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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 = {(- .0147761 + .16385*ii)x1  + (.409943 - .254522*ii)x1*x2 + (.0157967 -
     ------------------------------------------------------------------------
                  2                                          
     .313827*ii)x2  + (.04212 + .330469*ii)x1*x3 + (.331149 -
     ------------------------------------------------------------------------
                                                 2                          3
     .0576783*ii)x2*x3 + (.146989 - .128091*ii)x3 , (.158999 - .162163*ii)x1 
     ------------------------------------------------------------------------
                                 2                                  2     
     + (- .163957 + .644861*ii)x1 x2 + (- .395752 + .260611*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                            3                           2                
     .111135 + .052147*ii)x2  + (.505474 - .108616*ii)x1 x3 + (- .51718 +
     ------------------------------------------------------------------------
                                                   2               
     .702126*ii)x1*x2*x3 + (.202256 - .118793*ii)x2 x3 + (.245132 -
     ------------------------------------------------------------------------
                      2                                2               
     .0466419*ii)x1*x3  + (- .133428 + .187586*ii)x2*x3  + (- .213732 -
     ------------------------------------------------------------------------
                   3
     .0207295*ii)x3 }

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

o3 = {{.267847+.198181*ii, -.151478-.0041170*ii, .924533+.10611*ii}}

o3 : List

See also