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<head><title>sortColumns -- permutation giving sort order</title>
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<div><h1>sortColumns -- permutation giving sort order</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>sortColumns m</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>m</tt>, between free modules</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, of integers, representing the order which places the columns in order</span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_sort__Columns_lp..._cm_sp__Degree__Order_sp_eq_gt_sp..._rp.html">DegreeOrder => ...</a>, -- specify Ascending, Descending, or null</span></li>
<li><span><a href="_sort__Columns_lp..._cm_sp__Monomial__Order_sp_eq_gt_sp..._rp.html">MonomialOrder => ...</a>, -- specify Ascending or Descending monomial order</span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
See <a href="_sort_lp__Matrix_rp.html" title="sort the columns of a matrix">sort(Matrix)</a> for the ordering used. The meanings of the optional parameters is also the same.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[a..d,MonomialOrder=>Lex];</pre>
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<tr><td><pre>i2 : m = matrix{{a*d, b^2, b^100, b^50*d^50, c^2*d}}
o2 = | ad b2 b100 b50d50 c2d |
1 5
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : p = sortColumns m
o3 = {4, 1, 3, 2, 0}
o3 : List</pre>
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<tr><td><pre>i4 : m_p
o4 = | c2d b2 b50d50 b100 ad |
1 5
o4 : Matrix R <--- R</pre>
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<table class="examples"><tr><td><pre>i5 : p = sortColumns(m, DegreeOrder=>null, MonomialOrder=>Descending)
o5 = {0, 2, 3, 1, 4}
o5 : List</pre>
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<tr><td><pre>i6 : m_p
o6 = | ad b100 b50d50 b2 c2d |
1 5
o6 : Matrix R <--- R</pre>
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<table class="examples"><tr><td><pre>i7 : R = ZZ/101[a..c];</pre>
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<tr><td><pre>i8 : f = matrix{{1,a,a^2,b^2,b,c,c^2,a*b,b*c,a*c}}
o8 = | 1 a a2 b2 b c c2 ab bc ac |
1 10
o8 : Matrix R <--- R</pre>
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<tr><td><pre>i9 : s = sortColumns f
o9 = {0, 5, 4, 1, 6, 8, 9, 3, 7, 2}
o9 : List</pre>
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<tr><td><pre>i10 : f_s
o10 = | 1 c b a c2 bc ac b2 ab a2 |
1 10
o10 : Matrix R <--- R</pre>
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<tr><td><pre>i11 : s = sortColumns(f,DegreeOrder => Descending)
o11 = {6, 8, 9, 3, 7, 2, 5, 4, 1, 0}
o11 : List</pre>
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<tr><td><pre>i12 : f_s
o12 = | c2 bc ac b2 ab a2 c b a 1 |
1 10
o12 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_sort.html" title="sort a list or columns of a matrix">sort</a> -- sort a list or columns of a matrix</span></li>
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<div class="waystouse"><h2>Ways to use <tt>sortColumns</tt> :</h2>
<ul><li>sortColumns(Matrix)</li>
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