Numeric types:numberic type

From dis-Emi-A

Numeric Types

There are several classes of numbers in mathematics. Below is a brief overview of those.

Integer 

a numeric integral scalar

Rational 

a number that can be represented as x/y

Irrational 

a non-terminating number that cannot be represented as x/y

Real 

a 1-space scalar (incl: Algebraic and Transcendental, Rational, Irrational, Integer)

Complex 

a 2-space plane

Algebraic 

satisifies Pn(a)=0 for some polynomial Pn(x) with integer coefficients (incl: Integer, Rational)

Transcendental 

(Include: Real and !Algebraic)

Hierarchy

The hierarachy of numeric types is setup that each derived type is a subclass of its parent type and can be repesented as such without loss. (A problem that appears with a non-symbolic language however is that irrationals become functionally equivalent to ration numbers, as precision is not infinite).

• Complex
  • Real
    • Rational
      • Integer
    • Irrational
      • Transcendental

"Algebraic" is an additional trait, such that a function is_algebraic returns true for all but transcendental numbers". There can be no "algrbraic" in the hierarchy as it is not a clean separation.

Transcendental's cannot be ignored as they include several commonly used constants: π e, √2

Additionally, the full known class of a number is available to compilers that wish to do intelligent compilation.

Notes

Natural numbers and whole numbers are not distinct enough from Integer to warrant a new type and are better addressed by constrained types:constraints.