Limits involving branch cuts of elementary functions not handled

[sympy-issue-migrator]

Branch cuts of sqrt() and log() are not handled properly.

If that implies that sqrt() and log() have more than this issue in the complex plane I don't know.
Moreover, if that implies that other elementary functions are having similar problems with branch cuts I have not tested.

In [1]: from sympy import *                                        

Exmpl. 1-------------------sqrt()---------------------------
1st, numerically

In [2]: N(sqrt(-1.+I*1e-10))                                                                                   
Out[2]: 5.0e-11 + 1.0*I

In [3]: N(sqrt(-1.-I*1e-10))                                                                                   
Out[3]: 5.0e-11 - 1.0*I             

Ok. sqrt-branch seems to lie on neg. Re-axis and is selected properly
2nd, same thing symbolically

In [5]: eps=symbols('eps')                                                                                     
In [6]: limit(sqrt(-1+I*eps),eps,0,'+')                                                                        
Out[6]: I

In [7]: limit(sqrt(-1+I*eps),eps,0,'-')                                                                        
Out[7]: I

In [8]: limit(sqrt(-1-I*eps),eps,0,'+')                                                                        
Out[8]: I

In [9]: limit(sqrt(-1-I*eps),eps,0,'-')                                                                        
Out[9]: I

Symbolic sqrt() returns 'I' irrespective of approach to branch cut. Wrong.

Exmpl. 2-------------log()--------------
1st, numerically

In [10]: log(-1I*1e-10)                                                                                       
Out[10]: 5.0e-21 - 3.14159265348979*I

In [11]: log(-1+I*1e-10)                                                                                       
Out[11]: 5.0e-21 + 3.14159265348979*I

Ok. log-branch seems to lie on neg. Re-axis and is selected properly
2nd, same thing symbolically

In [12]: limit(log(-1+I*eps),eps,0,'+')                                                                         
Out[12]: I*pi

In [13]: limit(log(-1+I*eps),eps,0,'-')                                                                         
Out[13]: I*pi

In [14]: limit(log(-1-I*eps),eps,0,'+')                                                                         
Out[14]: I*pi

In [15]: limit(log(-1-I*eps),eps,0,'-')                                                                         
Out[15]: I*pi

Symbolic log() returns 'I*pi' irrespective of approach to branch cut. Wrong.

Original issue for #7216: http://code.google.com/p/sympy/issues/detail?id=4117
Original author: https://code.google.com/u/112689286102358441542/

[asmeurer]

**Status:** Valid  
**Labels:** Series WrongResult  

Original comment: http://code.google.com/p/sympy/issues/detail?id=4117#c1
Original author: https://code.google.com/u/asmeurer@gmail.com/

[asmeurer]

Summary: Limits involving branch cuts of elementary functions not handled (was: Branch cuts of elementary functions not handled)

Original comment: http://code.google.com/p/sympy/issues/detail?id=4117#c2
Original author: https://code.google.com/u/asmeurer@gmail.com/