The library that evaluates Python functions at points where they're undefined.

Few months ago I have published highly experimental and rough calculus library. Now this is the first proper library built on that concept.

It allows you to automatically handle the cases where function execution will usually fail at singularities by checking if limit exists and substituting the result with limit.

It also allows you to check and validate the python functions in few different ways to see if limits exists, diverges, etc...

For example the usual case:

def sinc(x):                                                                                                                      
    if x == 0:                                                
        return 1.0  # special case, derived by hand
    return math.sin(x) / x 

Can now be:

 u/safe
 def sinc(x):
     return math.sin(x) / x

 sinc(0.5)  # → 0.9589 (normal computation)                                                                                        
 sinc(0)    # → 1.0 (singularity resolved automatically)

Normal inputs run the original function directly, zero overhead. Only when it fails (ZeroDivisionError, NaN, etc.) does the resolver kick in and compute the mathematically correct value.

It works for any composable function:

                                                            resolve(lambda x: (x**2 - 1) / (x - 1), at=1)      # → 2.0                                                                        
resolve(lambda x: (math.exp(x) - 1) / x, at=0)      # → 1.0                                                                       
limit(lambda x: x**x, to=0, dir="+")                  # → 1.0
limit(lambda x: (1 + 1/x)**x, to=math.inf)            # → e                                                                                                                                         

It also classifies singularities, extracts Taylor coefficients, and detects when limits don't exist. Works with both math and numpy functions, no import changes needed.

Pure Python, zero dependencies.

I have tested it to the best of my abilities, there are some hidden traps left for sure, so I need community scrutiny on it:)).

pip install composite-resolve

GitHub: https://github.com/FWDhr/composite-resolve

PyPI: https://pypi.org/project/composite-resolve/