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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 = {(.162571 + .00589652*ii)x1  + (- .212737 - .144487*ii)x1*x2 + (.0437019
     ------------------------------------------------------------------------
                     2                                             
     - .0631825*ii)x2  + (.0871419 + .117817*ii)x1*x3 + (.0862938 -
     ------------------------------------------------------------------------
                                                 2                          3
     .633896*ii)x2*x3 + (.0103352 - .214297*ii)x3 , (.0258427 + .12496*ii)x1 
     ------------------------------------------------------------------------
                               2                                 2     
     + (.0728045 - .26432*ii)x1 x2 + (- .578088 + .52883*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                           3                           2                 
     .17848 + .058092*ii)x2  + (.260686 + .257848*ii)x1 x3 + (- .144578 -
     ------------------------------------------------------------------------
                                                    2                 
     .156827*ii)x1*x2*x3 + (.0117779 + .344498*ii)x2 x3 + (- .173287 -
     ------------------------------------------------------------------------
                      2                                 2             
     .0842985*ii)x1*x3  + (- .138648 + .0559269*ii)x2*x3  + (.435908 -
     ------------------------------------------------------------------------
                  3
     .300222*ii)x3 }

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

o3 = {{-.459634+.697568*ii, -.117911+.417387*ii, .331817-.0625895*ii}}

o3 : List

Ways to use randomSd :