"""
Relations test
"""
import src
from relations import Relation, random_relation, random_adjacent_relation
from itertools import product

print('Create a binary relation on the set {0,1,2} whose members are the \
pairs (0,0), (0,1), and (2,0).\n\
Note that the pair (0,0) is repeated at the end of our list of pairs. \
Such duplicates are ignored by the constructor for the `Relation` class.')
print()
R = Relation([[0, 0], [0, 1], [2, 0], [0, 0]], 3)

print('We can display some basic information about the relation.')
print(R)
print()

print('The relation has a frozenset of tuples.')
print(R.tuples)
print()

print('In many ways it acts like a frozenset. It has a length, which is the \
number of tuples in the relation.')
print(len(R))
print()

print('There is a convenience function for printing the members of \
`R.tuples`.')
R.show()
print()

print('We can create another relation which has the same tuples and \
universe.\n\
Note that we can pass in any iterable of iterables as long as the innermost \
iterables are pairs of integers.')
S = Relation([(2, 0), (0, 1), [0, 0]], 3)
print()

print('Show the basic information about both relations we created.')
print(R)
print(S)
print()

print('We can check the tuples in each of these relations.')
print('The tuples in `R`:')
R.show()
print('The tuples in `S`:')
S.show()
print()

print('Observe that `R` and `S` are different objects as far as Python is \
concerned.')
print(R is S)
print()

print('You can also see this by printing their object ids.')
print(id(R))
print(id(S))
print()

print('However, `R` and `S` are equal to each other.')
print(R == S)
print()

print('We can also do comparisons. We have that `R` is contained in `S`, but \
this containment isn\'t proper.')
print(R <= S)
print(R < S)
print()

print('If we create a relation whose set of tuples is contained in those for \
`R` but whose universe is a different size, we will see that these \
comparisons must be between relations with the same universe and arity.')
T = Relation({(0, 0), (0, 1)}, 2)
print(T.tuples < R.tuples)
try:
    print(T < R)
except AssertionError:
    print('This will be printed because an AssertionError is thrown when \
comparing two relations on different universes.')
print()

print('Naturally, comparisons in the reverse direction work, as well.')
print(R >= S)
print(R > S)
print()

print('Since `Relation` objects are hashable, we can use them as entries in \
tuples, members of sets, or keys of dictionaries.')
tup = (R, S, T)
set_of_relations = {R, S, T}
D = {R: 1, S: 'a', T: R}
print()

print('Arithmetic operations are also possible for relations.')
print('We can create the bitwise complement of a relation.')
U = ~R
U.show()
print()

print('We can take the symmetric difference of two relations if they have the \
same universe and arity.')
X = Relation({(0, 0, 1), (0, 1, 1)}, 2)
Y = Relation({(0, 0, 1), (1, 0, 1)}, 2)
(X ^ Y).show()
print()

print('Similarly to the order comparisons, we will get an AssertionError if \
we try to add two relations with different universes or arities.')
Z = Relation({(0, 0, 1), (0, 1, 1)}, 3)
try:
    X ^ Z
except AssertionError:
    print('This will print since we have raised an AssertionError by trying \
to take the symmetric difference of two relations with different universes.')
print()

print('Taking the set difference of two relations can be done as follows.')
(X - Y).show()
print()

print('Taking the set intersection is done using the & operator. It is \
bitwise multiplication.')
(X & Y).show()
print()

print('Taking the set union is done using the | operator.')
(X | Y).show()
print()

print('Any of these binary operations can be done with augmented assignment \
as well.')
print(X)
X -= Y
print(X)
print()

print('We can take the dot product of two relations modulo 2, which is the \
same as the size of the intersection modulo 2.')
val1 = X.dot(Y)
val2 = len(X & Y) % 2
print(val1, val2)
print()

print('We can check whether a given tuple belongs to a relation.')
print((0, 0, 1) in Z)
print((0, 1, 0) in Z)
print()

print('For binary relations, there are a few options for displaying the \
relation.')
W = Relation(((0, 0), (1, 1), (1, 2), (2, 0)), 3)
W.show()
print()
W.show('binary_pixels')
print()
W.show('sparse')
print()
print('We can even produce LaTeX for a matrix.')
W.show('latex_matrix')
print()

print('Let\'s show off a little bit.')
m = 29
# Create the circle of radius 0 in over Z/mZ.
A = Relation(((i, j) for (i, j) in product(range(m), repeat=2)
if (i ** 2 + j ** 2) % m == 0), m)
# Create two translates of it.
B = Relation(((i, j) for (i, j) in product(range(m), repeat=2)
if ((i+2) ** 2 + j ** 2) % m == 0), m)
C = Relation(((i, j) for (i, j) in product(range(m), repeat=2)
if ((i+3) ** 2 + (j-1) ** 2) % m == 0), m)
# Find all points which lie on the complement of the first circle and either \
# of the two translates.
D = ~A & (B | C)
D.show('sparse')
print()

print('Note that relations are iterable.')
for tup in Z:
    print(tup)
print(list(Z))
print()

print('Relations can also be used as boolean values.')
if Z:
    print('There are members of `Z.tuples`.')
if Z ^ Z:
    print('This won\'t be printed because `Z ^ Z` is empty.')
print()

print('We can create a random binary relation.')
random_rel = random_relation(28)
random_rel.show('sparse')
print()

print('We can also find a random relation that differs from the previous \
one by one pixel.')
new_random_rel = random_adjacent_relation(random_rel)
new_random_rel.show('sparse')