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<head><title>selectInSubring -- select columns in a subring</title>
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<div><h1>selectInSubring -- select columns in a subring</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>selectInSubring(i,m)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>m</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, with the same target and ring as <tt>m</tt>, consisting of those columns of <tt>m</tt> which lie in the subring where the first <tt>i</tt> blocks of the monomial order are zero</span></li>
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<div class="single"><h2>Description</h2>
<div>For example, consider the following block (or product) order.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,a..d,t,MonomialOrder=>{2,4,1}];</pre>
</td></tr>
<tr><td><pre>i2 : m = matrix{{x*a-d^2, a^3-1, x-a^100, a*b*d+t*c^3, t^3-t^2-t+1}}
o2 = | xa-d2 a3-1 x-a100 c3t+abd t3-t2-t+1 |
1 5
o2 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i3 : selectInSubring(1,m)
o3 = | a3-1 c3t+abd t3-t2-t+1 |
1 3
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : selectInSubring(2,m)
o4 = | t3-t2-t+1 |
1 1
o4 : Matrix R <--- R</pre>
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<p/>
The lexicographic order is considered as one block, as in the following example.<table class="examples"><tr><td><pre>i5 : S = QQ[a..d,MonomialOrder=>Lex];</pre>
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<tr><td><pre>i6 : m = matrix{{a^2-b, b^2-c, c^2-d, d^2-1}}
o6 = | a2-b b2-c c2-d d2-1 |
1 4
o6 : Matrix S <--- S</pre>
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<tr><td><pre>i7 : selectInSubring(1,m)
o7 = 0
1
o7 : Matrix S <--- 0</pre>
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<p/>
If you wish to be able to pick out the elements not involving a, or a and b, etc, then create a block monomial order.<table class="examples"><tr><td><pre>i8 : S = QQ[a..d,MonomialOrder=>{4:1}];</pre>
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<tr><td><pre>i9 : m = matrix{{a^2-b, b^2-c, c^2-d, d^2-1}}
o9 = | a2-b b2-c c2-d d2-1 |
1 4
o9 : Matrix S <--- S</pre>
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<tr><td><pre>i10 : selectInSubring(1,m)
o10 = | b2-c c2-d d2-1 |
1 3
o10 : Matrix S <--- S</pre>
</td></tr>
<tr><td><pre>i11 : selectInSubring(2,m)
o11 = | c2-d d2-1 |
1 2
o11 : Matrix S <--- S</pre>
</td></tr>
<tr><td><pre>i12 : selectInSubring(3,m)
o12 = | d2-1 |
1 1
o12 : Matrix S <--- S</pre>
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<div class="single"><h2>Caveat</h2>
<div>This routine doesn't do what one would expect for graded orders such as <tt>GLex</tt>. There, the first part of the monomial order is the degree, which is usually not zero.</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_monomial_sporderings.html" title="">monomial orderings</a></span></li>
<li><span><a href="_lead__Term.html" title="get the greatest term">leadTerm</a> -- get the greatest term</span></li>
<li><span><a href="../../Elimination/html/_eliminate.html" title="">eliminate</a></span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>selectInSubring</tt> :</h2>
<ul><li>selectInSubring(ZZ,Matrix)</li>
</ul>
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