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

r""" 

Lie Groups 

""" 

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

# 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.misc.abstract_method import abstract_method 

from sage.misc.cachefunc import cached_method 

from sage.categories.category_types import Category_over_base_ring 

from sage.categories.groups import Groups 

from sage.categories.manifolds import Manifolds 

class LieGroups(Category_over_base_ring): 

r""" 

The category of Lie groups. 

A Lie group is a topological group with a smooth manifold structure. 

EXAMPLES:: 

sage: from sage.categories.lie_groups import LieGroups 

sage: C = LieGroups(QQ); C 

Category of Lie groups over Rational Field 

TESTS:: 

sage: TestSuite(C).run(skip="_test_category_over_bases") 

""" 

@cached_method 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.lie_groups import LieGroups 

sage: LieGroups(QQ).super_categories() 

[Category of topological groups, 

Category of smooth manifolds over Rational Field] 

""" 

return [Groups().Topological(), Manifolds(self.base()).Smooth()] 

def additional_structure(self): 

r""" 

Return ``None``. 

Indeed, the category of Lie groups defines no new 

structure: a morphism of topological spaces and of smooth 

manifolds is a morphism as Lie groups. 

.. SEEALSO:: :meth:`Category.additional_structure` 

EXAMPLES:: 

sage: from sage.categories.lie_groups import LieGroups 

sage: LieGroups(QQ).additional_structure() 

""" 

return None 

# Because Lie is a name that deserves to be capitalized 

def _repr_object_names(self): 

""" 

EXAMPLES:: 

sage: from sage.categories.lie_groups import LieGroups 

sage: LieGroups(QQ) # indirect doctest 

Category of Lie groups over Rational Field 

""" 

return "Lie groups over {}".format(self.base_ring())