From d87c1c214b2a17e31eaa57a3dd1c5bc4c8350105 Mon Sep 17 00:00:00 2001 From: Kwankyu Lee Date: Tue, 29 Oct 2024 20:43:46 +0900 Subject: [PATCH] Update files for Binder --- .github/Dockerfile | 57 + .github/icons/blue.ico | Bin 0 -> 36200 bytes .github/icons/orange.ico | Bin 0 -> 36750 bytes .github/workflows/create-wsl-image.yml | 311 ++++ .github/workflows/update-dockerfile-dev.yml | 82 + .../workflows/update-dockerfile-master.yml | 83 + .gitignore | 0 Dockerfile | 44 + LICENSE | 674 ++++++++ README.rst | 43 + notebooks/Start here.ipynb | 1371 +++++++++++++++++ 11 files changed, 2665 insertions(+) create mode 100644 .github/Dockerfile create mode 100644 .github/icons/blue.ico create mode 100644 .github/icons/orange.ico create mode 100644 .github/workflows/create-wsl-image.yml create mode 100644 .github/workflows/update-dockerfile-dev.yml create mode 100644 .github/workflows/update-dockerfile-master.yml create mode 100644 .gitignore create mode 100644 Dockerfile create mode 100644 LICENSE create mode 100644 README.rst create mode 100644 notebooks/Start here.ipynb diff --git a/.github/Dockerfile b/.github/Dockerfile new file mode 100644 index 0000000..239d8d6 --- /dev/null +++ b/.github/Dockerfile @@ -0,0 +1,57 @@ +# Multi-stage Dockerfile for slim Sage +# https://docs.docker.com/build/building/multi-stage + +FROM ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-targets:10.4 AS target + +# Resolve symbolic links to recreate them later +RUN readlink /sage/prefix >> /sage/prefix_link +RUN readlink /sage/venv >> /sage/venv_link + +WORKDIR /sage + +# Strip executables in /sage +RUN LC_ALL=C find local src pkgs -type f -exec strip '{}' ';' 2>&1 | grep -v "file format not recognized" || true + +# Clean up before copying in the next stage +RUN rm -rf local/share/doc local/share/*/doc local/share/*/examples local/share/singular/html + +# Remove all __pycache__ directories +RUN find /sage -type d -name "__pycache__" -exec rm -rf {} + +# Remove all .c .cpp files corresponding to .pyx files +RUN find /sage -name "*.pyx" | sed 's/\(.*\)[.]pyx$/\1.c \1.cpp/' | xargs rm -f + + +FROM ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-system-packages:10.4 + +USER root + +# Remove warnings +ENV DEBIAN_FRONTEND noninteractive +ENV DEBCONF_NOWARNINGS="yes" + +# Install JupyterLab to the system +RUN apt-get update +RUN apt-get install -y --no-install-recommends python3-pip +RUN python3 -m pip install --no-warn-script-location --no-cache-dir notebook jupyterlab ipywidgets + +# Disable annoying popup for Jupyter news +RUN jupyter labextension disable "@jupyterlab/apputils-extension:announcements" + +# Install /sage from target +COPY --from=target /sage/local /sage/local +COPY --from=target /sage/src/bin /sage/src/bin +COPY --from=target /sage/src/sage /sage/src/sage +COPY --from=target /sage/sage /sage/sage +COPY --from=target /sage/pkgs/sage-conf /sage/pkgs/sage-conf + +# Recreate symbolic links +COPY --from=target /sage/prefix_link /sage/prefix_link +COPY --from=target /sage/venv_link /sage/venv_link +RUN ln -s $(cat /sage/prefix_link) /sage/prefix && rm /sage/prefix_link +RUN ln -s $(cat /sage/venv_link) /sage/venv && rm /sage/venv_link + +# Configure Sage library +RUN /sage/sage -pip install --root-user-action=ignore /sage/pkgs/sage-conf + +# Remove problematic lines! +RUN sed -i '/^__requires__/d' /sage/venv/bin/sage-venv-config +RUN sed -i '/^__import__/d' /sage/venv/bin/sage-venv-config diff --git a/.github/icons/blue.ico b/.github/icons/blue.ico new file mode 100644 index 0000000000000000000000000000000000000000..4b010bd1ede0d6e3e05b1f002a2c980d2485a3a6 GIT binary patch literal 36200 zcmZr%byyVN*Pks|dg+FxL8Jtv1eO*FK|qi$0Tt=ar8`9U(y)L6A}QS+qJ)HW3DPCq z`||t$op|QXbN`!j=G^;<0|21=^M3~jKmsq~0D$U#9HphHLWEC;e?KHreX984f3yF) z;W+mXW0zu^|Ghc7XzGGS@;x&E01c=r%ISK|?wQ~kB&^F=+3A*QxO)vXhEl5 zaK2b2CizoPn1X zLOB5Y=vXbwepXr3oXZ?|#W>%#fK#V07F4^FDferZ*Zd|+2Ps%im*(rJJdze`PmD$+ zZR|{I01Ex@VYY^g5Mk;An?Urg#dCdGy;H<)E52Os3bWkS`d19*f+BH)8Nz}WfimBf 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workflow_dispatch: + +jobs: + build-and-export: + runs-on: ubuntu-latest + outputs: + upload_url: ${{ steps.create_release.outputs.upload_url }} + version: ${{ steps.extract_version.outputs.version }} + steps: + + # Create WSL export (a tar file) of the minimal Sage install + + - name: Prepare Dockerfile + run: | + curl -o Dockerfile https://raw.githubusercontent.com/sagemath/sage-binder-env/master/Dockerfile + sed -i '/COPY notebooks/d' Dockerfile # remove the line from Dockerfile + + - name: Extract version from Dockerfile + id: extract_version + run: | + VERSION=$(grep '^FROM ghcr.io/sagemath/sage-binder-env:' Dockerfile | sed 's/^FROM ghcr.io\/sagemath\/sage-binder-env://') + echo "VERSION=$VERSION" >> $GITHUB_ENV + echo "version=$VERSION" >> $GITHUB_OUTPUT + + - name: Build and export Docker image + run: | + docker build -t sagemath-container . + export CONTAINER_ID=$(docker create sagemath-container) + docker export $CONTAINER_ID -o sagemath-$VERSION-wsl.tar + + - name: Upload tar file as artifact + id: upload-artifact + uses: actions/upload-artifact@v4 + with: + name: sagemath-${{ env.VERSION }}-wsl + path: sagemath-${{ env.VERSION }}-wsl.tar + + # Make a release + + - name: Get latest release version + id: get_latest_release + run: | + LATEST_VERSION=$(curl -s https://api.github.com/repos/${{ github.repository }}/releases/latest | jq -r '.tag_name // "0.0.0"' | sed 's/v//') + echo "LATEST_VERSION=$LATEST_VERSION" >> $GITHUB_ENV + + - name: Zip the tar file + if: ${{ env.VERSION != env.LATEST_VERSION }} + run: | + zip sagemath-${{ env.VERSION }}-wsl.zip sagemath-${{ env.VERSION }}-wsl.tar + + - name: Create GitHub Release + if: ${{ env.VERSION != env.LATEST_VERSION }} + id: create_release + uses: actions/create-release@v1 + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + with: + tag_name: v${{ env.VERSION }} + release_name: Run SageMath ${{ env.VERSION }} on WSL + body: | + We recommend you check if WSL is enabled before running the installer. + + The .ps1 installer downloads the .zip file and imports a minimized SageMath ${{ env.VERSION }} into WSL. + + After downloading the installer, right-click it to open the context menu and run it with PowerShell. + You may also open the installer as a text file, and copy and paste all lines into a PowerShell window. + + The installer should create two shortcuts on your desktop: one for launching SageMath + and another to start the Jupyter server for SageMath. + + The minimized SageMath is the same as the one used in the Binder environment, meaning no bells and whistles. + Notably the Sage build system is not included. + draft: false + prerelease: false + + - name: Upload release asset + if: ${{ env.VERSION != env.LATEST_VERSION }} + uses: actions/upload-release-asset@v1 + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + with: + upload_url: ${{ steps.create_release.outputs.upload_url }} + asset_path: ./sagemath-${{ env.VERSION }}-wsl.zip + asset_name: sagemath-${{ env.VERSION }}-wsl.zip + asset_content_type: application/zip + + # Generate a Windows PowerShell script + + - name: Checkout repo + uses: actions/checkout@v3 + + - name: Generate PowerShell Script + run: | + cat << EOF > download_and_import_sagemath_to_wsl.ps1 + # ---------------------------------------------------- + # Copy and paste all lines into the Windows PowerShell + # ---------------------------------------------------- + + [Console]::OutputEncoding = [System.Text.Encoding]::UTF8 + try { + Write-Host "Checking WSL installation." + wsl --install --no-distribution + if (\$LASTEXITCODE -ne 0) { + Write-Host "WSL installation failed." + Read-Host -Prompt "Press any key to exit"; exit + } + } catch { + Write-Host "Could not check WSL installation, proceeding with fingers crossed." + } + # Check if SageMath already exists in WSL + \$sagemathWSL = "SageMath-$VERSION" + if ((wsl -l -q) -split 'n' -contains \$sagemathWSL) { + # Ask user if they want to reinstall SageMath + \$response = Read-Host "\$sagemathWSL is already installed. Do you want to reinstall it? (y/n)" + if (\$response -eq "y") { + Write-Host "Uninstalling \$sagemathWSL." + # Unregister the existing SageMath WSL distribution + wsl --unregister \$sagemathWSL + } else { + Read-Host "OK. Press any key to exit"; exit + } + } + \$artifactUrl = "https://github.com/sagemath/sage-binder-env/releases/download/v$VERSION/sagemath-$VERSION-wsl.zip" + \$zipFilePath = "\$PWD\\artifact.zip" + \$dataPath = "\$HOME\\AppData\\Local\\SageMath" + \$tarFilePath = "\$dataPath\\sagemath-$VERSION-wsl.tar" + # Ensure the path exists + if (-Not (Test-Path \$dataPath)) { New-Item -Path \$dataPath -ItemType Directory > \$null } + # Skip downloading and extracting if the tar file already exists + if (-Not (Test-Path \$tarFilePath)) { + Write-Host "Downloading \$sagemathWSL..." + Start-BitsTransfer -Source \$artifactUrl -Destination \$zipFilePath + Write-Host "Extracting..." + Expand-Archive -Path \$zipFilePath -DestinationPath \$dataPath -Force + if (Test-Path \$tarFilePath) { Remove-Item \$zipFilePath } + } else { + Write-Host "\$sagemathWSL was already downloaded." + } + # Import the WSL image + Write-Host "Start importing..." + wsl --import SageMath-$VERSION \$dataPath \$tarFilePath + # Check if importing succeeded + if (-Not ((wsl -l -q) -split 'n' -contains \$sagemathWSL)) { + Write-Host "Importing \$sagemathWSL into WSL failed." + Write-Host "If WSL was freshly installed by this installer, try again after rebooting the computer." + Read-Host "Press any key to exit"; exit + } + Write-Host "Creating shortcults at:" + # Download icons for shortcuts + \$iconUrlOrange = "https://raw.githubusercontent.com/sagemath/sage-binder-env/refs/heads/master/.github/icons/orange.ico" + \$iconUrlBlue = "https://raw.githubusercontent.com/sagemath/sage-binder-env/refs/heads/master/.github/icons/blue.ico" + \$iconPathOrange = "\$dataPath\\orange.ico" + \$iconPathBlue = "\$dataPath\\blue.ico" + # Download the icon if it doesn't exist + if (-Not (Test-Path \$iconPathBlue)) { + Start-BitsTransfer -Source \$iconUrlBlue -Destination \$iconPathBlue + } + if (-Not (Test-Path \$iconPathOrange)) { + Start-BitsTransfer -Source \$iconUrlOrange -Destination \$iconPathOrange + } + # Create shortcuts + \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Sage.lnk" + \$TargetPath = "C:\\Windows\\System32\\wsl.exe" + \$Arguments = "-d \$sagemathWSL --user user --cd ~ /sage/sage" + \$WScriptShell = New-Object -ComObject WScript.Shell + \$Shortcut = \$WScriptShell.CreateShortcut(\$ShortcutFile) + \$Shortcut.TargetPath = \$TargetPath + \$Shortcut.Arguments = \$Arguments + \$Shortcut.IconLocation = \$iconPathBlue + \$Shortcut.Save() + Write-Host "\$ShortcutFile" + # Create a shortcut that starts Jupyter on Desktop + \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Jupyter.lnk" + \$TargetPath = "C:\\Windows\\System32\\wsl.exe" + \$Arguments = "-d \$sagemathWSL --user user --cd ~ jupyter lab --no-browser" + \$WScriptShell = New-Object -ComObject WScript.Shell + \$Shortcut = \$WScriptShell.CreateShortcut(\$ShortcutFile) + \$Shortcut.TargetPath = \$TargetPath + \$Shortcut.Arguments = \$Arguments + \$Shortcut.IconLocation = \$iconPathOrange + \$Shortcut.Save() + Write-Host "\$ShortcutFile" + Read-Host "\`n\$sagemathWSL installation succeeded!