Module maths_traits::analysis::ordered

Traits for ordered structures

Macros

Ord	Derive macro generating an impl of the trait Ord.
PartialOrd	Derive macro generating an impl of the trait PartialOrd.

Traits

AddOrdered	A marker trait signifying that for x > y, x+z > x+z and z+x > z+x for all z
ArchimedeanDiv	Division with remainder using an ordering and the Archimedean Property
ArchimedeanProperty	The property that if x < y, there exists some natural n where n*x = x*...*x > y
MulOrdered	A marker trait signifying that for x > y, x*z > x*z and z*x > z*x for all z > 0
Ord	Trait for types that form a total order.
PartialOrd	Trait for values that can be compared for a sort-order.
Sign	Helpful methods for manipulating an element's order relative to 0
Signed	Helpful methods for measuring an element's order relative to 0

Trait aliases

ArchAbelianGroup	An ordered abeliean group with the Archimedean property
ArchCommutativeRing	An ordered commutative ring with the Archimedean property and Archimedean division
ArchCommutativeSemiring	An ordered commutative semiring with the Archimedean property and Archimedean division
ArchDivisionRing	An ordered division ring with the Archimedean property and Archimedean division
ArchDivisionSemiring	An ordered division semiring with the Archimedean property and Archimedean division
ArchField	An ordered field ring with the Archimedean property and Archimedean division
ArchGroup	An ordered group with the Archimedean property
ArchMonoid	An ordered monoid with the Archimedean property
ArchRing	An ordered ring with the Archimedean property
ArchSemigroup	An ordered semigroup with the Archimedean property
ArchSemiring	An ordered semiring with the Archimedean property
ArchUnitalRing	An ordered unital ring with the Archimedean property and Archimedean division
ArchUnitalSemiring	An ordered unital semiring with the Archimedean property and Archimedean division
OrdAbelianGroup	An additive abelian group with an ordered addition operation
OrdCommutativeRing	A commutative ring with ordered addition and multiplication
OrdCommutativeSemiring	A commutative semiring with ordered addition and multiplication
OrdDivisionRing	A division ring with ordered addition and multiplication
OrdDivisionSemiring	A division semiring with ordered addition and multiplication
OrdField	A field with ordered addition and multiplication
OrdGroup	An additive group with an ordered addition operation
OrdLoop	An additive loop with an ordered addition operation
OrdMagma	An additive magma with an ordered addition operation
OrdMonoid	An additive monoid with an ordered addition operation
OrdRing	A ring with ordered addition and multiplication
OrdSemigroup	An additive semigroup with an ordered addition operation
OrdSemiring	A semiring with ordered addition and multiplication
OrdUnitalRing	A unital ring with ordered addition and multiplication
OrdUnitalSemiring	A unitial semiring with ordered addition and multiplication