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<head><title>index -- numeric index of a ring variable</title>
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<div><h1>index -- numeric index of a ring variable</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>index v</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>v</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, the integer index, starting at 0, of v, if it is a variable. If v is not a variable, then <a href="_null.html" title="the unique member of the empty class">null</a> is returned</span></li>
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<div class="single"><h2>Description</h2>
<div>Variables are indexed in the following way: the first variable has index 0, the second index 1, and so on, until n-1, where n is the number of generators of R, the ring of v. Then, if the coefficient ring is a polynomial ring, those variables are numbered starting at n, and so on.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d,t]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : index a
o2 = 0</pre>
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<tr><td><pre>i3 : index t
o3 = 4</pre>
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<table class="examples"><tr><td><pre>i4 : A = ZZ[a..d]; B = A[r,s,t]; C = B[x,y,z]
o6 = C
o6 : PolynomialRing</pre>
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<tr><td><pre>i7 : index x
o7 = 0</pre>
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<tr><td><pre>i8 : index z
o8 = 2</pre>
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<tr><td><pre>i9 : index r
o9 = 0</pre>
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Notice that r is an element of B, and so indices are taken from that ring. If we consider r as an element of C, we get a different answer. Variables of coefficient rings of coefficient rings have an index too.<table class="examples"><tr><td><pre>i10 : index(r*1_C)
o10 = 3</pre>
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<tr><td><pre>i11 : index(b*1_C)
o11 = 7</pre>
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The symbol <tt>index</tt> is also as a key used in <a href="___General__Ordered__Monoid.html" title="the class of all ordered free commutative monoids">GeneralOrderedMonoid</a>s to store a table that is used to map generator names to the position of the generator in the list of generators.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_indices.html" title="indices of a polynomial; also components for a direct sum">indices</a> -- indices of a polynomial; also components for a direct sum</span></li>
<li><span><a href="_support.html" title="list of variables occurring in a polynomial or matrix">support</a> -- list of variables occurring in a polynomial or matrix</span></li>
<li><span><a href="___Ring_sp_us_sp__Z__Z.html" title="get a ring variable by index">Ring _ ZZ</a> -- get a ring variable by index</span></li>
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<div class="waystouse"><h2>Ways to use <tt>index</tt> :</h2>
<ul><li>index(RingElement)</li>
</ul>
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