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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 = {(.412881 - .0156589*ii)x1  + (- .160654 + .00955165*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                           2                                            
     .110067 - .10844*ii)x2  + (.112736 + .278741*ii)x1*x3 + (.0263202 -
     ------------------------------------------------------------------------
                                                 2              
     .0829468*ii)x2*x3 + (.198508 + .179197*ii)x3 , (- .280968 -
     ------------------------------------------------------------------------
                  3                           2                 
     .294484*ii)x1  + (.231677 + .374037*ii)x1 x2 + (- .381117 -
     ------------------------------------------------------------------------
                     2                               3              
     .321722*ii)x1*x2  + (- .0448251 + .0575822*ii)x2  + (.0115994 -
     ------------------------------------------------------------------------
                  2                                                   
     .146515*ii)x1 x3 + (- .460878 - .197715*ii)x1*x2*x3 + (.0419764 -
     ------------------------------------------------------------------------
                  2                               2             
     .610417*ii)x2 x3 + (.208936 - .24001*ii)x1*x3  + (.303759 +
     ------------------------------------------------------------------------
                      2                            3
     .0565775*ii)x2*x3  + (.0387127 + .335465*ii)x3 }

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

o3 = {{-.273064+.123388*ii, -.570294-.278401*ii, .704876+.103051*ii}}

o3 : List

See also