Coverage for local/lib/python2.7/site-packages/sage/combinat/posets/elements.py : 45%

r""" 

Elements of posets, lattices, semilattices, etc. 

""" 

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

# Copyright (C) 2008 Peter Jipsen <jipsen@chapman.edu>, 

# Franco Saliola <saliola@gmail.com> 

# 

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

# 

# This code is distributed in the hope that it will be useful, 

# but WITHOUT ANY WARRANTY; without even the implied warranty of 

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 

# General Public License for more details. 

# 

# The full text of the GPL is available at: 

# 

# http://www.gnu.org/licenses/ 

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

from sage.structure.element import Element 

from sage.structure.element import have_same_parent 

class PosetElement(Element): 

def __init__(self, poset, element, vertex): 

r""" 

Establish the parent-child relationship between ``poset`` 

and ``element``, where ``element`` is associated to the 

vertex ``vertex`` of the Hasse diagram of the poset. 

INPUT: 

- ``poset`` -- a poset object 

- ``element`` -- any object 

- ``vertex`` -- a vertex of the Hasse diagram of the poset 

TESTS:: 

sage: from sage.combinat.posets.elements import PosetElement 

sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False) 

sage: e = P(0) 

sage: e.parent() is P 

True 

sage: TestSuite(e).run() 

""" 

Element.__init__(self, poset) 

if isinstance(element, self.parent().element_class): 

self.element = element.element 

else: 

self.element = element 

self.vertex = vertex 

def __hash__(self): 

r""" 

TESTS:: 

sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False) 

sage: e = P(0) 

sage: hash(e) 

0 

""" 

return hash(self.element) 

def _repr_(self): 

""" 

TESTS:: 

sage: Poset([[1,2],[4],[3],[4],[]], facade = False)(0)._repr_() 

'0' 

""" 

return "%s" % str(self.element) 

def _latex_(self): 

r""" 

Return the latex code of the poset element. 

EXAMPLES:: 

sage: m = matrix(2,[1,2,3,4]) 

sage: m.set_immutable() 

sage: P = Poset(([m],[]), facade = False) 

sage: [e] = P 

sage: type(e) 

<class 'sage.combinat.posets.posets.FinitePoset_with_category.element_class'> 

sage: latex(e) #indirect doctest 

\left(\begin{array}{rr} 

1 & 2 \\ 

3 & 4 

\end{array}\right) 

""" 

from sage.misc.latex import latex 

return latex(self.element) 

def __eq__(self, other): 

""" 

TESTS:: 

sage: P = Poset([["a","b"],["d"],["c"],["d"],[]], facade = False) 

sage: Q = Poset([["a","b"],["d"],["c"],[],[]], facade = False) 

sage: P(0).__eq__(P(4)) 

False 

sage: from sage.combinat.posets.elements import PosetElement 

sage: PosetElement(P,0,"c") == PosetElement(P,0,"c") 

True 

sage: PosetElement(P,0,"c") == PosetElement(Q,0,"c") 

False 

sage: PosetElement(P,0,"b") == PosetElement(P,0,"c") 

False 

.. warning:: as an optimization, this only compares the parent 

and vertex, using the invariant that, in a proper poset 

element, ``self.element == other.element`` if and only 

``self.vertex == other.vertex``:: 

sage: PosetElement(P,1,"c") == PosetElement(P,0,"c") 

True 

Test that :trac:`12351` is fixed:: 

sage: P(0) == int(0) 

False 

""" 

# This should instead exploit unique representation, using 

# self is other, or best inherit __eq__ from there. But there 

# are issues around pickling and rich comparison functions. 

return have_same_parent(self, other) \ 

and self.vertex == other.vertex 

def __ne__(self, other): 

r""" 

TESTS:: 

sage: P = Poset([[1,2],[4],[3],[4],[]]) 

sage: P = Poset([["a","b"],["d"],["c"],["d"],[]]) 

sage: P(0).__ne__(P(4)) 

True 

sage: from sage.combinat.posets.elements import PosetElement 

sage: PosetElement(P,0,"c") != PosetElement(P,0,"c") 

False 

sage: PosetElement(P,0,"b") != PosetElement(P,0,"c") 

True 

For this one, see comment in :meth:`__eq__`:: 

sage: PosetElement(P,1,"c") != PosetElement(P,0,"c") 

False 

""" 

return not self == other 

def _cmp(self, other): 

""" 

TESTS:: 

sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False) 

sage: P(0)._cmp(P(4)) 

-1 

sage: P(4)._cmp(P(0)) 

1 

sage: P(0)._cmp(P(0)) 

0 

sage: P(1)._cmp(P(2)) 

""" 

return self.parent().compare_elements(self, other) 

def __lt__(self, other): 

""" 

TESTS 

:: 

sage: dag = DiGraph({0:[2,3], 1:[3,4], 2:[5], 3:[5], 4:[5]}) 

sage: P = Poset(dag, facade = False) 

sage: P(0) < P(1) 

False 

sage: P(4) < P(1) 

False 

sage: P(0) < P(0) 

False 

""" 

return self._cmp(other) == -1 or False 

def __le__(self, other): 

""" 

TESTS 

:: 

sage: dag = DiGraph({0:[2,3], 1:[3,4], 2:[5], 3:[5], 4:[5]}) 

sage: P = Poset(dag, facade = False) 

sage: P(1) <= P(0) 

False 

sage: P(0) <= P(1) 

False 

sage: P(0) <= P(3) 

True 

sage: P(0) <= P(0) 

True 

""" 

return self == other or self._cmp(other) == -1 or False 

def __gt__(self, other): 

""" 

TESTS 

:: 

sage: dag = DiGraph({0:[2,3], 1:[3,4], 2:[5], 3:[5], 4:[5]}) 

sage: P = Poset(dag) 

sage: P(0).__gt__(P(5)) 

False 

sage: P(5).__gt__(P(0)) 

True 

sage: P(0).__gt__(P(0)) 

False 

""" 

return self._cmp(other) == 1 or False 

def __ge__(self, other): 

""" 

TESTS 

:: 

sage: dag = DiGraph({0:[2,3], 1:[3,4], 2:[5], 3:[5], 4:[5]}) 

sage: P = Poset(dag) 

sage: P(0).__ge__(P(5)) 

False 

sage: P(5).__ge__(P(0)) 

True 

sage: P(0).__ge__(P(0)) 

True 

""" 

return self == other or self._cmp(other) == 1 or False 

class MeetSemilatticeElement(PosetElement): 

def __mul__(self, other): 

r""" 

Return the meet of ``self`` and ``other`` in the lattice. 

EXAMPLES:: 

sage: D = posets.DiamondPoset(5,facade=False) 

sage: D(1) * D(2) 

0 

sage: D(1) * D(1) 

1 

sage: D(1) * D(0) 

0 

sage: D(1) * D(4) 

1 

""" 

return self.parent().meet(self, other) 

class JoinSemilatticeElement(PosetElement): 

def __add__(self, other): 

r""" 

Return the join of ``self`` and ``other`` in the lattice. 

EXAMPLES:: 

sage: D = posets.DiamondPoset(5,facade=False) 

sage: D(1) + D(2) 

4 

sage: D(1) + D(1) 

1 

sage: D(1) + D(4) 

4 

sage: D(1) + D(0) 

1 

""" 

return self.parent().join(self, other) 

class LatticePosetElement(MeetSemilatticeElement, JoinSemilatticeElement): 

pass