125 lines
6 KiB
HTML
125 lines
6 KiB
HTML
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Copyright (C) 1996-1997, 2000-2005, 2009-2023 Free Software Foundation,
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Copyright (C) 2021 Maxime Devos
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Copyright (C) 2024 Tomas Volf
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<title>Complex Numbers (Guile Reference Manual)</title>
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Numbers.html" rel="up" title="Numbers">
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<link href="Exactness.html" rel="next" title="Exactness">
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<div class="subsubsection-level-extent" id="Complex-Numbers">
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<div class="nav-panel">
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<p>
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Next: <a href="Exactness.html" accesskey="n" rel="next">Exact and Inexact Numbers</a>, Previous: <a href="Reals-and-Rationals.html" accesskey="p" rel="prev">Real and Rational Numbers</a>, Up: <a href="Numbers.html" accesskey="u" rel="up">Numerical data types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<h4 class="subsubsection" id="Complex-Numbers-1"><span>6.6.2.4 Complex Numbers<a class="copiable-link" href="#Complex-Numbers-1"> ¶</a></span></h4>
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<a class="index-entry-id" id="index-Complex-numbers"></a>
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<a class="index-entry-id" id="index-complex_003f-2"></a>
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<p>Complex numbers are the set of numbers that describe all possible points
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in a two-dimensional space. The two coordinates of a particular point
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in this space are known as the <em class="dfn">real</em> and <em class="dfn">imaginary</em> parts of
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the complex number that describes that point.
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</p>
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<p>In Guile, complex numbers are written in rectangular form as the sum of
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their real and imaginary parts, using the symbol <code class="code">i</code> to indicate
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the imaginary part.
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</p>
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<div class="example lisp">
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<pre class="lisp-preformatted">3+4i
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⇒
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3.0+4.0i
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(* 3-8i 2.3+0.3i)
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⇒
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9.3-17.5i
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</pre></div>
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<a class="index-entry-id" id="index-polar-form"></a>
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<p>Polar form can also be used, with an ‘<samp class="samp">@</samp>’ between magnitude and
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angle,
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</p>
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<div class="example lisp">
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<pre class="lisp-preformatted">1@3.141592 ⇒ -1.0 (approx)
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-1@1.57079 ⇒ 0.0-1.0i (approx)
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</pre></div>
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<p>Guile represents a complex number as a pair of inexact reals, so the
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real and imaginary parts of a complex number have the same properties of
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inexactness and limited precision as single inexact real numbers.
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</p>
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<p>Note that each part of a complex number may contain any inexact real
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value, including the special values ‘<samp class="samp">+nan.0</samp>’, ‘<samp class="samp">+inf.0</samp>’ and
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‘<samp class="samp">-inf.0</samp>’, as well as either of the signed zeroes ‘<samp class="samp">0.0</samp>’ or
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‘<samp class="samp">-0.0</samp>’.
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</p>
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<dl class="first-deffn">
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<dt class="deffn" id="index-complex_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">complex?</strong> <var class="def-var-arguments">z</var><a class="copiable-link" href="#index-complex_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-scm_005fcomplex_005fp"><span class="category-def">C Function: </span><span><strong class="def-name">scm_complex_p</strong> <var class="def-var-arguments">(z)</var><a class="copiable-link" href="#index-scm_005fcomplex_005fp"> ¶</a></span></dt>
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<dd><p>Return <code class="code">#t</code> if <var class="var">z</var> is a complex number, <code class="code">#f</code>
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otherwise. Note that the sets of real, rational and integer
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values form subsets of the set of complex numbers, i.e. the
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predicate will also be fulfilled if <var class="var">z</var> is a real,
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rational or integer number.
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</p></dd></dl>
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<dl class="first-deftypefn">
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<dt class="deftypefn" id="index-scm_005fis_005fcomplex"><span class="category-def">C Function: </span><span><code class="def-type">int</code> <strong class="def-name">scm_is_complex</strong> <code class="def-code-arguments">(SCM val)</code><a class="copiable-link" href="#index-scm_005fis_005fcomplex"> ¶</a></span></dt>
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<dd><p>Equivalent to <code class="code">scm_is_true (scm_complex_p (val))</code>.
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</p></dd></dl>
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</div>
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<hr>
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<div class="nav-panel">
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<p>
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Next: <a href="Exactness.html">Exact and Inexact Numbers</a>, Previous: <a href="Reals-and-Rationals.html">Real and Rational Numbers</a>, Up: <a href="Numbers.html">Numerical data types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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