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]
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class
AdditiveAssociative
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
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class
AdditiveCommutative
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
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class
AdditiveUnital
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
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class
Associative
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
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AdditiveInverse
¶ alias of
sage.categories.rngs.Rngs
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Unital
¶ alias of
sage.categories.semirings.Semirings
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class
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class
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class
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class
CartesianProducts
(category, *args)¶ Bases:
sage.categories.cartesian_product.CartesianProductsCategory
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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
ParentMethods
¶ Bases:
object
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class