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 = {(.0776589 + .096155*ii)x1  + (- .0852526 + .0382641*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                           
     .0495421 - .191311*ii)x2  + (.250852 + .230829*ii)x1*x3 + (.112213 +
     ------------------------------------------------------------------------
                                                    2             
     .105111*ii)x2*x3 + (- .0386013 - .0551745*ii)x3 , (.0688506 +
     ------------------------------------------------------------------------
                  3                             2               
     .132756*ii)x1  + (- .484341 + .510608*ii)x1 x2 + (.187932 +
     ------------------------------------------------------------------------
                     2                             3             
     .568803*ii)x1*x2  + (- .263231 + .141409*ii)x2  + (.530362 +
     ------------------------------------------------------------------------
                 2                                                    
     .20599*ii)x1 x3 + (- .12074 - .0761177*ii)x1*x2*x3 + (- .633355 -
     ------------------------------------------------------------------------
                   2                                  2               
     .0680691*ii)x2 x3 + (- .519092 + .176317*ii)x1*x3  + (- .552712 -
     ------------------------------------------------------------------------
                     2                                3
     .229182*ii)x2*x3  + (- .00816596 + .0657827*ii)x3 }

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

o3 = {{.0363044+.251322*ii, -.249633-.52879*ii, .765444-.087632*ii}}

o3 : List

See also