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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="___Eliminate.html" title="elimination order">Eliminate</a></div>
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<div><h1>Eliminate -- elimination order</h1>
<div class="single"><h2>Description</h2>
<div>The option <tt>Eliminate => n</tt> is a shortcut for <tt>Weights => {n:1}</tt> The remaining variables are given weight 0.The monomial order is the elimination order eliminating the first n variables, refined by the graded reverse lexicographic order.<table class="examples"><tr><td><pre>i1 : R = QQ[a..i, MonomialOrder => Eliminate 3];</pre>
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This order enables intersections with the subring consisting of all but the first 3 variables. For this, use the command <a href="_select__In__Subring.html" title="select columns in a subring">selectInSubring</a>.<table class="examples"><tr><td><pre>i2 : I = ideal(a^2, b-f, d^4, i - b);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : selectInSubring(1, gens gb I)
o3 = | f-i d4 |
1 2
o3 : Matrix R <--- R</pre>
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Eliminate may be combined with block orders as well.<table class="examples"><tr><td><pre>i4 : R = QQ[a..i, MonomialOrder => {Eliminate 3,4,2}];</pre>
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<tr><td><pre>i5 : d^3 - a*e^4 + b^2*i + a*c*d*f +a*c^2*g + a*c*g
2 2 4 3
o5 = a*c g + a*c*d*f + b i + a*c*g - a*e + d
o5 : R</pre>
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In the last example, the order is block order: the first four variables are in the first block, the subsequent two variables are in the second block, the remaining variables are in the third block, and the weights of the variables are 1,1,1,0,..., 0. We illustrate the usage of <a href="_select__In__Subring.html" title="select columns in a subring">selectInSubring</a>.<table class="examples"><tr><td><pre>i6 : I = ideal(a..i)
o6 = ideal (a, b, c, d, e, f, g, h, i)
o6 : Ideal of R</pre>
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<tr><td><pre>i7 : selectInSubring(1, gens gb I);
1 6
o7 : Matrix R <--- R</pre>
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<tr><td><pre>i8 : selectInSubring(2, gens gb I);
1 5
o8 : Matrix R <--- R</pre>
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<tr><td><pre>i9 : selectInSubring(3, gens gb I);
1 3
o9 : Matrix R <--- R</pre>
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<div class="single"><h2>Caveat</h2>
<div>If the number of degree vectors is greater than one, this is currently only graded using the first degree vector. This will eventually change.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Weights.html" title="assigning weights to the variables">Weights</a> -- assigning weights to the variables</span></li>
<li><span><a href="_definition_spof_spproduct_sp_lpblock_rp_sporders.html" title="">definition of product (block) orders</a></span></li>
<li><span><a href="_select__In__Subring.html" title="select columns in a subring">selectInSubring</a> -- select columns in a subring</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Eliminate.html" title="elimination order">Eliminate</a> is <span>a <a href="___Self__Initializing__Type.html">self initializing type</a></span>, with ancestor classes <a href="___Basic__List.html" title="the class of all basic lists">BasicList</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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