How to display all the symbolic variables and functions?

edit

You may use show_identifiers:

sage: show_identifiers()
['In', 'Out', 'exit', 'get_ipython', 'quit']
sage: a = 2
sage: def function_square(b):
....:     return b^2
....: 
sage: show_identifiers()
['In', 'Out', 'a', 'exit', 'function_square', 'get_ipython', 'quit']

Then using the locals() which returns a dictionary containing the current scope's local variables, you can recover the objects:

sage: D = locals()
sage: D['a']
2
sage: D['function_square']
<function function_square at 0x7fa7ddd35f50>
sage: D['quit']
<IPython.core.autocall.ExitAutocall object at 0x7fa94bc4fa90>

These tools are used by the save_session function in Sage.

EDIT June 5th 2018: Another option is to use magic IPython functions %who and %whos :

sage: %who
a    function_square     
sage: %whos
Variable          Type        Data/Info
---------------------------------------
a                 Integer     2
function_square   function    <function function_square at 0x7f28cfb2ac08>

You can use

[k for k,v in list(globals().iteritems()) if isinstance(v,sage.symbolic.expression.Expression)]

to display all the names in the global namespace to which a symbolic expression is bound and

[k for k,v in list(globals().iteritems()) if isinstance(v,sage.symbolic.function.Function)]

to find all the names to which a symbolic function is bound. You can vary the query as desired.

You can of course look at globals().keys() directly, but you'll probably find that's a bit unwieldy (and it is what vars() ends up doing too (and as far as I can see it works as documented).

While it may seem at first that inspecting globals() gives you a lot of information about the system, it's in practice rarely useful. Whether something is bound to a global name ends up being not so important in Python.