Distributive Magmas and Additive Magmas¶
- class sage.categories.distributive_magmas_and_additive_magmas.DistributiveMagmasAndAdditiveMagmas(base_category)[source]¶
- Bases: - 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] - >>> from sage.all import * >>> from sage.categories.distributive_magmas_and_additive_magmas import DistributiveMagmasAndAdditiveMagmas >>> C = DistributiveMagmasAndAdditiveMagmas(); C Category of distributive magmas and additive magmas >>> C.super_categories() [Category of magmas and additive magmas] - class AdditiveAssociative(base_category)[source]¶
- Bases: - CategoryWithAxiom_singleton- class AdditiveCommutative(base_category)[source]¶
- Bases: - CategoryWithAxiom_singleton
 
 - class CartesianProducts(category, *args)[source]¶
- Bases: - CartesianProductsCategory- extra_super_categories()[source]¶
- 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'}) - >>> from sage.all import * >>> C = (Magmas() & AdditiveMagmas()).Distributive().CartesianProducts() >>> C.extra_super_categories() [Category of distributive magmas and additive magmas] >>> C.axioms() frozenset({'Distributive'})