage:\n", 577 | "\n", 578 | "- Navigating through the documentation \n", 579 | "- Tab-completion \n", 580 | "- Contextual help " 581 | ] 582 | }, 583 | { 584 | "cell_type": "markdown", 585 | "metadata": {}, 586 | "source": [ 587 | "### Navigating through the documentation\n", 588 | "\n", 589 | "The Help menu gives access to the HTML documentation for Sage (and other pieces of software). This includes the Sage tutorial, the Sage thematic tutorials, and the Sage reference manual. \n", 590 | "\n", 591 | "This documentation is also available online from Sage’s web site\n", 592 | "[https://doc.sagemath.org](https://doc.sagemath.org/html/en/index.html) ." 593 | ] 594 | }, 595 | { 596 | "cell_type": "markdown", 597 | "metadata": {}, 598 | "source": [ 599 | "### Completion and contextual documentation\n", 600 | "\n", 601 | "Start typing something and press the Tab key. The interface tries to complete it with a command name. If there is more than one completion, then they are all presented to you. Remember that Sage is case sensitive, i.e., it differentiates upper case from lower case. Hence the Tab completion of\n", 602 | "`klein` won’t show you the `KleinFourGroup` command that builds the group $ \\ZZ/2 \\times \\ZZ/2 $ as a permutation group. Try pressing the Tab key in the following cells (with cursor at the end):" 603 | ] 604 | }, 605 | { 606 | "cell_type": "code", 607 | "execution_count": null, 608 | "metadata": { 609 | "tags": [] 610 | }, 611 | "outputs": [], 612 | "source": [ 613 | "klein" 614 | ] 615 | }, 616 | { 617 | "cell_type": "code", 618 | "execution_count": null, 619 | "metadata": {}, 620 | "outputs": [], 621 | "source": [ 622 | "Klein" 623 | ] 624 | }, 625 | { 626 | "cell_type": "markdown", 627 | "metadata": {}, 628 | "source": [ 629 | "To see documentation and examples for a command, type a question mark `?` at the end of the command name and evaluate the cell.\n" 630 | ] 631 | }, 632 | { 633 | "cell_type": "code", 634 | "execution_count": null, 635 | "metadata": {}, 636 | "outputs": [], 637 | "source": [ 638 | "KleinFourGroup?" 639 | ] 640 | }, 641 | { 642 | "cell_type": "markdown", 643 | "metadata": {}, 644 | "source": [ 645 | "#### Exercise A\n", 646 | "\n", 647 | "What is the largest prime factor of $600851475143$?" 648 | ] 649 | }, 650 | { 651 | "cell_type": "code", 652 | "execution_count": null, 653 | "metadata": {}, 654 | "outputs": [], 655 | "source": [ 656 | "factor?" 657 | ] 658 | }, 659 | { 660 | "cell_type": "code", 661 | "execution_count": null, 662 | "metadata": {}, 663 | "outputs": [], 664 | "source": [] 665 | }, 666 | { 667 | "cell_type": "markdown", 668 | "metadata": {}, 669 | "source": [ 670 | "### Digression: assignments and methods\n", 671 | "\n", 672 | "In the above manipulations we did not store any data for later use. This can be done in Sage with the assignment symbol as in:" 673 | ] 674 | }, 675 | { 676 | "cell_type": "code", 677 | "execution_count": null, 678 | "metadata": {}, 679 | "outputs": [], 680 | "source": [ 681 | "a = 3\n", 682 | "b = 2\n", 683 | "a + b" 684 | ] 685 | }, 686 | { 687 | "cell_type": "markdown", 688 | "metadata": {}, 689 | "source": [ 690 | "This can be understood as Sage evaluating the expression to the right of the = sign and creating the appropriate object, and then associating that object with a label, given by the left-hand side. Multiple assignments can be done at once:" 691 | ] 692 | }, 693 | { 694 | "cell_type": "code", 695 | "execution_count": null, 696 | "metadata": {}, 697 | "outputs": [], 698 | "source": [ 699 | "a, b = 2, 3\n", 700 | "a" 701 | ] 702 | }, 703 | { 704 | "cell_type": "code", 705 | "execution_count": null, 706 | "metadata": {}, 707 | "outputs": [], 708 | "source": [ 709 | "b" 710 | ] 711 | }, 712 | { 713 | "cell_type": "markdown", 714 | "metadata": {}, 715 | "source": [ 716 | "This allows us to swap the values of two variables directly:" 717 | ] 718 | }, 719 | { 720 | "cell_type": "code", 721 | "execution_count": null, 722 | "metadata": {}, 723 | "outputs": [], 724 | "source": [ 725 | "a, b = 2, 3\n", 726 | "a, b = b, a\n", 727 | "a, b" 728 | ] 729 | }, 730 | { 731 | "cell_type": "markdown", 732 | "metadata": {}, 733 | "source": [ 734 | "We can also assign a common value to several variables simultaneously:" 735 | ] 736 | }, 737 | { 738 | "cell_type": "code", 739 | "execution_count": null, 740 | "metadata": {}, 741 | "outputs": [], 742 | "source": [ 743 | "c = d = 1\n", 744 | "c, d" 745 | ] 746 | }, 747 | { 748 | "cell_type": "code", 749 | "execution_count": null, 750 | "metadata": {}, 751 | "outputs": [], 752 | "source": [ 753 | "d = 2\n", 754 | "c, d" 755 | ] 756 | }, 757 | { 758 | "cell_type": "markdown", 759 | "metadata": {}, 760 | "source": [ 761 | "Note that when we use the word *variable* in the computer-science sense we\n", 762 | "mean “a label attached to some data stored by Sage”. Once an object is\n", 763 | "created, some *methods* apply to it. This means *functions* but instead of\n", 764 | "writing `f(my_object)` you write `my_object.f()`:" 765 | ] 766 | }, 767 | { 768 | "cell_type": "code", 769 | "execution_count": null, 770 | "metadata": {}, 771 | "outputs": [], 772 | "source": [ 773 | "p = 17\n", 774 | "p.is_prime()" 775 | ] 776 | }, 777 | { 778 | "cell_type": "markdown", 779 | "metadata": {}, 780 | "source": [ 781 | "See [Tutorial: Objects and Classes in Python and Sage](http://doc.sagemath.org/html/en/thematic_tutorials/tutorial-objects-and-classes.html#tutorial-objects-and-classes) for details." 782 | ] 783 | }, 784 | { 785 | "cell_type": "markdown", 786 | "metadata": {}, 787 | "source": [ 788 | "### Method discovery with tab-completion\n", 789 | "\n", 790 | "" 791 | ] 792 | }, 793 | { 794 | "cell_type": "markdown", 795 | "metadata": {}, 796 | "source": [ 797 | "To know all methods of an object you can once more use Tab-completion. Write the name of the object followed by a dot and then press Tab:" 798 | ] 799 | }, 800 | { 801 | "cell_type": "code", 802 | "execution_count": null, 803 | "metadata": {}, 804 | "outputs": [], 805 | "source": [ 806 | "a." 807 | ] 808 | }, 809 | { 810 | "cell_type": "markdown", 811 | "metadata": {}, 812 | "source": [ 813 | "#### Exercise B\n", 814 | "\n", 815 | "Create the permutation 51324 and assign it to the variable p." 816 | ] 817 | }, 818 | { 819 | "cell_type": "code", 820 | "execution_count": null, 821 | "metadata": { 822 | "tags": [] 823 | }, 824 | "outputs": [], 825 | "source": [ 826 | "Permutation?" 827 | ] 828 | }, 829 | { 830 | "cell_type": "code", 831 | "execution_count": null, 832 | "metadata": {}, 833 | "outputs": [], 834 | "source": [] 835 | }, 836 | { 837 | "cell_type": "markdown", 838 | "metadata": { 839 | "tags": [] 840 | }, 841 | "source": [ 842 | "What is the inverse of p?" 843 | ] 844 | }, 845 | { 846 | "cell_type": "code", 847 | "execution_count": null, 848 | "metadata": {}, 849 | "outputs": [], 850 | "source": [ 851 | "p.inv" 852 | ] 853 | }, 854 | { 855 | "cell_type": "markdown", 856 | "metadata": {}, 857 | "source": [ 858 | "Does $p$ have the pattern 123? What about 1234? And 312? (even if you don’t\n", 859 | "know what a pattern is, you should be able to find a command that does this)." 