def __iter__(self):
"""
TESTS::
sage: IntegerVectors(0, []).list()
[[]]
sage: IntegerVectors(5, []).list()
[]
sage: IntegerVectors(0, [1]).list()
[[0]]
sage: IntegerVectors(4, [1]).list()
[[4]]
sage: IntegerVectors(4, [2]).list()
[[4, 0], [3, 1], [2, 2]]
sage: IntegerVectors(4, [2,2]).list()
[[4, 0, 0, 0],
[3, 0, 1, 0],
[2, 0, 2, 0],
[2, 0, 1, 1],
[1, 0, 3, 0],
[1, 0, 2, 1],
[0, 0, 4, 0],
[0, 0, 3, 1],
[0, 0, 2, 2]]
sage: IntegerVectors(5, [1,1,1]).list()
[[5, 0, 0],
[4, 1, 0],
[4, 0, 1],
[3, 2, 0],
[3, 1, 1],
[3, 0, 2],
[2, 3, 0],
[2, 2, 1],
[2, 1, 2],
[2, 0, 3],
[1, 4, 0],
[1, 3, 1],
[1, 2, 2],
[1, 1, 3],
[1, 0, 4],
[0, 5, 0],
[0, 4, 1],
[0, 3, 2],
[0, 2, 3],
[0, 1, 4],
[0, 0, 5]]
sage: IntegerVectors(0, [2,3]).list()
[[0, 0, 0, 0, 0]]
"""
for iv in IntegerVectors(self.n, len(self.comp)):
blocks = [
IntegerVectors(iv[i], self.comp[i], max_slope=0).__iter__()
for i in range(len(self.comp))
]
for parts in cartesian_product.CartesianProduct(*blocks):
res = []
for part in parts:
res += part
yield res
def __iter__(self):
"""
TESTS::
sage: SignedCompositions(0).list() #indirect doctest
[[]]
sage: SignedCompositions(1).list() #indirect doctest
[[1], [-1]]
sage: SignedCompositions(2).list() #indirect doctest
[[1, 1], [1, -1], [-1, 1], [-1, -1], [2], [-2]]
"""
for comp in Compositions_n.__iter__(self):
l = len(comp)
a = [[1, -1] for i in range(l)]
for sign in cartesian_product.CartesianProduct(*a):
yield [sign[i] * comp[i] for i in range(l)]
import cartesian_product
if __name__ == '__main__':
set1 = (1, 2, 3)
set2 = ('a', 'b', 'c')
set3 = (1.1, 2.2, 3.3)
# check no arguments
c1 = cartesian_product.CartesianProduct()
for i in c1:
print(i)
# check cartesian product of two sets
c2 = cartesian_product.CartesianProduct(set1, set2)
for i in c2:
print(i)
# check cartesian product of three sets
c3 = cartesian_product.CartesianProduct(set1, set2, set3)
for i in c3:
print(i)
# check cartesian product of two sets but both of sets repeated twice
c4 = cartesian_product.CartesianProduct(set1, set1, set2, set2)
for i in c4:
print(i)