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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 = {(- .271436 + .491365*ii)x1  + (- .12323 - .17127*ii)x1*x2 + (.124409 -
     ------------------------------------------------------------------------
                   2                                                
     .0862105*ii)x2  + (- .157235 + .280943*ii)x1*x3 + (- .0853012 +
     ------------------------------------------------------------------------
                                                    2             
     .521826*ii)x2*x3 + (- .0340569 - .0566126*ii)x3 , (.0199263 +
     ------------------------------------------------------------------------
                  3                           2               
     .125174*ii)x1  + (.308519 - .134352*ii)x1 x2 + (.327798 +
     ------------------------------------------------------------------------
                     2                               3             
     .490051*ii)x1*x2  + (- .0932802 - .0764791*ii)x2  + (.128009 +
     ------------------------------------------------------------------------
                  2                                                
     .079337*ii)x1 x3 + (.835949 + .158845*ii)x1*x2*x3 + (.174831 +
     ------------------------------------------------------------------------
                  2                                 2               
     .363028*ii)x2 x3 + (- .162644 + .03034*ii)x1*x3  + (- .112452 -
     ------------------------------------------------------------------------
                    2                              3
     .29894*ii)x2*x3  + (- .0821348 - .165164*ii)x3 }

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

o3 = {{.043051-.585965*ii, .364027+.536599*ii, .472021-.107387*ii}}

o3 : List

See also