\`nPress any key to exit" + EOF + cat << EOF > remove_sagemath_from_wsl.ps1 + # ---------------------------------------------------- + # Copy and paste all lines into the Windows PowerShell + # ---------------------------------------------------- + + [Console]::OutputEncoding = [System.Text.Encoding]::UTF8 + try { + Write-Host "Checking WSL installation." + wsl --install --no-distribution + if (\$LASTEXITCODE -ne 0) { + Write-Host "WSL installation failed." + Read-Host -Prompt "Press any key to exit"; exit + } + } catch { + Write-Host "Could not check WSL installation, proceeding with fingers crossed." + } + # Check if SageMath already exists in WSL + \$sagemathWSL = "SageMath-$VERSION" + \$dataPath = "\$HOME\\AppData\\Local\\SageMath" + \$iconPathOrange = "\$dataPath\\orange.ico" + \$iconPathBlue = "\$dataPath\\blue.ico" + if ((wsl -l -q) -split 'n' -contains \$sagemathWSL) { + # Ask user if they want to reinstall SageMath + \$response = Read-Host "Do you want to uninstall \$(\$sagemathWSL) from WSL? (y/n)" + if (\$response -eq "y") { + Write-Host "Uninstalling \$sagemathWSL..." + try { + wsl --unregister \$sagemathWSL + } catch { + Write-Host "Failed: wsl --unregister \$sagemathWSL" + } + try { + rm -recurse \$dataPath + } catch { + Write-Host "Failed: rm -recurse \$dataPath" + } + try { + \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Sage.lnk" + rm \$ShortcutFile + } catch { + Write-Host "Failed: rm \$ShortcutFile" + } + try { + \$ShortcutFile = "\$([Environment]::GetFolderPath('Desktop'))\\Run Jupyter.lnk" + rm \$ShortcutFile + } catch { + Write-Host "Failed: rm \$ShortcutFile" + } + } else { + Read-Host "OK. Press any key to exit"; exit + } + } else { + Write-Host "\$sagemathWSL is not found." + Read-Host -Prompt "Press any key to exit"; exit + } + Read-Host "\`n\$sagemathWSL uninstallation succeeded!\`nPress any key to exit" + EOF + shell: bash + + - name: Upload installation script as artifact + uses: actions/upload-artifact@v4 + with: + name: download_and_import_sagemath_to_wsl + path: download_and_import_sagemath_to_wsl.ps1 + + - name: Upload uninstallation script as artifact + uses: actions/upload-artifact@v4 + with: + name: remove_sagemath_from_wsl + path: remove_sagemath_from_wsl.ps1 + + - name: Upload installation script as release asset + if: ${{ env.VERSION != env.LATEST_VERSION }} + uses: actions/upload-release-asset@v1 + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + with: + upload_url: ${{ steps.create_release.outputs.upload_url }} + asset_path: ./download_and_import_sagemath_to_wsl.ps1 + asset_name: sagemath-${{ env.VERSION }}-wsl-installer.ps1 + asset_content_type: application/octet-stream + + - name: Upload uninstallation script as release asset + if: ${{ env.VERSION != env.LATEST_VERSION }} + uses: actions/upload-release-asset@v1 + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + with: + upload_url: ${{ steps.create_release.outputs.upload_url }} + asset_path: ./remove_sagemath_from_wsl.ps1 + asset_name: sagemath-${{ env.VERSION }}-wsl-uninstaller.ps1 + asset_content_type: application/octet-stream + +# build-exe: +# runs-on: windows-latest +# needs: build-and-export +# if: ${{ contains(needs.build-and-export.outputs.upload_url || '', 'http') }} +# steps: +# - name: Checkout repository +# uses: actions/checkout@v3 +# +# - name: Download PowerShell Script artifact +# uses: actions/download-artifact@v4 +# with: +# name: download_and_import_sagemath_to_wsl +# +# - name: Install PS2EXE +# run: | +# Install-Module -Name ps2exe -Force +# Import-Module ps2exe +# Invoke-ps2exe -inputFile .\download_and_import_sagemath_to_wsl.ps1 -outputFile .\sagemath_installer.exe +# shell: powershell +# +# - name: Upload EXE to GitHub Release +# uses: actions/upload-release-asset@v1 +# env: +# GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} +# with: +# upload_url: ${{ needs.build-and-export.outputs.upload_url }} +# asset_path: ./sagemath_installer.exe +# asset_name: sagemath-${{ needs.build-and-export.outputs.version }}-wsl-installer.exe +# asset_content_type: application/octet-stream diff --git a/.github/workflows/update-dockerfile-dev.yml b/.github/workflows/update-dockerfile-dev.yml new file mode 100644 index 0000000..af6b15e --- /dev/null +++ b/.github/workflows/update-dockerfile-dev.yml @@ -0,0 +1,82 @@ +name: Update dev image + +on: + schedule: + - cron: '0 1 * * *' # Run every day + workflow_dispatch: + +env: + SAGE_TARGET: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-targets + SAGE_SYSTEM: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-system-packages + TAG: dev + BRANCH: dev + +jobs: + build: + runs-on: ubuntu-latest + permissions: + contents: write + packages: write + steps: + + # Prepare .github/Dockerfile for slim Sage image + + - name: Checkout code + uses: actions/checkout@v4 + with: + ref: ${{ env.BRANCH }} + - name: Prepare .github/Dockerfile + run: | + SAGE_VERSION=$(docker run --rm ${SAGE_TARGET}:$TAG /sage/sage --version | grep -oP 'SageMath version \K[0-9.]