Type::NonNegative -- a type
and a property representing nonnegative numbers
IntroductionType::NonNegative represents nonnegative numbers.
Type::NonNegative is a property, too, which can be used in an
assume call.
Call(s)testtype(obj, Type::NonNegative)
assume(x, Type::NonNegative)
is(ex, Type::NonNegative)
Parametersobj |
- | 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
Related
Functionstesttype, is, assume, Type::Real, Type::Property
Detailstesttype(obj, Type::NonNegative)
checks, whether obj is a nonnegative real number and
returns TRUE, if it
holds, otherwise FALSE.testtype only
performs a syntactical test identifying MuPAD objects of type
DOM_INT, DOM_RAT and DOM_FLOAT and checks, if bool(obj >= 0) holds. This does
not include arithmetical expressions such as exp(1), which
are not identified as of type Type::NonNegative.assume(x,
Type::NonNegative) marks the identifier x as a nonnegative
real number.
The call is(ex,
Type::NonNegative) derives, whether the expression ex is a
nonnegative real number (or this property can be derived).
assume and is.Type::NonNegative the assumption can also
be assume(x >=
0).
Example
1The following numbers are of type
Type::NonNegative:
>> testtype(2, Type::NonNegative), testtype(3/4, Type::NonNegative), testtype(0.123, Type::NonNegative), testtype(0, Type::NonNegative), testtype(1.02, Type::NonNegative)
TRUE, TRUE, TRUE, TRUE, TRUE
The following expressions are exact representations of
nonnegative numbers, but syntactically they are not of
Type::NonNegative:
>> testtype(exp(1), Type::NonNegative), testtype(PI^2 + 5, Type::NonNegative), testtype(sin(2), Type::NonNegative)
FALSE, FALSE, FALSE
The function is, however, can find these expressions
to be nonnegative:
>> is(exp(1), Type::NonNegative), is(PI^2 + 5, Type::NonNegative), is(sin(2), Type::NonNegative)
TRUE, TRUE, TRUE
Example
2Assume an identifier is nonnegative:
>> assume(x, Type::NonNegative): is(x, Type::NonNegative)
TRUE
This is equal to:
>> assume(x >= 0): is(x >= 0)
TRUE
Also nonnegative numbers are real:
>> assume(x, Type::NonNegative): is(x, Type::Real)
TRUE
But real numbers can be nonnegative or not:
>> assume(x, Type::Real): is(x, Type::NonNegative)
UNKNOWN
>> delete x: