Module scirust::algebra::structure::magma

Defines the magma algebraic structure.

A magma is a basic kind of algebraic structure. A magma is a set with a single binary operation. The binary operation must be closed. No other properties are imposed.

We define four kinds of magmas.

• Magma with an addition operation with partial equivalence
• Magma with an addition operation with full equivalence
• Magma with a multiplication operation with partial equivalence
• Magma with a multiplication operation with full equivalence

Types like float don't support full equivalence. That's why separate magma types are needed for them.

We define separate magma types for addition and multiplication operations. This gives us freedom in combining them to form algebraic structures with two operations.

In a sense, the traits defined in this module are marker traits. It is not really possible to verify the closure property for a type at the compile time. It is assumed that the implementation will ensure that (to a reasonable degree).

We also define a base trait MagmaBase. This trait imposes some basic requirements for all types taking advantage of the algebraic traits defined in SciRust`SciRust`SciRust. They all are required to supportDebug,`,`, Clone`Clone`Cloneand`and` and Sized`Sized`Sized`` traits.

References:

• http://en.wikipedia.org/wiki/Algebraic_structure

• http://en.wikipedia.org/wiki/Magma_(algebra)

Traits

MagmaAdd	Magma with an addition operation with full equivalence
MagmaAddPartial	Magma with an addition operation with partial equivalence
MagmaBase	Defines basic requirements for all types implementing the algebraic traits defined in SciRust
MagmaMul	Magma with a multiplication operation with full equivalence
MagmaMulPartial	Magma with a multiplication operation with partial equivalence