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Class Precedence List:

complex,number,t

Description:

Thetypecomplex includes all mathematical complex numbers other than those included in thetyperational.Complexes are expressed in Cartesian form with a real part and an imaginary part, each of which is areal. The real part and imaginary part are either bothrational or both of the samefloattype. The imaginary part can be afloat zero, but can never be arational zero, for such a number is always represented by Common Lisp as arational rather than acomplex.

Compound Type Specifier Kind:

Specializing.

Compound Type Specifier Syntax:

complex[typespec |*]

Compound Type Specifier Arguments:

typespec---atype specifier that denotes asubtype oftypereal.

Compound Type Specifier Description:

Every element of thistype is acomplex whose real part and imaginary part are each of type(upgraded-complex-part-typetypespec). Thistype encompasses thosecomplexes that can result by giving numbers oftypetypespec tocomplex.

(complextype-specifier) refers to allcomplexes that can result from givingnumbers oftypetype-specifier to thefunctioncomplex, plus all othercomplexes 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 acomplex with real part r and imaginary part i is#C(r i). For further details, seeSection 2.4 (Standard Macro Characters).

For everyfloat, n, there is acomplex which represents the same mathematical number and which can be obtained by(COERCE n 'COMPLEX).

• ARRAY-TYPE-ELEMENT-TYPE-SEMANTICS:UNIFY-UPGRADING