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ANSI Common Lisp  12 Numbers 12.2 Dictionary of Numbers
| 12.2.2 complex |
System Class |
- Class Precedence List:
-
complex,
number,
t
- Description:
-
The type complex includes all mathematical complex numbers
other than those included in the type rational.
Complexes are
expressed
in Cartesian form with a
real part and an imaginary part, each of which is a real.
The real part and imaginary part are either both
rational or both of the same float type.
The imaginary part can be a float zero, but can never
be a rational zero, for such a number is always represented
by Common Lisp as a rational rather than a complex.
- Compound Type Specifier Kind:
-
Specializing.
- Compound Type Specifier Syntax:
-
(complex [typespec | *])
- Compound Type Specifier Arguments:
-
typespec - a type specifier that denotes a subtype of type real.
- Compound Type Specifier Description:
-
Every element of this type is a complex whose
real part and imaginary part are each of type
(upgraded-complex-part-type typespec).
This type encompasses those complexes
that can result by giving numbers of type typespec
to complex.
(complex type-specifier)
refers to all complexes that can result from giving
numbers of type type-specifier to the function complex,
plus all other complexes of the same specialized representation.
- See Also:
-
Section 12.1.5.3 Rule of Canonical Representation for Complex Rationals,
Section 2.3.2 Constructing Numbers from Tokens,
Section 22.1.3.1.4 Printing Complexes
- Notes:
-
The input syntax for a complex with real part r and
imaginary part i is #C(r i).
For further details, see Section 2.4 Standard Macro Characters.
For every float, n, there is a complex
which represents the same mathematical number
and which can be obtained by (COERCE n 'COMPLEX).
- Allegro CL Implementation Details:
-
None.
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