+(?:beta\d+)?(?:rc\d+)?') + SAGE_TARGET_ESCAPED=$(echo "${SAGE_TARGET}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + SAGE_TARGET_VERSION_ESCAPED=$(echo "${SAGE_TARGET}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + sed -i "s/FROM ${SAGE_TARGET_ESCAPED}:\S*/FROM ${SAGE_TARGET_VERSION_ESCAPED}/g" .github/Dockerfile + SAGE_SYSTEM_ESCAPED=$(echo "${SAGE_SYSTEM}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + SAGE_SYSTEM_VERSION_ESCAPED=$(echo "${SAGE_SYSTEM}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + sed -i "s/FROM ${SAGE_SYSTEM_ESCAPED}:\S*/FROM ${SAGE_SYSTEM_VERSION_ESCAPED}/g" .github/Dockerfile + PACKAGE_NAME=ghcr.io/${{ github.repository }}:${SAGE_VERSION} + echo "PACKAGE_NAME=$PACKAGE_NAME" >> $GITHUB_ENV + git config --global user.email alice@wonderland + git config --global user.name alice + git commit -a --amend -m "Dockerfile for Sage ${SAGE_VERSION}" + git push -f origin $BRANCH + + # Build and publish the slim Sage image to github package registry (ghpr) + + - name: Log in to the Container registry + uses: docker/login-action@v3 + with: + registry: ghcr.io + username: ${{ github.actor }} + password: ${{ secrets.GITHUB_TOKEN }} + - name: Build and push Docker image + uses: docker/build-push-action@v5 + with: + context: .github + push: true + tags: ${{ env.PACKAGE_NAME }} + + # Update files for Binder + + - name: Checkout code + uses: actions/checkout@v4 + with: + ref: ${{ env.BRANCH }} + - name: Update files for Binder + run: | + PACKAGE_NAME=${{ env.PACKAGE_NAME }} + PACKAGE_NAME_ESCAPED=$(echo "${PACKAGE_NAME}" | sed 's/\//\\\//g') + sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" Dockerfile + sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" README.rst + git config --global user.email alice@wonderland + git config --global user.name alice + git commit -a --amend -m "Update files for Binder" + git push -f origin $BRANCH + + # Build docker image for Binder from Dockerfile at root + + - name: Binder build + timeout-minutes: 30 + continue-on-error: true + run: | + curl --keepalive-time 600 -L https://mybinder.org/build/gh/sagemath/sage-binder-env/$BRANCH diff --git a/.github/workflows/update-dockerfile-master.yml b/.github/workflows/update-dockerfile-master.yml new file mode 100644 index 0000000..f3252f4 --- /dev/null +++ b/.github/workflows/update-dockerfile-master.yml @@ -0,0 +1,83 @@ +name: Update master image + +on: + schedule: + - cron: '0 0 * * *' # Run every day + workflow_dispatch: + +env: + SAGE_TARGET: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-targets + SAGE_SYSTEM: ghcr.io/sagemath/sage/sage-ubuntu-jammy-minimal-with-system-packages + TAG: latest + BRANCH: master + +jobs: + build: + runs-on: ubuntu-latest + permissions: + contents: write + packages: write + steps: + + # Prepare .github/Dockerfile for slim Sage image + + - name: Checkout code + uses: actions/checkout@v4 + with: + ref: ${{ env.BRANCH }} + - name: Prepare .github/Dockerfile + run: | + SAGE_VERSION=$(docker run --rm ${SAGE_TARGET}:$TAG /sage/sage --version | grep -oP 'SageMath version \K[0-9.]+(?:beta\d+)?(?:rc\d+)?') + SAGE_TARGET_ESCAPED=$(echo "${SAGE_TARGET}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + SAGE_TARGET_VERSION_ESCAPED=$(echo "${SAGE_TARGET}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + sed -i "s/FROM ${SAGE_TARGET_ESCAPED}:\S*/FROM ${SAGE_TARGET_VERSION_ESCAPED}/g" .github/Dockerfile + SAGE_SYSTEM_ESCAPED=$(echo "${SAGE_SYSTEM}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + SAGE_SYSTEM_VERSION_ESCAPED=$(echo "${SAGE_SYSTEM}:${SAGE_VERSION}" | sed 's/\//\\\//g' | sed 's/\./\\\./g') + sed -i "s/FROM ${SAGE_SYSTEM_ESCAPED}:\S*/FROM ${SAGE_SYSTEM_VERSION_ESCAPED}/g" .github/Dockerfile + PACKAGE_NAME=ghcr.io/${{ github.repository }}:${SAGE_VERSION} + echo "PACKAGE_NAME=$PACKAGE_NAME" >> $GITHUB_ENV + git config --global user.email alice@wonderland + git config --global user.name alice + git commit -a --amend -m "Dockerfile for Sage ${SAGE_VERSION}" + git push -f origin $BRANCH + + # Build and publish the slim Sage image to github package registry (ghpr) + + - name: Log in to the Container registry + uses: docker/login-action@v3 + with: + registry: ghcr.io + username: ${{ github.actor }} + password: ${{ secrets.GITHUB_TOKEN }} + + - name: Build and push Docker image + uses: docker/build-push-action@v5 + with: + context: .github + push: true + tags: ${{ env.PACKAGE_NAME }} + + # Update files for Binder + + - name: Checkout code + uses: actions/checkout@v4 + with: + ref: ${{ env.BRANCH }} + - name: Update files for Binder + run: | + PACKAGE_NAME=${{ env.PACKAGE_NAME }} + PACKAGE_NAME_ESCAPED=$(echo "${PACKAGE_NAME}" | sed 's/\//\\\//g') + sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" Dockerfile + sed -i "s/FROM \S*/FROM ${PACKAGE_NAME_ESCAPED}/g" README.rst + git config --global user.email alice@wonderland + git config --global user.name alice + git commit -a --amend -m "Update files for Binder" + git push -f origin $BRANCH + + # Build docker image for Binder from Dockerfile at root + + - name: Binder build + timeout-minutes: 30 + continue-on-error: true + run: | + curl --keepalive-time 600 -L https://mybinder.org/build/gh/sagemath/sage-binder-env/$BRANCH diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e69de29 diff --git a/Dockerfile b/Dockerfile new file mode 100644 index 0000000..e8f185e --- /dev/null +++ b/Dockerfile @@ -0,0 +1,44 @@ +# Dockerfile for binder +# Reference: https://mybinder.readthedocs.io/en/latest/tutorials/dockerfile.html + +FROM ghcr.io/sagemath/sage-binder-env:10.4 + +USER root + +# Create user with uid 1000 +ARG NB_USER=user +ARG NB_UID=1000 +ENV NB_USER user +ENV NB_UID 1000 +ENV HOME /home/${NB_USER} +RUN adduser --disabled-password --gecos "Default user" --uid ${NB_UID} ${NB_USER} + +# Make sure the contents of the notebooks directory are in ${HOME} +COPY notebooks/* ${HOME}/ +RUN chown -R ${NB_USER}:${NB_USER} ${HOME} + +# Switch to the user +USER ${NB_USER} + +# Install Sage kernel to Jupyter +RUN mkdir -p $(jupyter --data-dir)/kernels +RUN ln -s /sage/venv/share/jupyter/kernels/sagemath $(jupyter --data-dir)/kernels + +# Make Sage accessible from anywhere +ENV PATH="/sage:$PATH" + +# Start in the home directory of the user +WORKDIR /home/${NB_USER} + +# Create the jupyter_lab_config.py file with a custom logging filter to +# suppress the perpetual nodejs warning +RUN mkdir -p /home/${NB_USER}/.jupyter +RUN echo "\ +import logging\n\ +\n\ +class NoNodeJSWarningFilter(logging.Filter):\n\ + def filter(self, record):\n\ + return 'Could not determine jupyterlab build status without nodejs' not in record.getMessage()\n\ +\n\ +logging.getLogger('LabApp').addFilter(NoNodeJSWarningFilter())\n\ +" > /home/${NB_USER}/.jupyter/jupyter_lab_config.py diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..f288702 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/README.rst b/README.rst new file mode 100644 index 0000000..a2bca25 --- /dev/null +++ b/README.rst @@ -0,0 +1,43 @@ +A Binder repo for SageMath computing environment +================================================ + +This repository is a Binder repo based on `SageMath `_. To +access a computing environment created by `Binder `_ using +SageMath kernel, click on this badge + +.. image:: https://mybinder.org/badge_logo.svg + :target: https://mybinder.org/v2/gh/sagemath/sage-binder-env/master + + +An example Binder repo for SageMath +----------------------------------- + +Have a repository full of Jupyter notebooks using SageMath? It's easy to set up +Binder to let anyone run them. Just fork this repo, put your notebooks in the +`notebooks` directory, and modify this `README.rst` to your needs. In +particular, you probably want to modify this line:: + + :target: https://mybinder.org/v2/gh/... + +with `...` filled with the name of your forked repo. This makes the Binder badge use your +repo to create the computing environment. + + +Extending the Dockerfile +------------------------ + +The `Dockerfile` is based on the Docker image:: + + FROM ghcr.io/sagemath/sage-binder-env:10.4 + +which contains the latest stable version of Sage. + +It includes Sage itself, and all the software packages typically +included in a standard Sage installation, though not *everything*. In +particular not optional Sage SPKGs, or other system software packages. + + +Authors +------- + +Nicolas M. Thiéry, E. Madison Bray, and Kwankyu Lee diff --git a/notebooks/Start here.ipynb b/notebooks/Start here.ipynb new file mode 100644 index 0000000..3f17a93 --- /dev/null +++ b/notebooks/Start here.ipynb @@ -0,0 +1,1371 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# About SageMath\n", + "\n", + "[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", + "\n", + "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", + "for Sage).\n", + "$\\def\\NN{\\mathbb{N}}\\def\\ZZ{\\mathbb{Z}}\\def\\QQ{\\mathbb{Q}}\\def\\RR{\\mathbb{R}}\\def\\CC{\\mathbb{C}}$\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A first calculation\n", + "\n", + "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." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "1 + 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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", + "\n", + "Congratulations, you have done your first calculations with Sage." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using the Jupyter notebook\n", + "\n", + "Now take some time to explore the Help menu. You find abundant information on Jupyter, Sage, and friends. \n", + "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", + "\n", + "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", + "\n", + "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", + "\n", + "$$\n", + " \\zeta(s)=\\sum_{n=1}^{\\infty}\\frac{1}{n^s}=\\prod_p \\left(\\frac{1}{1-p^{-s}}\\right)\n", + "$$\n", + "\n", + "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." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More interactions\n", + "\n", + "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. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "@interact\n", + "def f(n=(1..15), m=(1..15)):\n", + " print(\"n * m = {} = {}\".format(n * m, factor(n * m)))\n", + " P = polygon([(0, 0), (0, n), (m, n), (m, 0)])\n", + " P.show(aspect_ratio=1, gridlines='minor', figsize=[3, 3], xmax=14, ymax=14)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Also, you can try changing the slider ranges to something different by editing the input cell (make sure to also change `xmax`, `ymax`)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A brief tour\n", + "\n", + "We start showcasing the different areas of mathematics covered by Sage.\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This should output a rational number. If you know Python, notice the difference; Sage knows fractions!