r"""
Module that creates truth tables of boolean formulas.
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.
"""
__table = []
__vars_order = []
class Truthtable:
def __init__(self, t, vo):
r"""
Initialize the data fields
INPUT:
- ``self'' -- calling object
- ``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
OUTPUT:
None
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.
INPUT:
- ``self`` -- calling object
OUTPUT:
The latex representation of the table
EXAMPLES:
This example illustrates how to get the latex represenation 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}
"""
vars_len = []
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.
INPUT:
- ``self`` -- the calling object
OUTPUT:
The talbe as a 2-D 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 == True:
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.
INPUT:
- ``self`` -- calling 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
