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Top Forums Programming E**(i*pi)=-1 or e**(j*pi)=-1, something I found out in Python using part of Eulers Identit equation. Post 303042083 by wisecracker on Friday 13th of December 2019 01:54:58 PM
Old 12-13-2019
E**(i*pi)=-1 or e**(j*pi)=-1, something I found out in Python using part of Eulers Identit equation.

Well guys and gals I have discovered after all these years that Python does complex numbers without the 'complex()' function or 'cmath' import.
It is well known that Euler's Identity E**(i*pi)+1=0 so I decided to experiment
Code:
Last login: Fri Dec 13 18:27:30 on ttys000
AMIGA:amiga~> python3.8
Python 3.8.0rc1 (v3.8.0rc1:34214de6ab, Oct  1 2019, 12:56:49) 
[Clang 6.0 (clang-600.0.57)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> pi=3.14159265359
>>> e=2.71828182846
>>> 
>>> e**(pi*1j)
(-1-1.31038479358762e-12j)
>>> exit()
 AMIGA:amiga~> _

As you can see within the limitations of the floating point accuracy e**(pi*1j)=-1.
We all live and learn and it also works for Python 1.4.0 for the AMIGA.

Last edited by wisecracker; 12-13-2019 at 03:02 PM.. Reason: Added last two lines.
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isympy(1)																 isympy(1)

NAME
isympy - interactive shell for SymPy SYNOPSIS
isympy [-c | --console] isympy [ {-h | --help} | {-v | --version} ] DESCRIPTION
isympy is a Python shell for SymPy. It is just a normal python shell (ipython shell if you have the ipython package installed) that exe- cutes the following commands so that you don't have to: >>> from __future__ import division >>> from sympy import * >>> x, y, z = symbols("xyz") >>> k, m, n = symbols("kmn", integer=True) So starting isympy is equivalent to starting python (or ipython) and executing the above commands by hand. It is intended for easy and quick experimentation with SymPy. For more complicated programs, it is recommended to write a script and import things explicitly (using the "from sympy import sin, log, Symbol, ..." idiom). OPTIONS
-c shell, --console=shell Use the specified shell (python or ipython) as console backend instead of the default one (ipython if present or python otherwise). Example: isympy -c python FILES
${HOME}/.sympy-history Saves the history of commands when using the python shell as backend. BUGS
The upstreams BTS can be found at <http://code.google.com/p/sympy/issues/list> Please report all bugs that you find in there, this will help improve the overall quality of SymPy. SEE ALSO
ipython(1), python(1) 2007-10-8 isympy(1)
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