PlaneDomains Copyright (C) 2013  Marco Spadini
 
This program comes with ABSOLUTELY NO WARRANTY. 
This is free software, and you are welcome to redistribute it under certain 
conditions.  
See the GNU General Public License for more details.


About the author:
Marco Spadini                         
Dipartimento di Matematica e Informatica,
Via S. Marta 3, 50139 Firenze,       
ITALY 

web: http:\\www.dma.unifi.it\~spadini
e-mail: marco.spadini@unifi.it

Description:  
  The purpose of this program is to sketch plane domains defined by a
  complex sets of inequalities. 
  The user should provide a reference rectangle R (determined by two opposite 
  corners, south-west SW=(x0,y0) and north-east NE=(x1,y1)), and a set of 
  conditions (namely a bunch of inequalities joined by logical connectives as 
  ".and.", ".or.", ".xor.", or the operator ".not." ). The set of conditions can 
  be distributed on several lines (all logically linked by ".and.", but do **not**
  break a single condition over two lines: errors would ensue).
  The program tries to sketch the closure of the interior of the set D of those 
  points (x,y) in the reference rectangle R where the condition holds. (Note that 
  boundaries, albeit shown, are not necessarily included in the domain D, but do 
  belong to the closure of D).
  The functions  and conditions ought to be inserted as strings (using FORTRAN 
  90/95 conventions and intrinsics with the addition of the ".xor." operator and 
  of the "signum" function --realized as "signum(x)=sign(1.,x)"). All input boxes 
  accept simple Python expressions, like e/2 or pi. A word of caution concerns integer 
  division: recall that in FORTRAN, as in many other languages, 1./2. = 0.5 whereas 
  1/2 = 0. 
  **WARNING** Please be aware that because of how FORTRAN treats out-of-range values,
  expressions evaluating points outside of their domain yield NaN, hence quietly 
  evaluataes to .FALSE. in our context. This means, for instance, that expressions 
  like "sqrt(x)<1." do not yield an error even for negative x and behaves exactly 
  as "sqrt(abs(x))<1." (just a little slower). Whether this behaviour is a nice
  feature or a bad bug depends on the user awareness!


Components.
The program consists of three pieces of software: The interfaces (planeDomains.py and 
positivePlaneF.py) written in Python and the FORTRAN main program that actually makes 
the computations (dom2.f03);


Requirements:
A working gfortran installation is needed for the main program. A working
Python (I tested v. 2.7) installation with the Tkinter module is required 
for the interface. Also, to get graphics output, a working Gnuplot 
installation with x11 support is required.


Installation: 
Just copy this directory somewhere you have the rights to read write and 
execute.


RUNNING THE PROGRAM:
In a terminal, go to the directory where the program is installed.
At the prompt, issue the command "python pDomain.py". Enjoy!