Abstraction of numeric types with the usual binary operations:

- addition,
`x + y`

, - subtraction,
`x - y`

, - multiplication,
`x * y`

, and - division,
`x / y`

, along with - additive inverse
`-x`

.

A concrete class which implements this interface should be
a mathematical *ring*. That is:

- both addition,
`+`

, and multiplication,`*`

, should be associative and commutative, - there should be additive and multiplicative identities,
denoted
`0`

and`1`

respectively, satisfying`x+0 == x`

and`x*1 == x`

, - every instance
`x`

should have an additive inverse`-x`

, satisfying`x + -x == 0`

, and - multiplication should distribute over addition,
satisfying
`x*(y+z) == x*y + x*z`

.

It is preferred, but not required, that the class be a
mathematical *field*. That is, in addition to the above:

- every instance
`x`

such that`x!=0`

should have a multiplicative inverse`1/x`

, satisfying`x * 1/x == 1`

.

For numeric types which are not fields, for example,
`Integer`

, there is still a division operation, which is
understood to produce a remainder.
The division operation should satisfy:

`x*y / y == x`

for any instance `y`

other than `0`

.

For numeric types which *are* fields, division never
produces a remainder, and division should additionally
satisfy:

`x/y * y == x`

for any instance `y`

other than `0`

.

Some numeric types, for example complex numbers, do not
have a total order. Numeric types with a
total order also satisfy `Number`

.

By: Gavin

See also

`Number`

*no type hierarchy*

Inherited Attributes |

Attributes inherited from: `Object` |

Attributes inherited from: `Invertible<Other>` |

Methods | |

`divided` | `shared formal Other divided(Other other)` The quotient obtained by dividing this number by the given number. For integral numeric types, this operation results in a remainder. When the given number is See also `Integral.remainder()` , `infinity` |

`times` | `shared formal Other times(Other other)` The product of this number and the given number. |

Inherited Methods |

Methods inherited from: `Object` |

Methods inherited from: `Invertible<Other>` |

Methods inherited from: `Summable<Other>` |