next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 = {(.319356 - .175844*ii)x1  + (.196473 - .258772*ii)x1*x2 + (- .0632688 -
     ------------------------------------------------------------------------
                  2                                               
     .185976*ii)x2  + (- .394962 + .124428*ii)x1*x3 + (- .222702 -
     ------------------------------------------------------------------------
                                                  2            
     .277612*ii)x2*x3 + (- .277174 + .292892*ii)x3 , (.118477 +
     ------------------------------------------------------------------------
                   3                             2               
     .0359525*ii)x1  + (- .032043 + .223963*ii)x1 x2 + (.666621 +
     ------------------------------------------------------------------------
                    2                               3               
     .35618*ii)x1*x2  + (- .00178029 - .111001*ii)x2  + (- .307143 -
     ------------------------------------------------------------------------
                 2                                                  
     .44468*ii)x1 x3 + (- .097231 - .260555*ii)x1*x2*x3 + (.300104 -
     ------------------------------------------------------------------------
                   2                                  2             
     .0854023*ii)x2 x3 + (- .280082 + .216603*ii)x1*x3  + (.200431 -
     ------------------------------------------------------------------------
                     2                            3
     .197943*ii)x2*x3  + (.0328447 - .129943*ii)x3 }

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

o3 = {{-.350093+.096252*ii, -.123088+.517584*ii, .753342+.132677*ii}}

o3 : List

See also