860 | ] 861 | }, 862 | { 863 | "cell_type": "code", 864 | "execution_count": null, 865 | "metadata": {}, 866 | "outputs": [], 867 | "source": [ 868 | "p.pat" 869 | ] 870 | }, 871 | { 872 | "cell_type": "markdown", 873 | "metadata": {}, 874 | "source": [ 875 | "### Linear algebra" 876 | ] 877 | }, 878 | { 879 | "cell_type": "markdown", 880 | "metadata": {}, 881 | "source": [ 882 | "#### Exercise C\n", 883 | "\n", 884 | "Use the matrix() command to create the following matrix.\n", 885 | "\n", 886 | "$$\n", 887 | "M = \\left(\\begin{array}{rrrr}\n", 888 | "10 & 4 & 1 & 1 \\\\\n", 889 | "4 & 6 & 5 & 1 \\\\\n", 890 | "1 & 5 & 6 & 4 \\\\\n", 891 | "1 & 1 & 4 & 10\n", 892 | "\\end{array}\\right)\n", 893 | "$$" 894 | ] 895 | }, 896 | { 897 | "cell_type": "code", 898 | "execution_count": null, 899 | "metadata": {}, 900 | "outputs": [], 901 | "source": [ 902 | "matrix?" 903 | ] 904 | }, 905 | { 906 | "cell_type": "code", 907 | "execution_count": null, 908 | "metadata": {}, 909 | "outputs": [], 910 | "source": [] 911 | }, 912 | { 913 | "cell_type": "markdown", 914 | "metadata": {}, 915 | "source": [ 916 | "Then, using methods of the matrix,\n", 917 | "\n", 918 | "1. Compute the determinant of the matrix. \n", 919 | "1. Compute the echelon form of the matrix. \n", 920 | "1. Compute the eigenvalues of the matrix. \n", 921 | "1. Compute the kernel of the matrix. \n", 922 | "1. Compute the LLL decomposition of the matrix (and lookup the\n", 923 | " documentation for what LLL is if needed!) " 924 | ] 925 | }, 926 | { 927 | "cell_type": "code", 928 | "execution_count": null, 929 | "metadata": {}, 930 | "outputs": [], 931 | "source": [] 932 | }, 933 | { 934 | "cell_type": "markdown", 935 | "metadata": {}, 936 | "source": [ 937 | "Now that you know how to access the different methods of matrices,\n", 938 | "\n", 939 | "1. Create the vector $ v = (1, -1, -1, 1) $. \n", 940 | "1. Compute the two products: $ M \\cdot v $ and $ v \\cdot M $. What mathematical operation is Sage doing implicitly? " 941 | ] 942 | }, 943 | { 944 | "cell_type": "code", 945 | "execution_count": null, 946 | "metadata": {}, 947 | "outputs": [], 948 | "source": [ 949 | "vector?" 950 | ] 951 | }, 952 | { 953 | "cell_type": "code", 954 | "execution_count": null, 955 | "metadata": {}, 956 | "outputs": [], 957 | "source": [] 958 | }, 959 | { 960 | "cell_type": "markdown", 961 | "metadata": {}, 962 | "source": [ 963 | "Vectors in Sage can be used as row vectors or column vectors. A method such as eigenspaces might not\n", 964 | "return what you expect, so it is best to specify `eigenspaces_left` or `eigenspaces_right` instead. Same thing for kernel (`left_kernel` or `right_kernel`), and so on." 965 | ] 966 | }, 967 | { 968 | "cell_type": "markdown", 969 | "metadata": {}, 970 | "source": [ 971 | "### Plotting\n", 972 | "\n", 973 | "The `plot()` command allows you to draw plots of functions. Recall\n", 974 | "that you can access the documentation by pressing the Tab key\n", 975 | "after writing `plot?