## `Type::NonNegRat` -- a type and a property representing nonnegative rational numbers

#### Introduction

`Type::NonNegRat` represents nonnegative rational numbers. `Type::NonNegRat` is a property, too, which can be used in an `assume` call.

#### Call(s)

`testtype(obj,` Type::NonNegRat)
`assume(x,` Type::NonNegRat)
`is(ex,` Type::NonNegRat)

#### Parameters

`obj` | - | any MuPAD object
`x` | - | an identifier or one of the expressions `Re(u)` or `Im(u)` with an identifier `u`
`ex` | - | an arithmetical expression

#### Returns

see `testtype`, `assume` and `is`

#### Related Functions

`testtype`, `is`, `assume`, `Type::Rational`, `Type::Property`

#### Details

- The call `testtype(obj,` Type::NonNegRat) checks, whether `obj` is a nonnegative rational number and returns `TRUE`, if it holds, otherwise `FALSE`.
- `testtype` only performs a syntactical test identifying MuPAD objects of type `DOM_INT` and `DOM_RAT` and checks, if `bool(obj >= 0)` holds.
- The call `assume(x,` Type::NonNegRat) marks the identifier `x` as a nonnegative rational number.

  The call `is(ex,` Type::NonNegRat) derives, whether the expression `ex` is a nonnegative rational number (or this property can be derived).

- This type represents a property that can be used in `assume` and `is`.

#### Example 1

The following numbers are of type `Type::NonNegRat`:

    >> testtype(2, Type::NonNegRat),
       testtype(3/4, Type::NonNegRat),
       testtype(55/111, Type::NonNegRat),
       testtype(0, Type::NonNegRat),
       testtype(111/111111, Type::NonNegRat)

                           TRUE, TRUE, TRUE, TRUE, TRUE

#### Example 2

Assume an identifier is nonnegative rational:

    >> assume(x, Type::NonNegRat):
       is(x, Type::NonNegRat)

                                       TRUE

Also nonnegative rational numbers are rational:

    >> assume(x, Type::NonNegRat):
       is(x, Type::Rational)

                                       TRUE

However, rational numbers can be nonnegative rational or not:

    >> assume(x, Type::Rational):
       is(x, Type::NonNegRat)

                                      UNKNOWN

    >> delete x:

#### Changes

- no changes

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