#!/usr/bin/env python
# coding: utf-8

# > This is one of the 100 recipes of the [IPython Cookbook](http://ipython-books.github.io/), the definitive guide to high-performance scientific computing and data science in Python.
# 

# # 15.6. Finding a Boolean propositional formula from a truth table

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from sympy import *
init_printing()


# Let's define a few variables.

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var('x y z')


# We can define propositional formulas with symbols and a few operators.

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P = x & (y | ~z); P


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P.subs({x: True, y: False, z: True})


# Now, we want to find a propositional formula depending on x, y, z, with the following truth table:

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get_ipython().run_cell_magic('HTML', '', '<style>\ntable.truth_table tr {\n    margin: 0;\n    padding: 0;\n}\ntable.truth_table td, table.truth_table th {\n    width: 30px;\n    text-align: center;\n    margin: 0;\n    padding: 0;\n}\n</style>\n<table class="truth_table">\n<tr>\n<th>x</th><th>y</th><th>z</th><th>??</th>\n</tr>\n<tr>\n<td>T</td><td>T</td><td>T</td><th>*</th>\n</tr>\n<tr>\n<td>T</td><td>T</td><td>F</td><th>*</th>\n</tr>\n<tr>\n<td>T</td><td>F</td><td>T</td><th>T</th>\n</tr>\n<tr>\n<td>T</td><td>F</td><td>F</td><th>T</th>\n</tr>\n<tr>\n<td>F</td><td>T</td><td>T</td><th>F</th>\n</tr>\n<tr>\n<td>F</td><td>T</td><td>F</td><th>F</th>\n</tr>\n<tr>\n<td>F</td><td>F</td><td>T</td><th>F</th>\n</tr>\n<tr>\n<td>F</td><td>F</td><td>F</td><th>T</th>\n</tr>\n</table>\n')


# Let's write down all combinations that we want to evaluate to True, and those for which the outcome does not matter.

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minterms = [[1,0,1], [1,0,0], [0,0,0]]
dontcare = [[1,1,1], [1,1,0]]


# Now, we use the SOPform function to derive an adequate proposition.

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Q = SOPform(['x', 'y', 'z'], minterms, dontcare); Q


# Let's test that this proposition works.

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Q.subs({x: True, y: False, z: False}), Q.subs({x: False, y: True, z: True})


# > You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).
# 
# > [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (500 pages).