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NumericalAlgebraicGeometry :: randomSd

randomSd -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials T_i such that deg T_i = d_i. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.
i1 : T = randomSd {2,3}

                                 2                                        
o1 = {(- .252646 - .0354286*ii)x1  + (- .337222 - .000711678*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                           2                                            
     .498137 + .13888*ii)x2  + (.155644 - .283306*ii)x1*x3 + (.0438231 +
     ------------------------------------------------------------------------
                                                  2             
     .117284*ii)x2*x3 + (- .15286 + .0929289*ii)x3 , (.0524853 +
     ------------------------------------------------------------------------
                  3                            2               
     .449567*ii)x1  + (.0941783 - .246557*ii)x1 x2 + (.299145 -
     ------------------------------------------------------------------------
                      2                               3             
     .0132823*ii)x1*x2  + (- .00735157 - .151017*ii)x2  + (.270036 -
     ------------------------------------------------------------------------
                  2                                                 
     .161457*ii)x1 x3 + (.317062 + .0525052*ii)x1*x2*x3 + (.261765 -
     ------------------------------------------------------------------------
                  2                                2             
     .200039*ii)x2 x3 + (.330168 - .188137*ii)x1*x3  + (.166235 +
     ------------------------------------------------------------------------
                     2                               3
     .156931*ii)x2*x3  + (- .00596904 - .292795*ii)x3 }

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

o3 = {{.194365+.206763*ii, .273339+.263103*ii, .829306-.296286*ii}}

o3 : List

Ways to use randomSd :