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<head><title>randomInitialPair -- a random initial pair</title>
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<div><h1>randomInitialPair -- a random initial pair</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>(S,sol) =randomInitialPair T</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>T</tt>, list of polynomials</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>S</tt>, list of polynomials</span></li>
<li><span><tt>sol</tt>, a list containing (one) solution of S</span></li>
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<div class="single"><h2>Description</h2>
<div>Generates a start system S that has and equal chance of reaching any of the solutions of the target system T. <table class="examples"><tr><td><pre>i1 : T = randomSd {2,3};</pre>
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<tr><td><pre>i2 : (S,solsS) = randomInitialPair T
2
o2 = ({(- .0681066 - .0966079*ii)x1 + (.134052 - .494713*ii)x1*x2 + (-
------------------------------------------------------------------------
2
.0750381 - .00830672*ii)x2 + (.192941 + .0888703*ii)x1*x3 + (.26097 +
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2
.464787*ii)x2*x3 + (- .172377 - .0369359*ii)x3 , (- .07119 -
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3 2
.0625455*ii)x1 + (- .644731 - .0709334*ii)x1 x2 + (- .23262 +
------------------------------------------------------------------------
2 3
.0503516*ii)x1*x2 + (- .110523 - .227364*ii)x2 + (- .330197 -
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2
.573774*ii)x1 x3 + (- .626102 + .262181*ii)x1*x2*x3 + (.460949 -
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2 2
.440825*ii)x2 x3 + (.226273 - .143467*ii)x1*x3 + (.219083 -
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2 3
.0087443*ii)x2*x3 + (- .0244291 - .0165681*ii)x3 },
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{{.207643-.339001*ii, .230882-.24103*ii, .850686-.083029*ii}})
o2 : Sequence</pre>
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<tr><td><pre>i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)
o3 = {{{.714784-.165751*ii, .56242-.198353*ii, .289661-.14848*ii}, #steps =>
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12, status => REGULAR, last t => 1, cond#^{-1} => .528924}}
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>randomInitialPair</tt> :</h2>
<ul><li>randomInitialPair(List)</li>
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