Expand description
Abstractions over sets with certain structure.
The structure framework used by algebraeon_rings is established here.
Structs§
- Composition
Morphism - The composition A -> B -> C of two morphisms A -> B and B -> C
- Empty
SetStructure - Enumerated
Finite SetStructure - Finite
SetEndofunctions - The set of all endofunctions on a finite set X: functions X → X
- Functions
- Represent all functions from
domaintorange - Identity
Morphism - The identity morphism X -> X
- Pairs
Structure - The set of Pairs
- Singleton
SetStructure - Unordered
Pair - Unordered
Pairs - The set of unordered Pairs of distinct elements
Traits§
- Bijective
Function - Borrowed
Morphism - Borrowed
Set - Borrowed
Structure - Countable
SetSignature - Endofunction
- A function from a set into itself
- Endomorphism
- A morphism from an object to itself
- EqSignature
- Finite
SetSignature - Function
- Injective
Function - Maybe
Finite SetSignature - Meta
Type - Morphism
- OrdSignature
- Partial
OrdSignature - Permutation
- A permutation is a bijective function from a set to itself
- SetSignature
- Instances of a type implementing this trait represent
a set of elements of type
Self::Setwith some structure, for example, the structure of a ring. - Signature
- ToString
Signature
Derive Macros§
- Canonical
Structure - Generate a canonical structure type for a type
Tby decorating it with#[derive(CanonicalStructure)]. Optional additional structure can be generated by adding#[canonical_structure(eq, partial_ord, ord)]. The type must implementDebugandClone. The optional additional structures may requireTto implement further traits. RequiresMetaType,Signature, andSetSignatureto be in scope. The optional additional structures may require further items to be in scope.