Coverage for local/lib/python2.7/site-packages/sage/categories/examples/cw_complexes.py : 100%

""" 

Examples of CW complexes 

""" 

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

# Copyright (C) 2015 Travis Scrimshaw <tscrim at ucdavis.edu> 

# 

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

# http://www.gnu.org/licenses/ 

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

from sage.structure.parent import Parent 

from sage.structure.unique_representation import UniqueRepresentation 

from sage.structure.element import Element 

from sage.categories.cw_complexes import CWComplexes 

from sage.rings.integer import Integer 

from sage.rings.all import QQ 

from sage.sets.family import Family 

class Surface(UniqueRepresentation, Parent): 

r""" 

An example of a CW complex: a (2-dimensional) surface. 

This class illustrates a minimal implementation of a CW complex. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example(); X 

An example of a CW complex: the surface given by the boundary map (1, 2, 1, 2) 

sage: X.category() 

Category of finite finite dimensional CW complexes 

We conclude by running systematic tests on this manifold:: 

sage: TestSuite(X).run() 

""" 

def __init__(self, bdy=(1, 2, 1, 2)): 

r""" 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example((1, 2)); X 

An example of a CW complex: the surface given by the boundary map (1, 2) 

TESTS:: 

sage: TestSuite(X).run() 

""" 

self._bdy = bdy 

self._edges = frozenset(bdy) 

Parent.__init__(self, category=CWComplexes().Finite()) 

def _repr_(self): 

r""" 

TESTS:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: CWComplexes().example() 

An example of a CW complex: the surface given by the boundary map (1, 2, 1, 2) 

""" 

return "An example of a CW complex: the surface given by the boundary map {}".format(self._bdy) 

def cells(self): 

""" 

Return the cells of ``self``. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example() 

sage: C = X.cells() 

sage: sorted((d, C[d]) for d in C.keys()) 

[(0, (0-cell v,)), 

(1, (0-cell e1, 0-cell e2)), 

(2, (2-cell f,))] 

""" 

d = {0: (self.element_class(self, 0, 'v'),)} 

d[1] = tuple([self.element_class(self, 0, 'e'+str(e)) for e in self._edges]) 

d[2] = (self.an_element(),) 

return Family(d) 

def an_element(self): 

r""" 

Return an element of the CW complex, as per 

:meth:`Sets.ParentMethods.an_element`. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example() 

sage: X.an_element() 

2-cell f 

""" 

return self.element_class(self, 2, 'f') 

class Element(Element): 

""" 

A cell in a CW complex. 

""" 

def __init__(self, parent, dim, name): 

""" 

Initialize ``self``. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example() 

sage: f = X.an_element() 

sage: TestSuite(f).run() 

""" 

Element.__init__(self, parent) 

self._dim = dim 

self._name = name 

def _repr_(self): 

""" 

Return a string representation of ``self``. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example() 

sage: X.an_element() 

2-cell f 

""" 

return "{}-cell {}".format(self._dim, self._name) 

def __eq__(self, other): 

""" 

Check equality. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example() 

sage: f = X.an_element() 

sage: f == X(2, 'f') 

True 

sage: e1 = X(1, 'e1') 

sage: e1 == f 

False 

""" 

return (isinstance(other, Surface.Element) 

and self.parent() is other.parent() 

and self._dim == other._dim 

and self._name == other._name) 

def dimension(self): 

""" 

Return the dimension of ``self``. 

EXAMPLES:: 

sage: from sage.categories.cw_complexes import CWComplexes 

sage: X = CWComplexes().example() 

sage: f = X.an_element() 

sage: f.dimension() 

2 

""" 

return self._dim 

Example = Surface