Type and property representing imaginary numbers
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testtype(obj
,Type::Imaginary
) assume(x
,Type::Imaginary
) is(ex
,Type::Imaginary
)
Type::Imaginary
represents complex numbers
with vanishing real part. This type can also be used as a property
to mark identifiers as imaginary numbers.
The call testtype(obj, Type::Imaginary)
checks,
whether obj
is an imaginary number (or zero) and
returns TRUE
,
if it holds, otherwise FALSE
.
testtype
only
performs a syntactical test identifying MuPAD^{®} objects of type DOM_COMPLEX
and
checks, whether iszero(Re(obj))
holds, or whether iszero(obj)
is TRUE
. This
does not include arithmetical expressions such as I*exp(1)
,
which are not identified as of type Type::Imaginary
.
The call assume(x, Type::Imaginary)
marks
the identifier x
as an imaginary number.
The call is(ex, Type::Imaginary)
derives,
whether the expression ex
is an imaginary number
(or this property can be derived).
This type represents a property that can be used in assume
and is
.
The call assume(Re(x) = 0)
has the same meaning
as assume(x, Type::Imaginary)
.
The following numbers are of type Type::Imaginary
:
testtype(5*I, Type::Imaginary), testtype(3/2*I, Type::Imaginary), testtype(1.23*I, Type::Imaginary)
The following expressions are exact representations of imaginary
numbers. However, syntactically they are not of type Type::Imaginary
,
because their domain type is not DOM_COMPLEX
:
testtype(exp(3)*I, Type::Imaginary), testtype(PI*I, Type::Imaginary), testtype(sin(2*I), Type::Imaginary)
In contrast to testtype
,
the function is
performs
a semantical test:
is(exp(3)*I, Type::Imaginary), is(PI*I, Type::Imaginary), is(sin(2*I), Type::Imaginary)
Identifiers may be assumed to represent an imaginary number:
assume(x, Type::Imaginary): is(x, Type::Imaginary), Re(x), Im(x)
The imaginary numbers are a subset of the complex numbers:
is(x, Type::Complex)
unassume(x):

Any MuPAD object 

An identifier 
 

Any MuPAD object 