## `Type::NonNegInt` -- a type and a property representing nonnegative integers

#### Introduction

`Type::NonNegInt` represents nonnegative integers. `Type::NonNegInt` is a property, too, which can be used in an `assume` call.

#### Call(s)

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

#### 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::Integer`, `Type::Property`

#### Details

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

  The call `is(ex,` Type::NonNegInt) derives, whether the expression `ex` is a nonnegative integer 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::NonNegInt`:

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

                          TRUE, FALSE, FALSE, TRUE, FALSE

#### Example 2

Assume an identifier is nonnegative rational:

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

                                       TRUE

Also nonnegative integers are integers:

    >> assume(x, Type::NonNegInt):
       is(x, Type::Integer)

                                       TRUE

However, integers can be nonnegative or not:

    >> assume(x, Type::Integer):
       is(x, Type::NonNegInt)

                                      UNKNOWN

    >> delete x:

#### Changes

- no changes

Do you have questions or comments?
Copyright © SciFace Software GmbH & Co. KG 2000