Difference(s) between SR.var and SR.symbol ?

edit

SR.symbol() seems to be lower-level than SR.var(). Am I correct? I just checked the code of both functions, and the former seems to make the hard work for the latter. In simple terms, SR.var() seems to be a wrapper for SR.symbol() with additional functionality, like defining multiple symbols.

I really like the idea of an SR.symbols(). Could Sage define it just as SR.symbols = SR.var?

I do not get your timings:

sage: %timeit a = SR.symbol('a')                                                                                                                                                                             
743 ns ± 12.7 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
sage: %timeit a = SR.var('a')                                                                                                                                                                                
956 ns ± 23.4 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

I was going to open a ticket, but then i noticed that SR.symbols already means something:

sage: SR.symbols                                                                                                                                                                                             
{'a': a,
 'b': b,
 'c': c,
 'd': d,
 'f': f,
 'g': g,
 'h': h,
 'j': j,
 'k': k,
 'l': l,
...

I do not know the exact use of that, in particular if it could be replaced with a hidden dict somehow.

Hello, @tmonteil! I am sorry, but I didn't understand your comment about timings. On the other hand, concerning SR.symbols, you are right; I actually forgot about is already exists. However, I can contribute with some insight: SR.symbols is a dictionary where all predefined and user-defined symbols are stored. For example, if you do something like var('foo') or SR.var('bar') or even SR.symbol('foo'), then you will see that SR.symbols['foo'] contains the variable foo. My appreciation is that this is not intended to direct user access, so perhaps it should be renamed SR._symbols_ or something like that.

What I cannot answer is why SR.symbols stores a, b, etc. as predefined variables. Perhaps it is a matter of speed? (not totally convinced of that.) For example, when you run SR.var('a') or var('a'), this calls SR.symbol('a'), which in turn checks if SR.symbols['a'] is already defined.

Let me do a "grep" on the complete Sage code in order to determine if this can indeed can be renamed as SR._symbols_. Not only that would be convenient, but also Python-de-facto-compliant if indeed it is not intended for direct user access.