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<head><title>randomSd -- a random homogeneous system of polynomial equations</title>
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<div><h1>randomSd -- a random homogeneous system of polynomial equations</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>T = randomSd d</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>d</tt>, list of degrees</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>T</tt>, list of polynomials</span></li>
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<div class="single"><h2>Description</h2>
<div>Generates a system of homogeneous polynomials T_i such that deg T_i = d_i. The system is normalized, so that it is on a unit sphere in the Bombieri-Weyl norm.<table class="examples"><tr><td><pre>i1 : T = randomSd {2,3}
2
o1 = {(- .140881 + .0362927*ii)x1 + (- .345233 - .113454*ii)x1*x2 +
------------------------------------------------------------------------
2
(.0696385 - .099468*ii)x2 + (.165113 - .301216*ii)x1*x3 + (- .0444784 -
------------------------------------------------------------------------
2
.42838*ii)x2*x3 + (.126305 - .130924*ii)x3 , (- .202793 -
------------------------------------------------------------------------
3 2
.0486973*ii)x1 + (.475435 + .0535318*ii)x1 x2 + (.144154 +
------------------------------------------------------------------------
2 3
.227836*ii)x1*x2 + (.18094 + .149373*ii)x2 + (- .304144 -
------------------------------------------------------------------------
2
.529278*ii)x1 x3 + (- .315167 - .435886*ii)x1*x2*x3 + (.158091 +
------------------------------------------------------------------------
2 2
.380722*ii)x2 x3 + (.360205 - .44627*ii)x1*x3 + (- .538465 -
------------------------------------------------------------------------
2 3
.0932127*ii)x2*x3 + (- .0571094 + .269494*ii)x3 }
o1 : List</pre>
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<tr><td><pre>i2 : (S,solsS) = goodInitialPair T;</pre>
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<tr><td><pre>i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)
o3 = {{{-.224943-.319742*ii, -.396944+.122555*ii, .79769+.195632*ii}, #steps
------------------------------------------------------------------------
=> 11, status => REGULAR, last t => 1, cond#^{-1} => .382495}}
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>randomSd</tt> :</h2>
<ul><li>randomSd(List)</li>
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