` in a cell:" 976 | ] 977 | }, 978 | { 979 | "cell_type": "code", 980 | "execution_count": null, 981 | "metadata": {}, 982 | "outputs": [], 983 | "source": [ 984 | "plot?" 985 | ] 986 | }, 987 | { 988 | "cell_type": "markdown", 989 | "metadata": {}, 990 | "source": [ 991 | "Here is a simple example:" 992 | ] 993 | }, 994 | { 995 | "cell_type": "code", 996 | "execution_count": null, 997 | "metadata": {}, 998 | "outputs": [], 999 | "source": [ 1000 | "var('x') # make sure x is a symbolic variable" 1001 | ] 1002 | }, 1003 | { 1004 | "cell_type": "code", 1005 | "execution_count": null, 1006 | "metadata": {}, 1007 | "outputs": [], 1008 | "source": [ 1009 | "plot(sin(x^2), (x, 0, 10))" 1010 | ] 1011 | }, 1012 | { 1013 | "cell_type": "markdown", 1014 | "metadata": {}, 1015 | "source": [ 1016 | "Here is a more complicated plot. Try to change every single input to the plot\n", 1017 | "command in some way, evaluating to see what happens:" 1018 | ] 1019 | }, 1020 | { 1021 | "cell_type": "code", 1022 | "execution_count": null, 1023 | "metadata": {}, 1024 | "outputs": [], 1025 | "source": [ 1026 | "P = plot(sin(x^2), (x, -2, 2), rgbcolor=(0.8, 0, 0.2), thickness=3, linestyle='--', fill='axis')\n", 1027 | "show(P, gridlines=True)" 1028 | ] 1029 | }, 1030 | { 1031 | "cell_type": "markdown", 1032 | "metadata": {}, 1033 | "source": [ 1034 | "Above we used the `show(P)` command to show a plot after it was created. You can\n", 1035 | "also use `P.show()` instead:" 1036 | ] 1037 | }, 1038 | { 1039 | "cell_type": "code", 1040 | "execution_count": null, 1041 | "metadata": {}, 1042 | "outputs": [], 1043 | "source": [ 1044 | "P.show(gridlines=True)" 1045 | ] 1046 | }, 1047 | { 1048 | "cell_type": "markdown", 1049 | "metadata": {}, 1050 | "source": [ 1051 | "Try putting the cursor right after `P.show(` and pressing Tab key to get a list of\n", 1052 | "the options for how you can change the values of the given inputs." 1053 | ] 1054 | }, 1055 | { 1056 | "cell_type": "code", 1057 | "execution_count": null, 1058 | "metadata": {}, 1059 | "outputs": [], 1060 | "source": [ 1061 | "P.show(" 1062 | ] 1063 | }, 1064 | { 1065 | "cell_type": "markdown", 1066 | "metadata": {}, 1067 | "source": [ 1068 | "Plotting multiple functions at once is as easy as adding the plots together:" 1069 | ] 1070 | }, 1071 | { 1072 | "cell_type": "code", 1073 | "execution_count": null, 1074 | "metadata": {}, 1075 | "outputs": [], 1076 | "source": [ 1077 | "P1 = plot(sin(x), (x, 0, 2*pi))\n", 1078 | "P2 = plot(cos(x), (x, 0, 2*pi), rgbcolor='red')\n", 1079 | "P1 + P2" 1080 | ] 1081 | }, 1082 | { 1083 | "cell_type": "markdown", 1084 | "metadata": {}, 1085 | "source": [ 1086 | "### Symbolic Expressions\n", 1087 | "\n", 1088 | "Here is an example of a symbolic function:" 1089 | ] 1090 | }, 1091 | { 1092 | "cell_type": "code", 1093 | "execution_count": null, 1094 | "metadata": {}, 1095 | "outputs": [], 1096 | "source": [ 1097 | "f(x) = x^4 - 8*x^2 - 3*x + 2\n", 1098 | "f(x)" 1099 | ] 1100 | }, 1101 | { 1102 | "cell_type": "code", 1103 | "execution_count": null, 1104 | "metadata": {}, 1105 | "outputs": [], 1106 | "source": [ 1107 | "f(-3)" 1108 | ] 1109 | }, 1110 | { 1111 | "cell_type": "markdown", 1112 | "metadata": {}, 1113 | "source": [ 1114 | "This is an example of a function in the *mathematical* variable $ x $. When Sage\n", 1115 | "starts, it defines the symbol $ x $ to be a mathematical variable. If you want\n", 1116 | "to use other symbols for variables, you must define them first:" 1117 | ] 1118 | }, 1119 | { 1120 | "cell_type": "code", 1121 | "execution_count": null, 1122 | "metadata": {}, 1123 | "outputs": [], 1124 | "source": [ 1125 | "x^2" 1126 | ] 1127 | }, 1128 | { 1129 | "cell_type": "code", 1130 | "execution_count": null, 1131 | "metadata": {}, 1132 | "outputs": [], 1133 | "source": [ 1134 | "u + v" 1135 | ] 1136 | }, 1137 | { 1138 | "cell_type": "code", 1139 | "execution_count": null, 1140 | "metadata": {}, 1141 | "outputs": [], 1142 | "source": [ 1143 | "var('u v')" 1144 | ] 1145 | }, 1146 | { 1147 | "cell_type": "code", 1148 | "execution_count": null, 1149 | "metadata": {}, 1150 | "outputs": [], 1151 | "source": [ 1152 | "u + v" 1153 | ] 1154 | }, 1155 | { 1156 | "cell_type": "markdown", 1157 | "metadata": {}, 1158 | "source": [ 1159 | "Still, it is possible to define symbolic functions without first\n", 1160 | "defining their variables:" 1161 | ] 1162 | }, 1163 | { 1164 | "cell_type": "code", 1165 | "execution_count": null, 1166 | "metadata": {}, 1167 | "outputs": [], 1168 | "source": [ 1169 | "f(w) = w^2\n", 1170 | "f(3)" 1171 | ] 1172 | }, 1173 | { 1174 | "cell_type": "markdown", 1175 | "metadata": {}, 1176 | "source": [ 1177 | "In this case those variables are defined implicitly:" 1178 | ] 1179 | }, 1180 | { 1181 | "cell_type": "code", 1182 | "execution_count": null, 1183 | "metadata": {}, 1184 | "outputs": [], 1185 | "source": [ 1186 | "w" 1187 | ] 1188 | }, 1189 | { 1190 | "cell_type": "markdown", 1191 | "metadata": {}, 1192 | "source": [ 1193 | "#### Exercise D\n", 1194 | "\n", 1195 | "Define the symbolic function $ f(x) = x \\sin x^2 $. Plot $ f $ on the\n", 1196 | "domain $ [-3, 3] $ and color it red. Use the `find_root()` method to\n", 1197 | "numerically approximate the root of $ f $ on the interval $ [1, 2] $:" 1198 | ] 1199 | }, 1200 | { 1201 | "cell_type": "code", 1202 | "execution_count": null, 1203 | "metadata": {}, 1204 | "outputs": [], 1205 | "source": [] 1206 | }, 1207 | { 1208 | "cell_type": "markdown", 1209 | "metadata": {}, 1210 | "source": [ 1211 | "Compute the tangent line to $ f $ at $ x = 1 $:" 1212 | ] 1213 | }, 1214 | { 1215 | "cell_type": "code", 1216 | "execution_count": null, 1217 | "metadata": {}, 1218 | "outputs": [], 1219 | "source": [] 1220 | }, 1221 | { 1222 | "cell_type": "markdown", 1223 | "metadata": {}, 1224 | "source": [ 1225 | "Plot $ f $ and the tangent line to $ f $ at $ x = 1 $ in one image:" 1226 | ] 1227 | }, 1228 | { 1229 | "cell_type": "code", 1230 | "execution_count": null, 1231 | "metadata": {}, 1232 | "outputs": [], 1233 | "source": [] 1234 | }, 1235 | { 1236 | "cell_type": "markdown", 1237 | "metadata": {}, 1238 | "source": [ 1239 | "#### Exercise E (Advanced)\n", 1240 | "\n", 1241 | "Solve the following equation for $y$\n", 1242 | "\n", 1243 | "$$\n", 1244 | "y = 1 + x y^2\n", 1245 | "$$\n", 1246 | "\n", 1247 | "There are two solutions, take the one for which $ \\lim_{x\\to0} y(x) = 1 $.\n", 1248 | "(Don’t forget to create the variables $ x $ and $ y $!)." 1249 | ] 1250 | }, 1251 | { 1252 | "cell_type": "code", 1253 | "execution_count": null, 1254 | "metadata": {}, 1255 | "outputs": [], 1256 | "source": [] 1257 | }, 1258 | { 1259 | "cell_type": "markdown", 1260 | "metadata": {}, 1261 | "source": [ 1262 | "Expand $ y $ as a truncated Taylor series around $ 0 $ containing\n", 1263 | "$ n = 10 $ terms." 