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Source for wiki ComplexRepresentations version 12

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cowan

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127.10.177.1

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ComplexRepresentations

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== Exact, inexact, and mixed complex numbers ==

Exact, inexact, and mixed complex number representations, where inexact and mixed numbers that are `=` are nevertheless distinct in the sense of `eqv?`: Gambit, Kawa, Chibi.  (Also CLISP, Pure.)

Exact, inexact, and mixed complex number representations, where inexact and mixed numbers that are `=` are the same in the sense of `eqv?`: MIT, STklos.

Exact and inexact complex number representations only (mixed complex numbers become inexact): Racket, Chicken with the numbers egg, Scheme48/scsh, Kawa, Chez, Vicare, Larceny, Ypsilon, !IronScheme, Spark, Wraith.  (Also ABCL, Allegro CL, Clozure CL, CMUCL, ECL, GNU CL, !LispWorks, SBCL, Scieneer CL.)

Inexact complex number representations only: Gauche, Guile, SISC, SCM, KSi, S7, UMB, Stalin.  (Also Fortran, C/C++, Python, etc.)

Exact complex number representations only: Owl Lisp (which has no inexact numbers).

No complex numbers: plain Chicken, Bigloo, Ikarus, NexJ, !SigScheme, Shoe, !TinyScheme, Scheme 9, Dream, RScheme, BDC, XLisp, Rep, Schemik, Elk, VX, Oaklisp, Llava, SXM, Sizzle, !FemtoLisp, Dfsch, Inlab.

Mosh has a bug whereby numbers that are `=` are always `eqv?` even if they differ in exactness; it supports exact, inexact, and mixed complex number representations, but doesn't differentiate exact from inexact properly.

== The imaginary part of an inexact real number ==

The value of `(imag-part 2.0)` is exact 0:  Racket, MIT, Gambit, Guile, Kawa, Chez, Vicare, Larceny, Ypsilon, Mosh, !IronScheme, STklos, RScheme (but see below), Sizzle, Spark.

The value of `(imag-part 2.0)` is inexact 0.0:  Gauche, Chicken with the numbers egg, Scheme48/scsh, SISC, Chibi, SCM, KSi, S7, UMB, SXM.

No `imag-part` procedure:  Bigloo, NexJ, Shoe, !TinyScheme, Scheme 9, BDC, XLisp, Rep, Schemik, Elk, VX, Llava, !FemtoLisp, Dfsch, Inlab.

No inexact numbers:  !SigScheme, Dream, Oaklisp, Owl Lisp.

Integrating both sets of results, this means that Racket, Guile, Chez, Vicare, Larceny, Ypsilon, !IronScheme, Spark behave ''as if'' they supported mixed-exactness complex numbers in the case where the real part is inexact and the imaginary part is exact 0, even though they do not support mixed-exactness complex numbers otherwise.

== Fake complex number support ==

Schemes that don't support non-real numbers can still fake support for `real-part` and `imag-part` by having the former return its argument and the latter return zero.  As usual, some do and some don't:

Fake support: plain Chicken, RScheme

No support: Shoe, !TinyScheme, BDC, XLisp, Sizzle, Bigloo, Scheme 9, Elk, Rep, Owl Lisp

== See also ==

See also NumericTower.

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2013-11-04 03:23:30