Magmas and Additive Magmas¶
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sage.categories.magmas_and_additive_magmas.
MagmasAndAdditiveMagmas
¶ The category of sets \((S,+,*)\) with an additive operation ‘+’ and a multiplicative operation \(*\)
EXAMPLES:
sage: from sage.categories.magmas_and_additive_magmas import MagmasAndAdditiveMagmas sage: C = MagmasAndAdditiveMagmas(); C Category of magmas and additive magmas
This is the base category for the categories of rings and their variants:
sage: C.Distributive() Category of distributive magmas and additive magmas sage: C.Distributive().Associative().AdditiveAssociative().AdditiveCommutative().AdditiveUnital().AdditiveInverse() Category of rngs sage: C.Distributive().Associative().AdditiveAssociative().AdditiveCommutative().AdditiveUnital().Unital() Category of semirings sage: C.Distributive().Associative().AdditiveAssociative().AdditiveCommutative().AdditiveUnital().AdditiveInverse().Unital() Category of rings
This category is really meant to represent the intersection of the categories of
Magmas
andAdditiveMagmas
; however Sage’s infrastructure does not allow yet to model this:sage: Magmas() & AdditiveMagmas() Join of Category of magmas and Category of additive magmas sage: Magmas() & AdditiveMagmas() # todo: not implemented Category of magmas and additive magmas