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<head><title>GroupLex -- defines a ring where some variables are inverted</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_rings.html" title="">rings</a> > <a href="_monomial_sporderings.html" title="">monomial orderings</a> > <a href="___Group__Lex.html" title="defines a ring where some variables are inverted">GroupLex</a></div>
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<div><h1>GroupLex -- defines a ring where some variables are inverted</h1>
<div class="single"><h2>Description</h2>
<div><tt>MonomialOrder => GroupLex => n</tt> inverts the first <tt>n</tt> variables in the polynomial ring. In the following example, <tt>a^-1</tt> is in the ring, but <tt>c^-1</tt> is not.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d, MonomialOrder=> GroupLex=>2];</pre>
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<tr><td><pre>i2 : a^-1
-1
o2 = a
o2 : R</pre>
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<tr><td><pre>i3 : try c^(-1) else "failed"
o3 = failed</pre>
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<div class="single"><h2>Caveat</h2>
<div>The element <tt>a/b</tt> is in the fraction ring, while <tt>a*b^(-1)</tt> belongs to <tt>R</tt>.<p/>
Currently, on cannot compute Gröbner bases in this ring.</div>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Group__Lex.html" title="defines a ring where some variables are inverted">GroupLex</a> is <span>a <a href="___Symbol.html">symbol</a></span>.</p>
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