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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials Ti such that deg(Ti) = di. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                                2                                            
o1 = {(- .213325 + .264032*ii)x1  + (- .201458 + .497949*ii)x1*x2 + (.0896498
     ------------------------------------------------------------------------
                     2                                               
     + .0533495*ii)x2  + (.00547124 - .396953*ii)x1*x3 + (- .298599 +
     ------------------------------------------------------------------------
                                                2              
     .163919*ii)x2*x3 + (.204031 + .176352*ii)x3 , (- .198521 +
     ------------------------------------------------------------------------
                  3                           2                
     .100812*ii)x1  + (.208834 + .154496*ii)x1 x2 + (.0593884 +
     ------------------------------------------------------------------------
                      2                            3                
     .0948223*ii)x1*x2  + (- .44533 - .268337*ii)x2  + (- .0868087 -
     ------------------------------------------------------------------------
                  2                                                     
     .167666*ii)x1 x3 + (.0646668 + .0814922*ii)x1*x2*x3 + (.000770541 -
     ------------------------------------------------------------------------
                  2                                   2             
     .293611*ii)x2 x3 + (- .158654 + .0296085*ii)x1*x3  + (.129867 -
     ------------------------------------------------------------------------
                     2                            3
     .062191*ii)x2*x3  + (- .12502 - .316026*ii)x3 }

o1 : List
i2 : (S,solsS) = goodInitialPair T;
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.060577-.687944*ii, .0979385+.198623*ii, .586001-.361419*ii}}

o3 : List

See also