Sympy zoo

[Paul Royik]

Why 1/0 is complex infinity and log(0) is complex infinity?

I also found a bug with oo**zoo. It is recursion error.

[Kalevi Suominen]

On Sunday, June 7, 2015 at 2:52:52 PM UTC+3, Paul Royik wrote:

Why 1/0 is complex infinity and log(0) is complex infinity?

They are shorthand notations for the limits of  1/z  and  log(z)  as  z  tends to  0. The default domain in SymPy is the complex field, so the limits are computed in a complex neighbourhood of  0.

[Paul Royik]

Thank you.

How to make it work in real field?

[Francesco Bonazzi]

Are you sure that SymPy's behaviour is well-defined?

In [1]: z = Symbol('z', imaginary=True)

In [2]: z.is_imaginary
Out[2]: True

In [3]: z.is_real
Out[3]: False

In [4]: limit(1/z, z, 0)
Out[4]: ∞

In [5]: type(_)
Out[5]: sympy.core.numbers.Infinity

[Aaron Meurer]

My guess is that limit() doesn't look at assumptions. Also, limit
uses real limits, not complex limits (which are much harder to work
with algorithmically).

The oo**zoo thing is a bug. Please open an issue in the issue tracker about it.

Aaron Meurer

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[Francesco Bonazzi]

On Monday, 8 June 2015 22:18:09 UTC+2, Aaron Meurer wrote:

My guess is that limit() doesn't look at assumptions.  Also, limit
uses real limits, not complex limits (which are much harder to work
with algorithmically).

Apparently not even Mathematica implements complex limits:

In[1]:= Limit[1/x, x->0]                                                                                  

Out[1]= Infinity

In[2]:= Limit[1/x, x->0, Assumptions -> NotElement[x, Reals]]                                            

                                                                                   1
Limit::cas: Warning: contradictory assumption(s) x \[NotElement] Reals && 0 < x < ---- encountered.
                                                                                  4096

              1
Out[2]= Limit[-, x -> 0, Assumptions -> x \[NotElement] Reals]
              x

 I guess that SymPy's limit( ... ) should raise an exception if the parameter is not real. Do you agree?