Examples of semirings¶
- sage.categories.examples.semirings.Example[source]¶
- alias of - TernaryLogic
- class sage.categories.examples.semirings.Ternary(parent, n)[source]¶
- Bases: - Element- Elements of the ternary-logic ring. - The semantic is as follows: - 0 – the integer 0 
- 1 – the integer 1 
- 2 – some integer greater than 1 
 - An alternative semantic is: - 0 – an empty set 
- 1 – a connected set 
- 2 – a disconnected set 
 - The same semantic works for graphs instead of sets. 
- class sage.categories.examples.semirings.TernaryLogic[source]¶
- Bases: - UniqueRepresentation,- Parent- An example of a semiring. - This class illustrates a minimal implementation of a semiring. - EXAMPLES: - sage: S = Semirings().example(); S An example of a semiring: the ternary-logic semiring - >>> from sage.all import * >>> S = Semirings().example(); S An example of a semiring: the ternary-logic semiring - This is the semiring that contains 3 objects: - sage: S.some_elements() [0, 1, many] - >>> from sage.all import * >>> S.some_elements() [0, 1, many] - The product rule is as expected: - sage: S(1) * S(1) 1 sage: S(1) + S(1) many - >>> from sage.all import * >>> S(Integer(1)) * S(Integer(1)) 1 >>> S(Integer(1)) + S(Integer(1)) many - an_element()[source]¶
- Return an element of the semiring. - EXAMPLES: - sage: Semirings().example().an_element() many - >>> from sage.all import * >>> Semirings().example().an_element() many 
 - one()[source]¶
- Return the unit of - self.- EXAMPLES: - sage: S = Semirings().example() sage: S.one() 1 - >>> from sage.all import * >>> S = Semirings().example() >>> S.one() 1 
 - product(x, y)[source]¶
- Return the product of - xand- yin the semiring as per- Semirings.ParentMethods.product().- EXAMPLES: - sage: S = Semirings().example() sage: S(1) * S(2) many - >>> from sage.all import * >>> S = Semirings().example() >>> S(Integer(1)) * S(Integer(2)) many