Module local_num 

Traits for “local” numbers

Sometimes, a given type T only has the concept of zero and one local to self. E.g. the 5-adic space ZZ_5 has zero in it, but it is not the same zero as in ZZ_7. Same with one, shared concepts but in a “subspace” of T.

So a function to create zero or one needs extra information than the traits Zero and One in num. The obvious “extra” information is self.

Built on top of this are the constructed traits of LocalNum and LocalInteger. These follow similarly to the num crate with two major differences:

• They only require LocalZero and LocalOne instead of Zero and One
• They don’t rely on information about number ordering, such as floor and ceil

Traits:

• LocalZero asks for zero(Self) rather than zero()
• LocalOne asks for one(Self) rather than one()
• LocalNum the base type for a ring-like structure, with local zero/one and ring ops
• LocalInteger a LocalNum that has an idea of GCD/LCM

Traits

LocalInteger

A LocalNum that allows division, remainder, GCD, and LCM

LocalNum

The base trait for numeric types, covering local 0 and 1 values, comparisons, basic numeric operations, and string conversion

LocalOne

Returns a multiplicative identity element for self

LocalZero

Returns an additive identity element for self