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NumericalAlgebraicGeometry :: randomInitialPair

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has an equal chance of reaching any of the solutions of the target system T. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                2                                     
o2 = ({(.399261 + .0851698*ii)x1  + (- .196225 - .377151*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                               2                                           
     .0278263 - .00530501*ii)x2  + (.116092 + .212861*ii)x1*x3 + (.119474 -
     ------------------------------------------------------------------------
                                                 2             
     .125257*ii)x2*x3 + (.217214 + .0226477*ii)x3 , (- .06908 +
     ------------------------------------------------------------------------
                  3                              2                 
     .207313*ii)x1  + (- .493699 - .0534398*ii)x1 x2 + (- .201124 +
     ------------------------------------------------------------------------
                     2                              3              
     .663388*ii)x1*x2  + (- .137542 + .0902794*ii)x2  + (- .11072 +
     ------------------------------------------------------------------------
                 2                                                    
     .43509*ii)x1 x3 + (- .22048 - .0470439*ii)x1*x2*x3 + (- .246514 +
     ------------------------------------------------------------------------
                   2                                 2               
     .0754482*ii)x2 x3 + (.0316193 + .104616*ii)x1*x3  + (- .292954 -
     ------------------------------------------------------------------------
                     2                            3
     .380651*ii)x2*x3  + (.0348531 - .275817*ii)x3 }, {{-.332108-.248894*ii,
     ------------------------------------------------------------------------
     .084855+.730356*ii, .508642-.168579*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.125726-.763535*ii, .48061-.332877*ii, .24375-.0007767*ii}}

o3 : List

See also

Ways to use randomInitialPair :