Coverage for local/lib/python2.7/site-packages/sage/logic/logictable.py : 87%

r""" 

Logic Tables 

A logic table is essentially a 2-D array that is created by the statement class 

and stored in the private global variable table, along with a list containing 

the variable names to be used, in order. 

The order in which the table is listed essentially amounts to counting in 

binary. For instance, with the variables `A`, `B`, and `C` the truth table 

looks like:: 

A B C value 

False False False ? 

False False True ? 

False True False ? 

False True True ? 

True False False ? 

True False True ? 

True True False ? 

True True True ? 

This is equivalent to counting in binary, where a table would appear thus; 

:: 

2^2 2^1 2^0 value 

0 0 0 0 

0 0 1 1 

0 1 0 2 

0 1 1 3 

1 0 0 4 

1 0 1 5 

1 1 0 6 

1 1 1 7 

Given that a table can be created corresponding to any range of acceptable 

values for a given statement, it is easy to find the value of a statement 

for arbitrary values of its variables. 

AUTHORS: 

- William Stein (2006): initial version 

- Chris Gorecki (2006): initial version 

- Paul Scurek (2013-08-03): updated docstring formatting 

EXAMPLES: 

Create a truth table of a boolean formula:: 

sage: import sage.logic.propcalc as propcalc 

sage: s = propcalc.formula("a&b|~(c|a)") 

sage: s.truthtable() 

a b c value 

False False False True 

False False True False 

False True False True 

False True True False 

True False False False 

True False True False 

True True False True 

True True True True 

Get the letex code for a truth table:: 

sage: latex(s.truthtable(5,11)) 

\\\begin{tabular}{llll}c & b & a & value \\\hline True & False & True & False \\True & True & False & True \\True & True & True & True\end{tabular} 

It is not an error to use nonsensical numeric inputs:: 

sage: s = propcalc.formula("a&b|~(c|a)") 

sage: s.truthtable(5, 9) 

a b c value 

True False True False 

True True False True 

True True True True 

sage: s.truthtable(9, 5) 

a b c value 

If one argument is provided, truthtable defaults to the end:: 

sage: s.truthtable(-1) 

a b c value 

False False False True 

False False True False 

False True False True 

False True True False 

True False False False 

True False True False 

True True False True 

True True True True 

If the second argument is negative, truthtable defaults to the end:: 

sage: s.truthtable(4, -2) 

a b c value 

True False False False 

True False True False 

True True False True 

True True True True 

.. NOTE:: 

For statements that contain a variable list that when printed is longer 

than the latex page, the columns of the table will run off the screen. 

""" 

#***************************************************************************** 

# Copyright (C) 2006 William Stein <wstein@gmail.com> 

# Copyright (C) 2006 Chris Gorecki <chris.k.gorecki@gmail.com> 

# Copyright (C) 2013 Paul Scurek <scurek86@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# as published by the Free Software Foundation; either version 2 of 

# the License, or (at your option) any later version. 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

# Global variables 

__table = [] 

__vars_order = [] 

class Truthtable: 

""" 

A truth table. 

INPUT: 

- ``t`` -- a 2-D array containing the table values 

- ``vo`` -- a list of the variables in the expression in order, 

with each variable occurring only once 

""" 

def __init__(self, t, vo): 

r""" 

Initialize the data fields. 

EXAMPLES: 

This example illustrates the creation of a table 

:: 

sage: import sage.logic.propcalc as propcalc 

sage: s = propcalc.formula("a&b|~(c|a)") 

sage: s.truthtable() 

a b c value 

False False False True 

False False True False 

False True False True 

False True True False 

True False False False 

True False True False 

True True False True 

True True True True 

""" 

self.__table = t 

self.__vars_order = vo 

def _latex_(self): 

r""" 

Return a latex representation of the calling table object. 

OUTPUT: 

The latex representation of the table. 

EXAMPLES: 

This example illustrates how to get the latex representation of 

the table:: 

sage: import sage.logic.propcalc as propcalc 

sage: s = propcalc.formula("man->monkey&human") 

sage: latex(s.truthtable()) 

\\\begin{tabular}{llll}human & monkey & man & value \\\hline False & False & False & True \\False & False & True & True \\False & True & False & True \\False & True & True & True \\True & False & False & False \\True & False & True & False \\True & True & False & False \\True & True & True & True\end{tabular} 

Now, we show that strange parameters can lead to a table header 

with no body:: 

sage: latex(s.truthtable(2, 1)) 

\\\begin{tabular}{llll}human & monkey & man & value \\\hli\end{tabular} 

""" 

rt = s = "" 

self.__vars_order.reverse() 

s = r'\\\begin{tabular}{' 

s += 'l' * (len(self.__vars_order) + 1) + '}' 

for var in self.__vars_order: 

s += var + ' & ' 

rt += s + r'value \\' + r'\hline ' 

for row in self.__table: 

s = "" 

for i in row: 

s += str(i) + ' & ' 

rt += s[:-3] + r' \\' 

rt = rt[:-3] + r'\end{tabular}' 

self.__vars_order.reverse() 

return rt 

def __repr__(self): 

r""" 

Return a string representation of the calling table object. 

OUTPUT: 

The table as a 2-D string array. 

EXAMPLES: 

This example illustrates how to display the truth table of a 

boolean formula:: 

sage: import sage.logic.propcalc as propcalc 

sage: s = propcalc.formula("man->monkey&human") 

sage: s.truthtable() 

man monkey human value 

False False False True 

False False True True 

False True False True 

False True True True 

True False False False 

True False True False 

True True False False 

True True True True 

We now show that strange parameters can lead to the table 

header with no body:: 

sage: s.truthtable(2, 1) 

man monkey human value 

""" 

vars_len = [] 

line = rt = s = "" 

for var in self.__vars_order: 

vars_len.append(len(var)) 

s = var + ' ' 

while len(s) < len('False '): 

s += ' ' 

s += ' ' 

line += s 

rt += line + 'value\n' 

for row in self.__table: 

line = s = "" 

i = 0 

for e in row: 

if e: 

j = 2 

else: 

j = 1 

s = str(e) + ' ' * j 

if i < len(vars_len): 

while len(s) <= vars_len[i]: 

s += ' ' 

s += ' ' 

line += s 

i += 1 

rt += line + '\n' 

return rt 

def get_table_list(self): 

r""" 

Return a list representation of the calling table object. 

OUTPUT: 

A list representation of the table. 

EXAMPLES: 

This example illustrates how to show the table as a list:: 

sage: import sage.logic.propcalc as propcalc 

sage: s = propcalc.formula("man->monkey&human") 

sage: s.truthtable().get_table_list() 

[['man', 'monkey', 'human'], [False, False, False, True], [False, False, True, True], [False, True, False, True], [False, True, True, True], [True, False, False, False], [True, False, True, False], [True, True, False, False], [True, True, True, True]] 

""" 

t = self.__table[:] 

t.insert(0, self.__vars_order) 

return t