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Following an example of how to extend and embed that I found in patch
file r67655 (the website is out of date [issue4586]), PyModule_Create
appears to not work (or example is not complete). When I run r67655
(attached also) I get an error saying that "emb" is not a module.

It seems that a call to "PyDict_SetItemString" is what is missing from
r67655:
PyObject* m = PyModule_Create(&EmbModule);
PyDict_SetItemString(PyImport_GetModuleDict(), EmbModule.m_name, m);
I am just guessing here though, don't know if this is correct way to do
things.

In python2.6, Py_InitModule4() calls PyImport_AddModule().
Why doesn't python3.0's PyModule_Create() do the same?
Index: Objects/moduleobject.c
===================================================================
--- Objects/moduleobject.c (revision 67577)
+++ Objects/moduleobject.c (working copy)
@@ -103,8 +103,9 @@
 _Py_PackageContext = NULL;
 }
 }
- if ((m = (PyModuleObject*)PyModule_New(name)) == NULL)
+ if ((m = (PyModuleObject*)PyImport_AddModule(name)) == NULL)
 return NULL;
+ Py_INCREF(m);
 if (module->m_size > 0) {
 m->md_state = PyMem_MALLOC(module->m_size);

Because the init function for extension modules are supposed to return
the module now and the import machinery adds the module itself.

So, does that mean that Python is fine and there is a problem in the
example? How do I get that example to work, there seems to be something
missing in it. Thanks.

The example is broken.
And the example under discussion is
http://docs.python.org/dev/3.0/extending/embedding.html#extending-embedded-python
.
I have changed the title to be more descriptive and assigned to Martin
to find out what the proper way is to handle this case.

The proper way of extending embedded Python can be seen in
Demo/embed/demo.c.
I can't contribute to the documentation, so I'm unassigning myself.

See attached documentation patch.
Instead of a direct call to PyModule_Create(), the main function must 
use
 PyImport_AppendInittab("emb", &PyInit_emb);
Note that the same line also works for all 2.x versions.
I'll try to add an item to howto/cporting.rst.

Applied in r67682.
Please don't add things directly to cporting.rst, rather amend the
PortingExtensionModulesToPy3k wiki page.