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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_numeric_sptypes.html" title="">numeric types</a></div>
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<div><h1>numeric types</h1>
<div><h3>Integers and rational numbers</h3>
In Macaulay2, integers and rational numbers have any number of digits (up to memory limits at least).<table class="examples"><tr><td><pre>i1 : 21672378126371263123123
o1 = 21672378126371263123123</pre>
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<tr><td><pre>i2 : 3748568762746238746278/5876584978947
1249522920915412915426
o2 = ----------------------
1958861659649
o2 : QQ</pre>
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Integers are elements of the ring <a href="___Z__Z.html" title="the class of all integers">ZZ</a> of integers, and rational numbers are elements of the ring <a href="___Q__Q.html" title="the class of all rational numbers">QQ</a> of rational numbers.<p/>
One point to notice is that there are two kinds of division, <a href="__sl.html" title="a binary operator, usually used for division">/</a> and <a href="__sl_sl.html" title="a binary operator, usually used for quotient">//</a>. The first returns a rational number (element of <a href="___Q__Q.html" title="the class of all rational numbers">QQ</a>), while the second does division in <a href="___Z__Z.html" title="the class of all integers">ZZ</a>.<table class="examples"><tr><td><pre>i3 : 6/3
o3 = 2
o3 : QQ</pre>
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<tr><td><pre>i4 : 7//3
o4 = 2</pre>
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<h3>Real and complex numbers</h3>
Real and complex numbers are approximate numbers, implemented using the <a href="___M__P__F__R.html" title="">MPFR</a> library.<table class="examples"><tr><td><pre>i5 : 1.372489274987
o5 = 1.372489274987
o5 : RR (of precision 53)</pre>
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<tr><td><pre>i6 : 1.3454353 * 10^20
o6 = 1.3454353e20
o6 : RR (of precision 53)</pre>
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<tr><td><pre>i7 : sqrt 4.5
o7 = 2.12132034355964
o7 : RR (of precision 53)</pre>
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<tr><td><pre>i8 : toRR_200 4.5
o8 = 4.5
o8 : RR (of precision 200)</pre>
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<tr><td><pre>i9 : sqrt oo
o9 = 2.12132034355964257320253308631454711785450781306542210976502
o9 : RR (of precision 200)</pre>
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<table class="examples"><tr><td><pre>i10 : 1/(1+ii)
o10 = .5-.5*ii
o10 : CC (of precision 53)</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Number.html" title="the class of all numbers">Number</a> -- the class of all numbers</span></li>
<li><span><a href="___Z__Z.html" title="the class of all integers">ZZ</a> -- the class of all integers</span></li>
<li><span><a href="___Q__Q.html" title="the class of all rational numbers">QQ</a> -- the class of all rational numbers</span></li>
<li><span><a href="___R__R.html" title="the class of all real numbers">RR</a> -- the class of all real numbers</span></li>
<li><span><a href="___C__C.html" title="the class of all complex numbers">CC</a> -- the class of all complex numbers</span></li>
<li><span><a href="_to__R__R.html" title="convert to high-precision real number">toRR</a> -- convert to high-precision real number</span></li>
<li><span><a href="_to__C__C.html" title="convert to high-precision complex number">toCC</a> -- convert to high-precision complex number</span></li>
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