Recent changes to Exact and approximate numbershttp://sourceforge.net/p/maxima/wiki/Exact%20and%20approximate%20numbers/2013-04-14T20:52:26ZExact and approximate numbers modified by Stavros Macrakis2013-04-14T20:52:26Z2013-04-14T20:52:26ZStavros Macrakishttp://sourceforge.net/u/macrakis/http://sourceforge.net498f4235f640807d3699a6266bc5a0e053930c37<div class="markdown_content"><p>Maxima supports both exact and approximate real numbers. Maxima also supports symbolic constants such as %pi and %i, and expressions such as sqrt(2) and log(-3), which denote real or complex numbers, but are not considered to be "numbers" by Maxima.</p>
<p>Exact numbers include:</p>
<ul>
<li>integers like 23 and -5</li>
<li>rational numbers like 3/4 and -5/12</li>
</ul>
<p>Approximate numbers are shown with decimal points, and include:</p>
<ul>
<li>floating point numbers like 23.0 and 0.75</li>
<li>big float numbers like 23.0b0, 0.75b0, and 1.234b6000</li>
</ul>
<p>Maxima guarantees that calculations on exact numbers will always give exact results. For example, 2/49<em>49 => 2, 27^(1/3) => 3, sin(0) => 0. Calculations on exact numbers may return expressions rather than numbers, for example, sqrt(2) => sqrt(2), asin(1) => %pi/2, sqrt(12) => 2</em>sqrt(3).</p>
<p>Calculations on approximate numbers give approximate number results: 1.0/3.0 => 0.33333333333333, 2.0/49.0*49.0-2.0 => -2.22e-16, sqrt(2.0) => 1.414214, asin(1.0) => 1.570796, sqrt(12.0) => 3.464101.</p>
<p>Calculations which mix exact and approximate numbers give approximate numbers: 2/49.0*49-2 =< -2.22e-16.</p>
<p>For more on calculating with approximate numbers, see <span>[Floating-point computation]</span> and <span>[Bigfloat computation]</span>.</p>
<p>For more on getting approximate numerical results from exact expressions, see <span>[Numerical evaluation]</span>.</p></div>