1264 | ] 1265 | }, 1266 | { 1267 | "cell_type": "code", 1268 | "execution_count": null, 1269 | "metadata": {}, 1270 | "outputs": [], 1271 | "source": [] 1272 | }, 1273 | { 1274 | "cell_type": "markdown", 1275 | "metadata": {}, 1276 | "source": [ 1277 | "Do you recognize the coefficients of the Taylor series expansion? You might want to use the [On-Line Encyclopedia of Integer Sequences](https://oeis.org/), or better yet, Sage’s class OEIS which queries the encyclopedia:" 1278 | ] 1279 | }, 1280 | { 1281 | "cell_type": "code", 1282 | "execution_count": null, 1283 | "metadata": {}, 1284 | "outputs": [], 1285 | "source": [ 1286 | "oeis?" 1287 | ] 1288 | }, 1289 | { 1290 | "cell_type": "code", 1291 | "execution_count": null, 1292 | "metadata": {}, 1293 | "outputs": [], 1294 | "source": [] 1295 | }, 1296 | { 1297 | "cell_type": "markdown", 1298 | "metadata": {}, 1299 | "source": [ 1300 | "Congratulations for completing your first Sage tutorial!" 1301 | ] 1302 | }, 1303 | { 1304 | "cell_type": "markdown", 1305 | "metadata": {}, 1306 | "source": [ 1307 | "## Exploring further" 1308 | ] 1309 | }, 1310 | { 1311 | "cell_type": "markdown", 1312 | "metadata": {}, 1313 | "source": [ 1314 | "### Accessing Sage\n", 1315 | "\n", 1316 | "- The [Sage cell service](https://sagecell.sagemath.org) lets you evaluate individual Sage commands. \n", 1317 | "- In general, Sage computations can be embedded in any web page using [Thebe](https://thebe.readthedocs.io/en/stable).\n", 1318 | "- [Binder](https://mybinder.org) is a service that lets you run Jupyter online on top of an arbitrary software stack. \n", 1319 | " Sessions are free, anonymous, and temporary. You can use one of the existing repositories, or create your own. \n", 1320 | "\n", 1321 | "" 1322 | ] 1323 | }, 1324 | { 1325 | "cell_type": "markdown", 1326 | "metadata": {}, 1327 | "source": [ 1328 | "### Ways to use Sage\n", 1329 | "\n", 1330 | "There are other ways beyond the Jupyter Notebook to use Sage: interactive command line, program scripts, etc.\n", 1331 | "See [Sage tutorial](https://doc.sagemath.org/html/en/tutorial/introduction.html#ways-to-use-sage)." 1332 | ] 1333 | }, 1334 | { 1335 | "cell_type": "markdown", 1336 | "metadata": {}, 1337 | "source": [ 1338 | "### Resources\n", 1339 | "\n", 1340 | "- [Sage tutorial](https://doc.sagemath.org/html/en/tutorial/index.html) \n", 1341 | "- [Sage thematic tutorials](https://doc.sagemath.org/html/en/thematic_tutorials/index.html) \n", 1342 | "- [The open book *Computational Mathematics with Sage*](https://www.sagemath.org/sagebook/english.html)\n", 1343 | "- [Sage quick reference cards](https://wiki.sagemath.org/quickref) \n", 1344 | "- [Sage webpage https://www.sagemath.org](https://www.sagemath.org) \n", 1345 | "- [Ask Sage https://ask.sagemath.org](https://ask.sagemath.org) \n", 1346 | "- [Sage GitHub repo](https://github.com/sagemath/sage/issues)" 1347 | ] 1348 | } 1349 | ], 1350 | "metadata": { 1351 | "kernelspec": { 1352 | "display_name": "SageMath 10.1.rc0", 1353 | "language": "sage", 1354 | "name": "sagemath" 1355 | }, 1356 | "language_info": { 1357 | "codemirror_mode": { 1358 | "name": "ipython", 1359 | "version": 3 1360 | }, 1361 | "file_extension": ".py", 1362 | "mimetype": "text/x-python", 1363 | "name": "python", 1364 | "nbconvert_exporter": "python", 1365 | "pygments_lexer": "ipython3", 1366 | "version": "3.11.5" 1367 | } 1368 | }, 1369 | "nbformat": 4, 1370 | "nbformat_minor": 4 1371 | } 1372 | --------------------------------------------------------------------------------