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<head><title>GRevLex -- graded reverse lexicographical monomial order.</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="___G__Rev__Lex.html" title="graded reverse lexicographical monomial order.">GRevLex</a></div>
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<div><h1>GRevLex -- graded reverse lexicographical monomial order.</h1>
<div class="single"><h2>Description</h2>
<div> The graded reverse lexicographic order is defined by: <i>x<sup>A</sup> > x<sup>B</sup></i> if either <i>degree(x<sup>A</sup>) > degree(x<sup>B</sup>)</i> or <i>degree(x<sup>A</sup>) = degree(x<sup>B</sup>)</i> and the LAST non-zero entry of the vector of integers <i>A-B</i> is NEGATIVE. <p/>
This is the default order in Macaulay2, in large part because it is often the most efficient order for use with Gröbner bases. By giving GRevLex a list of integers, one may change the definition of the order: <i>degree(x<sup>A</sup>)</i> is the dot product of <i>A</i> with the argument of GRevLex.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : a^3 + b^2 + b*c
3 2
o2 = a + b + b*c
o2 : R</pre>
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<tr><td><pre>i3 : S = QQ[a..d, MonomialOrder => GRevLex => {1,2,3,4}];</pre>
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<tr><td><pre>i4 : a^3 + b^2 + b*c
2 3
o4 = b*c + b + a
o4 : S</pre>
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The largest possible exponent of variables in the <tt>GRevLex</tt> order is 2^31-1. For efficiency reasons, it is sometimes useful to limit the size of monomials (this often makes computations more efficient).Use <tt>MonomialSize => 16</tt>, which allows maximal exponent 2^15-1, or <tt>MonomialSize => 8</tt>, which allows maximal exponent 2^7-1.<table class="examples"><tr><td><pre>i5 : B1 = QQ[a..d,MonomialSize=>16,MonomialOrder=>GRevLex];</pre>
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<tr><td><pre>i6 : B = QQ[a..d,MonomialSize=>16];</pre>
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<tr><td><pre>i7 : a^(2^15-1)
32767
o7 = a
o7 : B</pre>
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<tr><td><pre>i8 : C = QQ[a..d,MonomialSize=>8,MonomialOrder=>GRevLex];</pre>
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<tr><td><pre>i9 : try a^(2^15-1) else "failed"
o9 = failed</pre>
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<tr><td><pre>i10 : a^(2^7-1)
127
o10 = a
o10 : C</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_packing_spmonomials_spfor_spefficiency.html" title="">packing monomials for efficiency</a></span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___G__Rev__Lex.html" title="graded reverse lexicographical monomial order.">GRevLex</a> is <span>a <a href="___Symbol.html">symbol</a></span>.</p>
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