Following up on this, I think we can do this with relatively small impact:
https://github.com/sagemath/sage/pull/38780
previously,
limit(1/x,'+',x=0)
did work, but the recommended way to spell this was
limit(1/x,x=0,dir="+")
so I'm not sure if we need to provide a special case and intercept this.
On Thursday 3 October 2024 at 09:07:29 UTC-7 Nils Bruin wrote:
> The function in question is sort-of available as
> sage.functions.other.symbolic_limit (which is an inert form, so it requires
> a further "simplify").
>
> On Thursday 3 October 2024 at 08:29:50 UTC-7 Nils Bruin wrote:
>
>> On Thursday 3 October 2024 at 04:44:12 UTC-7 Emmanuel Charpentier wrote:
>>
>> sage: F.limit(X[0]=3) Cell In[9], line 1
>> F.limit(X[Integer(0)]=Integer(3)) ^ SyntaxError: expression cannot contain
>> assignment, perhaps you meant "=="?
>>
>> Indeed, the current limit function and method get their arguments
>> (variable and value) by analysing a single named argument, whose name must
>> be a literal. From limit?? :
>>
>> The restriction here is python's processing of optional arguments. These
>> must have simple names. You can already use
>> """
>> limit(x0,**{str(X[0]):1})
>> """
>> now, which isn't beautiful but at least it establishes the function.
>> Allowing an explicit dictionary argument would likely open up a whole slew
>> of other issues. It looks to me like we're missing a very simple form for
>> limit that should be the primitive to all of this:
>> limit( f, x, 1)
>> i.e.: expression to take limit of, variable with respect to take limit,
>> limit value. Then one could just write limit( F, X[0], 0) and one would get
>> the default processing of arguments for python for free. We wouldn't rely
>> on the programmatic pun of using python identifiers to stand in for our
>> symbolic variables.
>> Further convenience routines that use syntactic sugar to make things
>> resemble more mathematical notation can then be built on top, but at least
>> the general primitive is available underneath.
>> It may be hard to figure out a way to make such a routine available under
>> an easily found name while remaining compatible with what exists now.
>>
>
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