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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 = {(.103573 - .218526*ii)x1  + (- .0518914 - .0086533*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                             
     .497792 - .131701*ii)x2  + (- .237385 - .309203*ii)x1*x3 + (.206418 +
     ------------------------------------------------------------------------
                                                  2              
     .41074*ii)x2*x3 + (- .268527 + .0135225*ii)x3 , (- .107249 +
     ------------------------------------------------------------------------
                  3                           2              
     .232555*ii)x1  + (.250982 + .118261*ii)x1 x2 + (.10419 +
     ------------------------------------------------------------------------
                     2                                 3              
     .372576*ii)x1*x2  + (- .0487745 + .000714907*ii)x2  + (- .41576 -
     ------------------------------------------------------------------------
                  2                                                  
     .383953*ii)x1 x3 + (.124918 - .196173*ii)x1*x2*x3 + (- .365822 +
     ------------------------------------------------------------------------
                  2                                2             
     .236097*ii)x2 x3 + (.332163 - .138043*ii)x1*x3  + (.240582 -
     ------------------------------------------------------------------------
                    2                             3
     .17995*ii)x2*x3  + (- .13051 - .0913385*ii)x3 }

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

o3 = {{-.13545-.607595*ii, .384439+.611741*ii, .289106+.0829422*ii}}

o3 : List

Ways to use randomSd :