gh-37878: Run sage doc server for jupyterlab 
    
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Reopen #35139 because of the renewed interest:
https://groups.google.com/g/sage-devel/c/kzSWB8ps7VA

New environment variables added to `sage.env`:
```
SAGE_DOC_SERVER_URL = var("SAGE_DOC_SERVER_URL")
SAGE_DOC_LOCAL_PORT = var("SAGE_DOC_LOCAL_PORT", "0")
```
When Jupyter notebook launches,
- If `SAGE_DOC_SERVER_URL` is set, the url is used;
- else if local sage documentation is installed, a doc http server with
port `SAGE_DOC_LOCAL_PORT` starts. If the port is 0 (the default), then
a random port is selected by the system and stored to the environment
variable;
- else the online official documentation website
https://doc.sagemath.org is used

for the help menu of the Jupyter notebook.

Fixes #34794.

### 📝 Checklist

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- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: #37878
Reported by: Kwankyu Lee
Reviewer(s): Kwankyu Lee, Marc Culler

Author: Release Manager

src/bin/sage-notebook

@@ -7,6 +7,8 @@ import ast
 import argparse
 import logging
 import textwrap
+from contextlib import contextmanager
+
 logging.basicConfig()
 logger = logging.getLogger()
 
@@ -19,7 +21,6 @@ _system_jupyter_url = "https://doc.sagemath.org/html/en/installation/launching.h
 class NotebookJupyter():
 
     def print_banner(self):
-        banner()
         print('Please wait while the Sage Jupyter Notebook server starts...')
 
     @classmethod
@@ -50,7 +51,6 @@ class NotebookJupyter():
 
 class NotebookJupyterlab():
     def print_banner(self):
-        banner()
         print('Please wait while the Jupyterlab server starts...')
 
     @classmethod
@@ -77,7 +77,6 @@ class NotebookJupyterlab():
 class SageNBExport(NotebookJupyter):
 
     def print_banner(self):
-        banner()
         print('Please wait while the SageNB export server starts...')
 
     @classmethod
@@ -131,7 +130,6 @@ EXAMPLES:
 
 """
 
-
 notebook_launcher = {
     'default': NotebookJupyter,   # change this to change the default
     'ipython': NotebookJupyter,
@@ -140,7 +138,6 @@ notebook_launcher = {
     'export': SageNBExport,
 }
 
-
 notebook_names = ', '.join(notebook_launcher.keys())
 
 
@@ -187,6 +184,32 @@ def trac_23428_browser_workaround():
         os.environ['BROWSER'] = 'open'
 
 
+@contextmanager
+def sage_doc_server():
+    from functools import partial
+    from http.server import SimpleHTTPRequestHandler, ThreadingHTTPServer
+    from threading import Thread
+    from sage.env import SAGE_DOC, SAGE_DOC_LOCAL_PORT as port
+
+    server = ThreadingHTTPServer(('127.0.0.1', int(port)),
+        partial(SimpleHTTPRequestHandler, directory=SAGE_DOC))
+
+    if port == '0':
+        port = str(server.server_address[1])
+        os.environ['SAGE_DOC_LOCAL_PORT'] = port
+
+    server_thread = Thread(target=server.serve_forever, name="sage_doc_server")
+    server_thread.start()
+    print(f'Sage doc server started running at http://127.0.0.1:{port}')
+
+    try:
+        yield
+    finally:
+        server.shutdown()
+        server_thread.join()
+        print(f'Sage doc server stopped runnning at http://127.0.0.1:{port}')
+
+
 if __name__ == '__main__':
     parser = make_parser()
     args, unknown = parser.parse_known_args(sys.argv[1:])
@@ -227,4 +250,19 @@ if __name__ == '__main__':
             launcher.print_help()
         sys.exit(0)
 
-    launcher(unknown)
+    banner()
+
+    # Start a Sage doc server if the Sage documentation is available locally.
+    # See the corresponding code in src/sage/repl/ipython_kernel/kernel.py.
+
+    from sage.env import SAGE_DOC_SERVER_URL
+    from sage.features.sagemath import sagemath_doc_html
+
+    if SAGE_DOC_SERVER_URL:
+        print(f'Sage doc server is running at {SAGE_DOC_SERVER_URL}')
+        launcher(unknown)
+    elif sagemath_doc_html().is_present():
+        with sage_doc_server():
+            launcher(unknown)
+    else:
+        launcher(unknown)

src/sage/env.py

@@ -187,6 +187,11 @@ def var(key: str, *fallbacks: Optional[str], force: bool = False) -> Optional[st
 SAGE_PKGS = var("SAGE_PKGS", join(SAGE_ROOT, "build", "pkgs"))
 SAGE_ROOT_GIT = var("SAGE_ROOT_GIT", join(SAGE_ROOT, ".git"))
 
