diff --git a/.ci/retrofit-worktree.sh b/.ci/retrofit-worktree.sh
new file mode 100755
index 00000000000..f926e59059e
--- /dev/null
+++ b/.ci/retrofit-worktree.sh
@@ -0,0 +1,39 @@
+#!/bin/sh
+if [ $# != 2 ]; then
+    echo >&2 "usage: $0 WORKTREE_NAME WORKTREE_DIRECTORY"
+    echo >&2 "Ensures that the current working directory is a git repository,"
+    echo >&2 "then makes WORKTREE_DIRECTORY a git worktree named WORKTREE_NAME."
+fi
+WORKTREE_NAME="$1"
+WORKTREE_DIRECTORY="$2"
+
+export GIT_AUTHOR_NAME="ci-sage workflow"
+export GIT_AUTHOR_EMAIL="ci-sage@example.com"
+export GIT_COMMITTER_NAME="$GIT_AUTHOR_NAME"
+export GIT_COMMITTER_EMAIL="$GIT_AUTHOR_EMAIL"
+
+set -ex
+
+# If actions/checkout downloaded our source tree using the GitHub REST API
+# instead of with git (because do not have git installed in our image),
+# we first make the source tree a repo.
+if [ ! -d .git ]; then git init && git add -A && git commit --quiet -m "new"; fi
+
+# Tag this state of the source tree "new". This is what we want to build and test.
+git tag -f new
+
+# Our container image contains a source tree in $WORKTREE_DIRECTORY with a full build of Sage.
+# But $WORKTREE_DIRECTORY is not a git repository.
+# We make $WORKTREE_DIRECTORY a worktree whose index is at tag "new".
+# We then commit the current sources and set the tag "old". (This keeps all mtimes unchanged.)
+# Then we update worktree and index with "git reset --hard new".
+# (This keeps mtimes of unchanged files unchanged and mtimes of changed files newer than unchanged files.)
+# Finally we reset the index to "old". (This keeps all mtimes unchanged.)
+# The changed files now show up as uncommitted changes.
+# The final "git add -N" makes sure that files that were added in "new" do not show
+# as untracked files, which would be removed by "git clean -fx".
+git worktree add --detach $WORKTREE_NAME
+rm -rf $WORKTREE_DIRECTORY/.git && mv $WORKTREE_NAME/.git $WORKTREE_DIRECTORY/
+rm -rf $WORKTREE_NAME && ln -s $WORKTREE_DIRECTORY $WORKTREE_NAME
+if [ ! -f $WORKTREE_NAME/.gitignore ]; then cp .gitignore $WORKTREE_NAME/; fi
+(cd $WORKTREE_NAME && git add -A && git commit --quiet --allow-empty -m "old" -a && git tag -f old && git reset --hard new && git reset --quiet old && git add -N . && git status)
diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 062fa973ac3..89ed87ecf91 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -69,30 +69,8 @@ jobs:
         id: worktree
         run: |
           set -ex
-          git config --global user.email "ci-sage@example.com"
-          git config --global user.name "Build & Test workflow"
           git config --global --add safe.directory $(pwd)
-          # If actions/checkout downloaded our source tree using the GitHub REST API
-          # instead of with git (because do not have git installed in our image),
-          # we first make the source tree a repo.
-          if [ ! -d .git ]; then git init && git add -A && git commit --quiet -m "new"; fi
-          # Tag this state of the source tree "new". This is what we want to build and test.
-          git tag -f new
-          # Our container image contains a source tree in /sage with a full build of Sage.
-          # But /sage is not a git repository.
-          # We make /sage a worktree whose index is at tag "new".
-          # We then commit the current sources and set the tag "old". (This keeps all mtimes unchanged.)
-          # Then we update worktree and index with "git reset --hard new".
-          # (This keeps mtimes of unchanged files unchanged and mtimes of changed files newer than unchanged files.)
-          # Finally we reset the index to "old". (This keeps all mtimes unchanged.)
-          # The changed files now show up as uncommitted changes.
-          # The final "git add -N" makes sure that files that were added in "new" do not show
-          # as untracked files, which would be removed by "git clean -fx".
-          git worktree add --detach worktree-image
-          rm -rf /sage/.git && mv worktree-image/.git /sage/
-          rm -rf worktree-image && ln -s /sage worktree-image
-          if [ ! -f worktree-image/.gitignore ]; then cp .gitignore worktree-image/; fi
-          (cd worktree-image && git add -A && git commit --quiet --allow-empty -m "old" -a && git tag -f old && git reset --hard new && git reset --quiet old && git add -N . && git status)
+          .ci/retrofit-worktree.sh worktree-image /sage
 
       - name: Download upstream artifact
         uses: actions/download-artifact@v3
diff --git a/.github/workflows/doc-build-pdf.yml b/.github/workflows/doc-build-pdf.yml
index 0413954210b..50a836b3b10 100644
--- a/.github/workflows/doc-build-pdf.yml
+++ b/.github/workflows/doc-build-pdf.yml
@@ -62,31 +62,10 @@ jobs:
       - name: Add prebuilt tree as a worktree
         id: worktree
         run: |
-          set -ex
+          git config --global --add safe.directory $(pwd)
           git config --global user.email "ci-sage@example.com"
           git config --global user.name "Build & Test workflow"
-          git config --global --add safe.directory $(pwd)
-          # If actions/checkout downloaded our source tree using the GitHub REST API
-          # instead of with git (because do not have git installed in our image),
-          # we first make the source tree a repo.
-          if [ ! -d .git ]; then git init && git add -A && git commit --quiet -m "new"; fi
-          # Tag this state of the source tree "new". This is what we want to build and test.
-          git tag -f new
-          # Our container image contains a source tree in /sage with a full build of Sage.
-          # But /sage is not a git repository.
-          # We make /sage a worktree whose index is at tag "new".
-          # We then commit the current sources and set the tag "old". (This keeps all mtimes unchanged.)
-          # Then we update worktree and index with "git reset --hard new".
-          # (This keeps mtimes of unchanged files unchanged and mtimes of changed files newer than unchanged files.)
-          # Finally we reset the index to "old". (This keeps all mtimes unchanged.)
-          # The changed files now show up as uncommitted changes.
-          # The final "git add -N" makes sure that files that were added in "new" do not show
-          # as untracked files, which would be removed by "git clean -fx".
-          git worktree add --detach worktree-image
-          rm -rf /sage/.git && mv worktree-image/.git /sage/
-          rm -rf worktree-image && ln -s /sage worktree-image
-          if [ ! -f worktree-image/.gitignore ]; then cp .gitignore worktree-image/; fi
-          (cd worktree-image && git add -A && git commit --quiet --allow-empty -m "old" -a && git tag -f old && git reset --hard new && git reset --quiet old && git add -N . && git status)
+          .ci/retrofit-worktree.sh worktree-image /sage
           # Keep track of changes to built HTML
           new_version=$(cat src/VERSION.txt); (cd /sage/local/share/doc/sage/html/en && find . -name "*.html" | xargs sed -i '/class="sidebar-brand-text"/s/Sage [0-9a-z.]* /Sage '$new_version' /'; git init && (echo "*.svg binary"; echo "*.pdf binary") >> .gitattributes && (echo ".buildinfo"; echo '*.inv'; echo '.git*'; echo '*.svg'; echo '*.pdf'; echo '*.png'; echo 'searchindex.js') > .gitignore; git add -A && git commit --quiet -m "old")
 
diff --git a/.github/workflows/doc-build.yml b/.github/workflows/doc-build.yml
index 355e07ab78e..f8b338f50d6 100644
--- a/.github/workflows/doc-build.yml
+++ b/.github/workflows/doc-build.yml
@@ -53,31 +53,10 @@ jobs:
       - name: Add prebuilt tree as a worktree
         id: worktree
         run: |
-          set -ex
+          git config --global --add safe.directory $(pwd)
           git config --global user.email "ci-sage@example.com"
           git config --global user.name "Build & Test workflow"
-          git config --global --add safe.directory $(pwd)
-          # If actions/checkout downloaded our source tree using the GitHub REST API
-          # instead of with git (because do not have git installed in our image),
-          # we first make the source tree a repo.
-          if [ ! -d .git ]; then git init && git add -A && git commit --quiet -m "new"; fi
-          # Tag this state of the source tree "new". This is what we want to build and test.
-          git tag -f new
-          # Our container image contains a source tree in /sage with a full build of Sage.
-          # But /sage is not a git repository.
-          # We make /sage a worktree whose index is at tag "new".
-          # We then commit the current sources and set the tag "old". (This keeps all mtimes unchanged.)
-          # Then we update worktree and index with "git reset --hard new".
-          # (This keeps mtimes of unchanged files unchanged and mtimes of changed files newer than unchanged files.)
-          # Finally we reset the index to "old". (This keeps all mtimes unchanged.)
-          # The changed files now show up as uncommitted changes.
-          # The final "git add -N" makes sure that files that were added in "new" do not show
-          # as untracked files, which would be removed by "git clean -fx".
-          git worktree add --detach worktree-image
-          rm -rf /sage/.git && mv worktree-image/.git /sage/
-          rm -rf worktree-image && ln -s /sage worktree-image
-          if [ ! -f worktree-image/.gitignore ]; then cp .gitignore worktree-image/; fi
-          (cd worktree-image && git add -A && git commit --quiet --allow-empty -m "old" -a && git tag -f old && git reset --hard new && git reset --quiet old && git add -N . && git status)
+          .ci/retrofit-worktree.sh worktree-image /sage
           # Keep track of changes to built HTML
           new_version=$(cat src/VERSION.txt); (cd /sage/local/share/doc/sage/html/en && find . -name "*.html" | xargs sed -i '/class="sidebar-brand-text"/s/Sage [0-9a-z.]* /Sage '$new_version' /'; git init && (echo "*.svg binary"; echo "*.pdf binary") >> .gitattributes && (echo ".buildinfo"; echo '*.inv'; echo '.git*'; echo '*.svg'; echo '*.pdf'; echo '*.png'; echo 'searchindex.js') > .gitignore; git add -A && git commit --quiet -m "old")