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 = {(.00534991 - .0419227*ii)x1  + (- .156208 - .242372*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                              
     .277805 - .285209*ii)x2  + (- .125762 + .0918592*ii)x1*x3 + (.624028 -
     ------------------------------------------------------------------------
                                                 2             
     .0801226*ii)x2*x3 + (.282219 - .190404*ii)x3 , (- .16652 +
     ------------------------------------------------------------------------
                   3                            2                 
     .0173775*ii)x1  + (.0177598 - .087716*ii)x1 x2 + (- .384701 -
     ------------------------------------------------------------------------
                     2                             3              
     .224715*ii)x1*x2  + (.0941323 + .0417109*ii)x2  + (.0739115 -
     ------------------------------------------------------------------------
                   2                                                  
     .0834171*ii)x1 x3 + (- .544908 - .140338*ii)x1*x2*x3 + (.229936 +
     ------------------------------------------------------------------------
                   2                                2               
     .0724076*ii)x2 x3 + (.282148 + .451131*ii)x1*x3  + (- .269543 +
     ------------------------------------------------------------------------
                     2                             3
     .487322*ii)x2*x3  + (- .249204 + .169038*ii)x3 }

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

o3 = {{.30542+.0038267*ii, -.365675+.0086336*ii, .809544+.342855*ii}}

o3 : List

See also