Distributive Magmas and Additive Magmas¶
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class
sage.categories.distributive_magmas_and_additive_magmas.
DistributiveMagmasAndAdditiveMagmas
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
The category of sets \((S,+,*)\) with \(*\) distributing on \(+\).
This is similar to a ring, but \(+\) and \(*\) are only required to be (additive) magmas.
EXAMPLES:
sage: from sage.categories.distributive_magmas_and_additive_magmas import DistributiveMagmasAndAdditiveMagmas sage: C = DistributiveMagmasAndAdditiveMagmas(); C Category of distributive magmas and additive magmas sage: C.super_categories() [Category of magmas and additive magmas]
TESTS:
sage: from sage.categories.magmas_and_additive_magmas import MagmasAndAdditiveMagmas sage: C is MagmasAndAdditiveMagmas().Distributive() True sage: C is (Magmas() & AdditiveMagmas()).Distributive() True sage: TestSuite(C).run()
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class
AdditiveAssociative
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
TESTS:
sage: C = Sets.Finite(); C Category of finite sets sage: type(C) <class 'sage.categories.finite_sets.FiniteSets_with_category'> sage: type(C).__base__.__base__ <class 'sage.categories.category_with_axiom.CategoryWithAxiom_singleton'> sage: TestSuite(C).run()
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class
AdditiveCommutative
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
TESTS:
sage: C = Sets.Finite(); C Category of finite sets sage: type(C) <class 'sage.categories.finite_sets.FiniteSets_with_category'> sage: type(C).__base__.__base__ <class 'sage.categories.category_with_axiom.CategoryWithAxiom_singleton'> sage: TestSuite(C).run()
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class
AdditiveUnital
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
TESTS:
sage: C = Sets.Finite(); C Category of finite sets sage: type(C) <class 'sage.categories.finite_sets.FiniteSets_with_category'> sage: type(C).__base__.__base__ <class 'sage.categories.category_with_axiom.CategoryWithAxiom_singleton'> sage: TestSuite(C).run()
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class
Associative
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
TESTS:
sage: C = Sets.Finite(); C Category of finite sets sage: type(C) <class 'sage.categories.finite_sets.FiniteSets_with_category'> sage: type(C).__base__.__base__ <class 'sage.categories.category_with_axiom.CategoryWithAxiom_singleton'> sage: TestSuite(C).run()
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class
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class
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class
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class
DistributiveMagmasAndAdditiveMagmas.
CartesianProducts
(category, *args)¶ Bases:
sage.categories.cartesian_product.CartesianProductsCategory
TESTS:
sage: from sage.categories.covariant_functorial_construction import CovariantConstructionCategory sage: class FooBars(CovariantConstructionCategory): ....: _functor_category = "FooBars" ....: _base_category_class = (Category,) sage: Category.FooBars = lambda self: FooBars.category_of(self) sage: C = FooBars(ModulesWithBasis(ZZ)) sage: C Category of foo bars of modules with basis over Integer Ring sage: C.base_category() Category of modules with basis over Integer Ring sage: latex(C) \mathbf{FooBars}(\mathbf{ModulesWithBasis}_{\Bold{Z}}) sage: import __main__; __main__.FooBars = FooBars # Fake FooBars being defined in a python module sage: TestSuite(C).run()
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extra_super_categories
()¶ Implement the fact that a Cartesian product of magmas distributing over additive magmas is a magma distributing over an additive magma.
EXAMPLES:
sage: C = (Magmas() & AdditiveMagmas()).Distributive().CartesianProducts() sage: C.extra_super_categories(); [Category of distributive magmas and additive magmas] sage: C.axioms() frozenset({'Distributive'})
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class
DistributiveMagmasAndAdditiveMagmas.
ParentMethods
¶
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class