Numbers

Number → Object

Any numeric value. Integer and Double are both Numbers, though presumeably quotients and complex numbers would also be valid. 

Integer → Object

Integral numbers with no decimal segment.

Example:

1
Double → Object

Double-precision floating-point numbers.

Example:

1.0
Rational → Object

Exact ratios between integers.

Example:

22/7
a + b → Number
  | a is-a?: Number
  | b is-a?: Number

Adds a and b. If either are Rationals, it returns a Rational; otherwise, if either are Doubles, it returns a Double.

Example:

> 1 + 2
3
> 1.0 + 2.0
3.0
> 1/2 + 3/4
5/4
> 1/2 + 2
5/2
> 1.0 + -2
-1.0

a - b → Number
  | a is-a?: Number
  | b is-a?: Number

Subtracts b from a. If either are Rationals, it returns a Rational; otherwise, if either are Doubles, it returns a Double.

Example:

> 1 - 2
-1
> 1.0 - 2.0
-1.0
> 1/2 - 3/4
-1/4
> 1/2 - 2.5
-2/1
> 1.0 - -2
3.0

a * b → Number
  | a is-a?: Number
  | b is-a?: Number

Multiplies a by b. If either are Rationals, it returns a Rational; otherwise, if either are Doubles, it returns a Double.

Example:

> 1 * 2
2
> 1.0 * 2.0
2.0
> 1/2 * 3/4
3/8
> 1/2 * 2.5
5/4
> 1.0 * -2
-2.0

a / b → Number
  | a is-a?: Number
  | b is-a?: Number

Divides a by b. If either are Rationals, it returns a Rational; otherwise, if either are Doubles, it returns a Double. If both are Integers, it performs integer division.

Example:

> 1 / 2
0
> 1.0 / 2.0
0.5
> 1/2 / 3/4
2/3
> 1/2 / 2.5
1/5
> 1.0 / -2
-0.5

a ^ b → Number
  | a is-a?: Number
  | (b is-a?: Integer) || (b is-a?: Double)

Raises a to the power of b. If either are Doubles, it returns a Double. If a is a Rational, b must be an Integer.

Example:

> 1 ^ 2
1
> 1.0 ^ 2.0
1.0
> 1/2 ^ 4
1/16
> 1.0 ^ -2
1.0

a % b → Integer
  | a is-a?: Integer
  | b is-a?: Integer

Modulus operator.

Example:

> 3 % 2
1
> 6 % 2
0
> 7 % -2
-1

a quotient: b → Integer
  | a is-a?: Integer
  | b is-a?: Integer

Returns the quotient of dividing a by b.

Example:

> 22 quotient: 5
4

a remainder: b → Integer
  | a is-a?: Integer
  | b is-a?: Integer

Returns the remainder of dividing a by b.

Example:

> 22 remainder: 5
2

n sqrt → Double
  | (n is-a?: Integer) || (n is-a?: Double)

Returns the square root of n.

Example:

> 5 sqrt
2.23606797749979
> 5.8 sqrt
2.4083189157584592

d ceiling → Integer
  | d is-a?: Double

Converts d into an Integer by rounding up.

Example:

> 1.9 ceiling
2
> 1.1 ceiling
2
> 1.0 ceiling
1

d round → Integer
  | d is-a?: Double

Rounds d down or up to the nearest Integer.

Example:

> 1.9 round
2
> 1.5 round
2
> 1.4 round
1
> 1.0 round
1

d floor → Integer
  | d is-a?: Double

Converts d into an Integer by rounding down.

Example:

> 1.9 floor
1
> 1.1 floor
1
> 1.0 floor
1

n reciprocal → Number
  | n is-a?: Number

Returns the reciprocal of n, returning either a Double (if n is an Integer or Double) or a Rational (if n is a Rational).

Example:

> 2 reciprocal
0.5
> 0.5 reciprocal
2.0
> 3/4 reciprocal
4/3

r numerator → Integer
  | r is-a?: Rational

Returns r's numerator.

Example:

> 3/4 numerator
3

r denominator → Integer
  | r is-a?: Rational

Returns r's denominator.

Example:

> 3/4 denominator
4

r approximate → Double
  | r is-a?: Rational

Approximates r as an (inexact) Double.

Example:

> 3/4 approximate
0.75

n rationalize → Rational
  | (n is-a?: Integer) || (n is-a?: Double)

Convert an Integer or an inexact Double into the simplest rational number within 0.001 of n.

Example:

> 5 rationalize
5/1
> 0.5 rationalize
1/2
> 0.1234 rationalize
6/49

n rationalize: epsilon → Rational
  | (n is-a?: Integer) || (n is-a?: Double)

Convert an Integer or an inexact Double into the simplest rational number within epsilon of n.

Example:

> 0.1234 rationalize: 1.0
0/1
> 0.1234 rationalize: 0.1
1/5
> 0.1234 rationalize: 0.01
1/8
> 0.1234 rationalize: 0.001
6/49
> 0.1234 rationalize: 0.0001
10/81
> 0.1234 rationalize: 0.0
8891907104280307/72057594037927936

d as: Integer → Integer
  | d is-a?: Double

Converts d into an Integer by sending floor to it.

Example:

> 0.75 as: Integer
0
> 1.75 as: Integer
1

d as: Rational → Rational
  | d is-a?: Double

Converts d into a Rational by sending rationalize to it.

Example:

> 0.75 as: Rational
3/4

i as: Double → Double
  | i is-a?: Integer

Converts i into a Double.

Example:

> 4 as: Double
4.0

i as: Rational → Rational
  | i is-a?: Integer

Converts i into a Rational.

Example:

> 4 as: Rational
4/1

r as: Double → Double
  | r is-a?: Rational

Converts r into a Double by sending approximate to it.

Example:

> 4/3 as: Double
1.3333333333333333

r as: Integer → Integer
  | r is-a?: Rational

Converts r into an Integer by sending approximate and floor to it.

Example:

> 4/3 as: Integer
1

n even? → Boolean
  | n is-a?: Integer

Is n even?. 

n odd? → Boolean
  | n is-a?: Integer

Is n odd?. 

a divides?: b → Boolean
  | a is-a?: Integer
  | b is-a?: Integer

Does a divide b? 

a divisible-by?: b → Boolean
  | a is-a?: Integer
  | b is-a?: Integer

Alias for b divides?: a.