def __init__(self, *iters):
"""
TESTS::
sage: from sage.combinat.cartesian_product import CartesianProduct_iters
sage: cp = CartesianProduct_iters([1,2],[3,4]); cp
Cartesian product of [1, 2], [3, 4]
sage: loads(dumps(cp)) == cp
True
sage: TestSuite(cp).run(skip='_test_an_element')
Check that :trac:`24558` is fixed::
sage: from sage.combinat.cartesian_product import CartesianProduct_iters
sage: from sage.sets.set_from_iterator import EnumeratedSetFromIterator
sage: I = EnumeratedSetFromIterator(Integers)
sage: CartesianProduct_iters(I, I)
Cartesian product of {0, 1, -1, 2, -2, ...}, {0, 1, -1, 2, -2, ...}
"""
self.iters = iters
self._mrange = xmrange_iter(iters)
category = EnumeratedSets()
try:
category = category.Finite() if self.is_finite() else category.Infinite()
except ValueError: # Unable to determine if it is finite or not
pass
def iterfunc():
# we can not use self.__iterate__ directly because
# that leads to an infinite recursion in __eq__
return self.__iterate__()
name = "Cartesian product of " + ", ".join(map(str, self.iters))
EnumeratedSetFromIterator.__init__(self, iterfunc,
name=name,
category=category,
cache=False)
def __init__(self, *iters):
"""
TESTS::
sage: import sage.combinat.cartesian_product as cartesian_product
sage: cp = cartesian_product.CartesianProduct_iters([1,2],[3,4]); cp
Cartesian product of [1, 2], [3, 4]
sage: loads(dumps(cp)) == cp
True
"""
self.iters = iters
self._mrange = xmrange_iter(iters)
CombinatorialClass.__init__(self)
def __init__(self, *iters):
"""
TESTS::
sage: import sage.combinat.cartesian_product as cartesian_product
sage: cp = cartesian_product.CartesianProduct_iters([1,2],[3,4]); cp
Cartesian product of [1, 2], [3, 4]
sage: loads(dumps(cp)) == cp
True
"""
self.iters = iters
self._mrange = xmrange_iter(iters)
CombinatorialClass.__init__(self)
def residues(self):
"""
Returns a iterator through a complete list of residues modulo this integral ideal.
An error is raised if this fractional ideal is not integral.
EXAMPLES::
sage: K.<a, w> = NumberFieldTower([x^2 - 3, x^2 + x + 1])
sage: I = K.ideal(6, -w*a - w + 4)
sage: list(I.residues())[:5]
[(25/3*w - 1/3)*a + 22*w + 1,
(16/3*w - 1/3)*a + 13*w,
(7/3*w - 1/3)*a + 4*w - 1,
(-2/3*w - 1/3)*a - 5*w - 2,
(-11/3*w - 1/3)*a - 14*w - 3]
"""
abs_ideal = self.absolute_ideal()
from_abs = abs_ideal.number_field().structure()[0]
from sage.misc.mrange import xmrange_iter
abs_residues = abs_ideal.residues()
return xmrange_iter(abs_residues.iter_list, lambda c: from_abs(abs_residues.typ(c)))
def residues(self):
"""
Returns a iterator through a complete list of residues modulo this integral ideal.
An error is raised if this fractional ideal is not integral.
EXAMPLES::
sage: K.<a, w> = NumberFieldTower([x^2 - 3, x^2 + x + 1])
sage: I = K.ideal(6, -w*a - w + 4)
sage: list(I.residues())[:5]
[(25/3*w - 1/3)*a + 22*w + 1,
(16/3*w - 1/3)*a + 13*w,
(7/3*w - 1/3)*a + 4*w - 1,
(-2/3*w - 1/3)*a - 5*w - 2,
(-11/3*w - 1/3)*a - 14*w - 3]
"""
abs_ideal = self.absolute_ideal()
from_abs = abs_ideal.number_field().structure()[0]
from sage.misc.mrange import xmrange_iter
abs_residues = abs_ideal.residues()
return xmrange_iter(abs_residues.iter_list, lambda c: from_abs(abs_residues.typ(c)))
