Specifying a limit for a symbolic function?

asked 2022-03-28 12:08:18 +0200

eatdust gravatar image

updated 2022-03-31 22:30:48 +0200

slelievre gravatar image

Hi there,

I am working with symbolic functions, and I do have a lot of integration by parts to be done, in which I have to evaluate some exact derivative terms at infinity.

I am defining this symbolic function, specifying its derivative.

def deriv_F_0(self, *args, **kwds):
    return -exp(2*i*args[kwds['diff_param']])/args[kwds['diff_param']]

F_0 = function('F_0', nargs=1, derivative_func=deriv_F_0)

It works fine, but, I would also like to add to it an option like "limit_func" doing this:

F_0 = function('F_0', nargs=1, derivative_func=deriv_F_0, limit_func=mylimit_F_0)

where "mylimit_F_0" would be a function of mine. Notice that my problem is just that "limit_func" does not exist :)

For instance, I could set:

def mylimit_F_0(self, x):
   if bool(x==infinity):
      return pi

the goal being to specify various asymptotic limits, and makes this


returning the value I specify, here pi.

I have started SageMath a few days ago, so any help welcome! Let me know if there are any alternative methods for setting limit on symbolic functions!

Cheers, chris.

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A similar argument could be made in favor of specifying an antiderivative...

As far as I know, the only way is to define a new function by deriving a new class from the appropriate parent class : how to do this exactly depends, IIRC, of what exactly you want to implement.

The "right" source of inspiration is probably Sage's symbolic functions source files. I have played a bit with them and implemented a couple of toys, but I couldn't for dear life recall exactly how tonight...

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2022-03-31 22:20:07 +0200 )edit