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Original file line number | Diff line number | Diff line change |
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r""" | ||
Super Algebras | ||
""" | ||
#***************************************************************************** | ||
# 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/ | ||
#****************************************************************************** | ||
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||
from sage.categories.super_modules import SuperModulesCategory | ||
from sage.categories.algebras import Algebras | ||
from sage.categories.modules import Modules | ||
from sage.misc.lazy_import import LazyImport | ||
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class SuperAlgebras(SuperModulesCategory): | ||
""" | ||
The category of super algebras. | ||
EXAMPLES:: | ||
sage: Algebras(ZZ).Super() | ||
Category of super algebras over Integer Ring | ||
TESTS:: | ||
sage: TestSuite(Algebras(ZZ).Super()).run() | ||
""" | ||
def extra_super_categories(self): | ||
""" | ||
EXAMPLES:: | ||
sage: Algebras(ZZ).Super().super_categories() | ||
[Category of graded algebras over Integer Ring, | ||
Category of super modules over Integer Ring] | ||
""" | ||
return [self.base_category().Graded()] | ||
|
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Original file line number | Diff line number | Diff line change |
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@@ -0,0 +1,39 @@ | ||
r""" | ||
Super algebras with basis | ||
""" | ||
#***************************************************************************** | ||
# 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.categories.super_modules import SuperModulesCategory | ||
from sage.categories.algebras import Algebras | ||
from sage.categories.modules import Modules | ||
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||
class SuperAlgebrasWithBasis(SuperModulesCategory): | ||
""" | ||
The category of super algebras with a distinguished basis | ||
EXAMPLES:: | ||
sage: C = Algebras(ZZ).WithBasis().Super(); C | ||
Category of super algebras with basis over Integer Ring | ||
TESTS:: | ||
sage: TestSuite(C).run() | ||
""" | ||
def extra_super_categories(self): | ||
""" | ||
EXAMPLES:: | ||
sage: C = Algebras(ZZ).WithBasis().Super() | ||
sage: sorted(C.super_categories(), key=str) # indirect doctest | ||
[Category of graded algebras with basis over Integer Ring, | ||
Category of super algebras over Integer Ring, | ||
Category of super modules with basis over Integer Ring] | ||
""" | ||
return [self.base_category().Graded()] | ||
|
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Original file line number | Diff line number | Diff line change |
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@@ -0,0 +1,30 @@ | ||
r""" | ||
Super Hopf algebras with basis | ||
""" | ||
#***************************************************************************** | ||
# 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.categories.super_modules import SuperModulesCategory | ||
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class SuperHopfAlgebrasWithBasis(SuperModulesCategory): | ||
""" | ||
The category of super algebras with a distinguished basis | ||
EXAMPLES:: | ||
sage: C = HopfAlgebras(ZZ).WithBasis().Super(); C | ||
Category of super hopf algebras with basis over Integer Ring | ||
sage: sorted(C.super_categories(), key=str) | ||
[Category of super algebras with basis over Integer Ring, | ||
Category of super coalgebras with basis over Integer Ring, | ||
Category of super hopf algebras over Integer Ring] | ||
TESTS:: | ||
sage: TestSuite(C).run() | ||
""" | ||
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