+# Sage doc server (local server with PORT if URL is not given)
+SAGE_DOC_SERVER_URL = var("SAGE_DOC_SERVER_URL")
+# The default port is 0 so that the system will assign a random unused port > 1024
+SAGE_DOC_LOCAL_PORT = var("SAGE_DOC_LOCAL_PORT", "0")
+
 # ~/.sage
 DOT_SAGE = var("DOT_SAGE", join(os.environ.get("HOME"), ".sage"))
 SAGE_STARTUP_FILE = var("SAGE_STARTUP_FILE", join(DOT_SAGE, "init.sage"))

src/sage/repl/ipython_kernel/kernel.py

@@ -100,62 +100,68 @@ def help_links(self):
             sage: sk = SageKernel.__new__(SageKernel)
             sage: sk.help_links
             [{'text': 'Sage Documentation',
-              'url': 'https://doc.sagemath.org/html/en/index.html'},
+              'url': '.../html/en/index.html'},
              ...]
         """
-        # DEPRECATED: The URLs in the form 'kernelspecs/...' were used for
-        # classical Jupyter notebooks. For instance,
-        #
-        #  'kernelspecs/sagemath/doc/html/en/index.html'
-        #
-        # is constructed by kernel_url('doc/html/en/index.html'), but these
-        # URLs of local files don't work for JupyterLab. Hence all URLs here
-        # have been replaced with URLs of online documents.
-
-        from sage.repl.ipython_kernel.install import SageKernelSpec
-        identifier = SageKernelSpec.identifier()
-
-        def kernel_url(x):
-            # URLs starting with 'kernelspecs' are prepended by the
-            # browser with the appropriate path
-            return 'kernelspecs/{0}/{1}'.format(identifier, x)
+        # A Sage doc server starts when Jupyter notebook launches if the Sage
+        # documentation is available locally.  See the corresponding code in
+        # src/bin/sage-notebook.
+
+        from sage.env import SAGE_DOC_SERVER_URL
+        from sage.features.sagemath import sagemath_doc_html
+
+        if SAGE_DOC_SERVER_URL:
+            def doc_url(path):
+                return f'{SAGE_DOC_SERVER_URL}/{path}'
+        elif sagemath_doc_html().is_present():
+            from sage.env import SAGE_DOC_LOCAL_PORT as port
+
+            def doc_url(path):
+                return f'http://127.0.0.1:{port}/{path}'
+        else:
+            def doc_url(path):
+                return f'https://doc.sagemath.org/{path}'
 
         return [
             {
                 'text': 'Sage Documentation',
-                'url': "https://doc.sagemath.org/html/en/index.html",
+                'url': doc_url('html/en/index.html'),
             },
             {
                 'text': 'A Tour of Sage',
-                'url': "https://doc.sagemath.org/html/en/a_tour_of_sage/index.html",
+                'url': doc_url('html/en/a_tour_of_sage/index.html'),
             },
             {
                 'text': 'Tutorial',
-                'url': "https://doc.sagemath.org/html/en/tutorial/index.html",
+                'url': doc_url('html/en/tutorial/index.html'),
             },
             {
                 'text': 'Thematic Tutorials',
-                'url': "https://doc.sagemath.org/html/en/thematic_tutorials/index.html",
+                'url': doc_url('html/en/thematic_tutorials/index.html'),
             },
             {
                 'text': 'PREP Tutorials',
-                'url': "https://doc.sagemath.org/html/en/prep/index.html",
+                'url': doc_url('html/en/prep/index.html'),
             },
             {
                 'text': 'Constructions',
-                'url': "https://doc.sagemath.org/html/en/constructions/index.html",
+                'url': doc_url('html/en/constructions/index.html'),
             },
             {
                 'text': 'FAQ',
-                'url': "https://doc.sagemath.org/html/en/faq/index.html",
+                'url': doc_url('html/en/faq/index.html'),
+            },
+            {
+                'text': 'Reference Manual',
+                'url': doc_url('html/en/reference/index.html'),
             },
             {
-                'text': 'Reference',
-                'url': "https://doc.sagemath.org/html/en/reference/index.html",
+                'text': "Installation Guide",
+                'url': doc_url('html/en/installation/index.html'),
             },
             {
-                'text': "Developer's Guide",
-                'url': "https://doc.sagemath.org/html/en/developer/index.html",
+                'text': "Developer Guide",
+                'url': doc_url('html/en/developer/index.html'),
             },
             {
                 'text': "Python",