## `Type::NegRat` -- a type and a property representing negative rational numbers

#### Introduction

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

#### Call(s)

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

#### 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::Property`

#### Details

- The call `testtype(obj,` Type::NegRat) checks, whether `obj` is a negative 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::NegRat) marks the identifier `x` as a negative rational number.

  The call `is(ex,` Type::NegRat) derives, whether the expression `ex` is a negative 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::NegRat`:

    >> testtype(-2, Type::NegRat),
       testtype(-3/4, Type::NegRat),
       testtype(-55/111, Type::NegRat),
       testtype(-1, Type::NegRat),
       testtype(-111/111111, Type::NegRat)

                           TRUE, TRUE, TRUE, TRUE, TRUE

#### Example 2

Assume an identifier is negative rational:

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

                                       TRUE

Also negative rational numbers are rational:

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

                                       TRUE

However, rational numbers can be negative rational or not:

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

                                      UNKNOWN

    >> delete x:

#### Changes

- no changes

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