ceylon.language.Exponentiable.ceylon Maven / Gradle / Ivy

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"Abstraction of [[numeric types|Numeric]] that may be raised 
 to a power using the _exponentiation_ operator `x ^ n` 
 which accepts an instance of `Exponentiable` as its first
 operand, and an exponent as its second operand.
 
     function exp(Float x) => e^x;
 
 The exponentiation operation should obey the usual index
 laws, including:
 
 - `x^0 == 1`
 - `x^1 == x`
 - `x^(-1) == 1/x`
 - `x^(m+n) == x^m * x^n`
 - `x^(m-n) == x^m / x^n`
 - `x^(m*n) == (x^m)^n`
 - `(x*y)^n == x^n * y^n`
 
 where `0` is the additive identity, and `1` is the 
 multiplicative identity.
 
 Note that in general, the type of the exponent may be 
 different to the numeric type which is exponentiated. For
 example, a `Rational` number class might be a subtype of
 `Exponentiable`, thus accepting only
 whole-number exponents."
see (`class Integer`, `class Float`)
tagged("Numbers")
shared interface Exponentiable of This
        satisfies Numeric
        given This satisfies Exponentiable 
        given Other satisfies Numeric {

    "The result of raising this number to the given power."
    shared formal This power(Other other);
    
}