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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 = {(- .0549189 + .0162432*ii)x1  + (.110106 + .564771*ii)x1*x2 + (.041577
     ------------------------------------------------------------------------
                    2                                             
     - .263583*ii)x2  + (.0284013 - .318822*ii)x1*x3 + (.0622701 +
     ------------------------------------------------------------------------
                                                   2             
     .331413*ii)x2*x3 + (- .0993977 - .104669*ii)x3 , (.0236553 -
     ------------------------------------------------------------------------
                   3                            2               
     .0958092*ii)x1  + (.0231084 + .176439*ii)x1 x2 + (.296059 -
     ------------------------------------------------------------------------
                     2                            3              
     .589337*ii)x1*x2  + (.139788 + .0162467*ii)x2  + (.0485073 +
     ------------------------------------------------------------------------
                  2                                                    
     .440503*ii)x1 x3 + (.00247363 + .173767*ii)x1*x2*x3 + (.00938169 -
     ------------------------------------------------------------------------
                  2                                2               
     .167993*ii)x2 x3 + (.216728 + .440398*ii)x1*x3  + (- .172445 -
     ------------------------------------------------------------------------
                      2                             3
     .0769754*ii)x2*x3  + (- .454723 - .258961*ii)x3 }

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

o3 = {{.164677+.180019*ii, .796938-.089465*ii, .513697-.182963*ii}}

o3 : List

See also