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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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