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<head><title>RevLex -- reverse lexicographic ordering</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="___Rev__Lex.html" title="reverse lexicographic ordering">RevLex</a></div>
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<div><h1>RevLex -- reverse lexicographic ordering</h1>
<div class="single"><h2>Description</h2>
<div>The reverse lexicographic order is defined by: x<sup>A</sup> > x<sup>B</sup> if the FIRST non-zero entry of the vector of integers <tt>A-B</tt> is NEGATIVE. This is a local order, not a global order. Therefore Gröbner bases over this ring only give generators over the local ring whose fractions are all elements not in the ideal generated by the variables.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d,MonomialOrder => RevLex, Global => false];</pre>
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<tr><td><pre>i2 : a^3 + b^2 + b*c + a*c^2 + b^2*c + a + b + c
2 2 2 3
o2 = c + b + b*c + b + b c + a + a*c + a
o2 : R</pre>
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Computations of Gröbner bases for local orders are done using Mora's algorithm.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___G__Rev__Lex.html" title="graded reverse lexicographical monomial order.">GRevLex</a> -- graded reverse lexicographical monomial order.</span></li>
<li><span><a href="___Monomial__Order.html" title="monomial ordering">Global</a> -- monomial ordering</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Rev__Lex.html" title="reverse lexicographic ordering">RevLex</a> is <span>a <a href="___Symbol.html">symbol</a></span>.</p>
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