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.
Specializing.
(complex{[typespec | *]})
| typespec | a type specifier that denotes a subtype of type real. |
[Editorial Note by KMP: If you ask me, this definition is a complete mess. Looking at issue ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS:UNIFY-UPGRADING does not help me figure it out, either. Anyone got any suggestions?]
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.
Rule of Canonical Representation for Complex Rationals, Constructing Numbers from Tokens, Printing Complexes
The input syntax for a complex with real part r and
imaginary part i is #C(r i).
For further details, see 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).