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "4/6" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Math display\n", + "\n", + "`%display latex` turns on math typesetting using MathJax. Type `%display plain` to turn it off." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%display latex" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "factor(x^10 - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%display plain\n", + "factor(x^10 - 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot(sin(10*x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interactive widgets" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "@interact\n", + "def plt(n=5, f=[sin, cos, tan]):\n", + " return plot(f(n*x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3D plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot3d(lambda x, y: x^2 + y^2, (-2,2), (-2,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Calculus" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%display latex\n", + "var('x,y')\n", + "f = (cos(pi/4 - x) - tan(x)) / (1 - sin(pi/4 + x))\n", + "limit(f, x = pi/4, dir='minus')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "solve([x^2+y^2 == 1, y^2 == x^3 + x + 1], x, y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot3d(sin(pi*sqrt(x^2 + y^2)) / sqrt(x^2 + y^2), (x, -5, 5), (y, -5, 5))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "contour_plot(y^2 + 1 - x^3 - x, (x,-pi,pi), (y,-pi,pi),\n", + " contours=[-8,-4,0,4,8], colorbar=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Algebra" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "factor(x^100 - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p = 54 * x^4 + 36*x^3 - 102*x^2 - 72*x - 12\n", + "p.factor()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "for K in [ZZ, QQ, ComplexField(16), QQ[sqrt(2)], GF(5)]:\n", + " print(K, \":\"); print(K['x'](p).factor())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ZZ.category()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sorted( ZZ.category().axioms() )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Linear algebra" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "A = matrix(GF(7), 4, [5,5,4,3,0,3,3,4,0,1,5,4,6,0,6,3]); A" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P = A.characteristic_polynomial(); P" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P(A) # Cayley-Hamilton" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "A.eigenspaces_left()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Computing the rank of a large sparse matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "M = random_matrix(GF(7), 10000, sparse=True, density=3/10000)\n", + "M.rank()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Geometry" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "polytopes.truncated_icosidodecahedron().plot()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Programming and plotting" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n, l, x, y = 10000, 1, 0, 0\n", + "p = [[0, 0]]\n", + "for k in range(n):\n", + " theta = (2 * pi * random()).n(digits=5)\n", + " x, y = x + l * cos(theta), y + l * sin(theta)\n", + " p.append([x, y])\n", + "g = line(p, thickness=.4) + line([p[n], [0, 0]], color='red', thickness=2)\n", + "g.show(aspect_ratio=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interactive plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var('x')\n", + "@interact\n", + "def g(f='x*sin(1/x)',\n", + " c=slider(-1, 1, .01, default=-.5),\n", + " n=(1..30),\n", + " xinterval=range_slider(-1, 1, .1, default=(-8,8), label=\"x-interval\"),\n", + " yinterval=range_slider(-1, 1, .1, default=(-3,3), label=\"y-interval\")):\n", + " f = eval(f)\n", + " x0 = c\n", + " degree = n\n", + " xmin,xmax = xinterval\n", + " ymin,ymax = yinterval\n", + " p = plot(f, xmin, xmax, thickness=4)\n", + " dot = point((x0,f(x=x0)),pointsize=80,rgbcolor=(1,0,0))\n", + " ft = f.taylor(x,x0,degree)\n", + " pt = plot(ft, xmin, xmax, color='red', thickness=2, fill=f)\n", + " show(dot + p + pt, ymin=ymin, ymax=ymax, xmin=xmin, xmax=xmax)\n", + " html(r'$f(x)\\;=\\;%s$' % latex(f))\n", + " html(r'$P_{%s}(x)\\;=\\;%s+R_{%s}(x)$' % (degree,latex(ft),degree))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Graph Theory\n", + "\n", + "Coloring graphs:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "g = graphs.PetersenGraph(); g\n", + "g.plot(partition=g.coloring())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Combinatorics\n", + "\n", + "Fast counting:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Partitions(100000).cardinality()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Playing poker:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Suits = Set([\"Hearts\", \"Diamonds\", \"Spades\", \"Clubs\"])\n", + "Values = Set([2, 3, 4, 5, 6, 7, 8, 9, 10, \"Jack\", \"Queen\", \"King\", \"Ace\"])\n", + "Cards = cartesian_product([Values, Suits])\n", + "Hands = Subsets(Cards, 5)\n", + "Hands.random_element()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Hands.cardinality()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Algebraic Combinatorics\n", + "\n", + "Drawing an affine root systems:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L = RootSystem([\"G\", 2, 1]).ambient_space()\n", + "p = L.plot(affine=False, level=1)\n", + "p.show(aspect_ratio=[1, 1, 2], frame=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Number Theory" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "E = EllipticCurve('389a')\n", + "plot(E, thickness=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Games\n", + "\n", + "Sudoku solver:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S = Sudoku('5...8..49...5...3..673....115..........2.8..........187....415..3...2...49..5...3'); S" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "list(S.solve())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Help system\n", + "\n", + "We review the three main ways to get help in Sage:\n", + "\n", + "- Navigating through the documentation \n", + "- Tab-completion \n", + "- Contextual help " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Navigating through the documentation\n", + "\n", + "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", + "\n", + "This documentation is also available online from Sage’s web site\n", + "[https://doc.sagemath.org](https://doc.sagemath.org/html/en/index.html) ." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Completion and contextual documentation\n", + "\n", + "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", + "`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):" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "klein" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Klein" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To see documentation and examples for a command, type a question mark `?` at the end of the command name and evaluate the cell.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "KleinFourGroup?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Exercise A\n", + "\n", + "What is the largest prime factor of $600851475143$?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "factor?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Digression: assignments and methods\n", + "\n", + "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:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = 3\n", + "b = 2\n", + "a + b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a, b = 2, 3\n", + "a" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This allows us to swap the values of two variables directly:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a, b = 2, 3\n", + "a, b = b, a\n", + "a, b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also assign a common value to several variables simultaneously:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "c = d = 1\n", + "c, d" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "d = 2\n", + "c, d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that when we use the word *variable* in the computer-science sense we\n", + "mean “a label attached to some data stored by Sage”. Once an object is\n", + "created, some *methods* apply to it. This means *functions* but instead of\n", + "writing `f(my_object)` you write `my_object.f()`:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p = 17\n", + "p.is_prime()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Method discovery with tab-completion\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Exercise B\n", + "\n", + "Create the permutation 51324 and assign it to the variable p." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "Permutation?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "What is the inverse of p?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p.inv" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Does $p$ have the pattern 123? What about 1234? And 312? (even if you don’t\n", + "know what a pattern is, you should be able to find a command that does this)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p.pat" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Linear algebra" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Exercise C\n", + "\n", + "Use the matrix() command to create the following matrix.\n", + "\n", + "$$\n", + "M = \\left(\\begin{array}{rrrr}\n", + "10 & 4 & 1 & 1 \\\\\n", + "4 & 6 & 5 & 1 \\\\\n", + "1 & 5 & 6 & 4 \\\\\n", + "1 & 1 & 4 & 10\n", + "\\end{array}\\right)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "matrix?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, using methods of the matrix,\n", + "\n", + "1. Compute the determinant of the matrix. \n", + "1. Compute the echelon form of the matrix. \n", + "1. Compute the eigenvalues of the matrix. \n", + "1. Compute the kernel of the matrix. \n", + "1. Compute the LLL decomposition of the matrix (and lookup the\n", + " documentation for what LLL is if needed!) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that you know how to access the different methods of matrices,\n", + "\n", + "1. Create the vector $ v = (1, -1, -1, 1) $. \n", + "1. Compute the two products: $ M \\cdot v $ and $ v \\cdot M $. What mathematical operation is Sage doing implicitly? " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "vector?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vectors in Sage can be used as row vectors or column vectors. A method such as eigenspaces might not\n", + "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." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plotting\n", + "\n", + "The `plot()` command allows you to draw plots of functions. Recall\n", + "that you can access the documentation by pressing the Tab key\n", + "after writing `plot?` in a cell:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a simple example:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var('x') # make sure x is a symbolic variable" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot(sin(x^2), (x, 0, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a more complicated plot. Try to change every single input to the plot\n", + "command in some way, evaluating to see what happens:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P = plot(sin(x^2), (x, -2, 2), rgbcolor=(0.8, 0, 0.2), thickness=3, linestyle='--', fill='axis')\n", + "show(P, gridlines=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above we used the `show(P)` command to show a plot after it was created. You can\n", + "also use `P.show()` instead:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P.show(gridlines=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Try putting the cursor right after `P.show(` and pressing Tab key to get a list of\n", + "the options for how you can change the values of the given inputs." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P.show(" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting multiple functions at once is as easy as adding the plots together:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P1 = plot(sin(x), (x, 0, 2*pi))\n", + "P2 = plot(cos(x), (x, 0, 2*pi), rgbcolor='red')\n", + "P1 + P2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Symbolic Expressions\n", + "\n", + "Here is an example of a symbolic function:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "f(x) = x^4 - 8*x^2 - 3*x + 2\n", + "f(x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "f(-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is an example of a function in the *mathematical* variable $ x $. When Sage\n", + "starts, it defines the symbol $ x $ to be a mathematical variable. If you want\n", + "to use other symbols for variables, you must define them first:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x^2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u + v" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var('u v')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "u + v" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Still, it is possible to define symbolic functions without first\n", + "defining their variables:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "f(w) = w^2\n", + "f(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this case those variables are defined implicitly:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "w" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Exercise D\n", + "\n", + "Define the symbolic function $ f(x) = x \\sin x^2 $. Plot $ f $ on the\n", + "domain $ [-3, 3] $ and color it red. Use the `find_root()` method to\n", + "numerically approximate the root of $ f $ on the interval $ [1, 2] $:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute the tangent line to $ f $ at $ x = 1 $:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot $ f $ and the tangent line to $ f $ at $ x = 1 $ in one image:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Exercise E (Advanced)\n", + "\n", + "Solve the following equation for $y$\n", + "\n", + "$$\n", + "y = 1 + x y^2\n", + "$$\n", + "\n", + "There are two solutions, take the one for which $ \\lim_{x\\to0} y(x) = 1 $.\n", + "(Don’t forget to create the variables $ x $ and $ y $!)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Expand $ y $ as a truncated Taylor series around $ 0 $ containing\n", + "$ n = 10 $ terms." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "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:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "oeis?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Congratulations for completing your first Sage tutorial!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exploring further" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Accessing Sage\n", + "\n", + "- The [Sage cell service](https://sagecell.sagemath.org) lets you evaluate individual Sage commands. \n", + "- In general, Sage computations can be embedded in any web page using [Thebe](https://thebe.readthedocs.io/en/stable).\n", + "- [Binder](https://mybinder.org) is a service that lets you run Jupyter online on top of an arbitrary software stack. \n", + " Sessions are free, anonymous, and temporary. You can use one of the existing repositories, or create your own. \n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Ways to use Sage\n", + "\n", + "There are other ways beyond the Jupyter Notebook to use Sage: interactive command line, program scripts, etc.\n", + "See [Sage tutorial](https://doc.sagemath.org/html/en/tutorial/introduction.html#ways-to-use-sage)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Resources\n", + "\n", + "- [Sage tutorial](https://doc.sagemath.org/html/en/tutorial/index.html) \n", + "- [Sage thematic tutorials](https://doc.sagemath.org/html/en/thematic_tutorials/index.html) \n", + "- [The open book *Computational Mathematics with Sage*](https://www.sagemath.org/sagebook/english.html)\n", + "- [Sage quick reference cards](https://wiki.sagemath.org/quickref) \n", + "- [Sage webpage https://www.sagemath.org](https://www.sagemath.org) \n", + "- [Ask Sage https://ask.sagemath.org](https://ask.sagemath.org) \n", + "- [Sage GitHub repo](https://github.com/sagemath/sage/issues)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 10.1.rc0", + "language": "sage", + "name": "sagemath" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}