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 = {(- .0996486 - .0659443*ii)x1  + (- .373341 + .324256*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                             
     (.067794 + .0868354*ii)x2  + (- .461773 + .117747*ii)x1*x3 + (.205428 -
     ------------------------------------------------------------------------
                                                   2               
     .0212302*ii)x2*x3 + (.0514008 + .0280003*ii)x3 , (.000467152 -
     ------------------------------------------------------------------------
                  3                             2                
     .222152*ii)x1  + (- .139835 + .420767*ii)x1 x2 + (.0827362 +
     ------------------------------------------------------------------------
                     2                              3               
     .026367*ii)x1*x2  + (- .016523 + .0812171*ii)x2  + (- .318198 +
     ------------------------------------------------------------------------
                  2                                                    
     .279965*ii)x1 x3 + (- .265384 - .174444*ii)x1*x2*x3 + (- .133448 -
     ------------------------------------------------------------------------
                  2                                 2               
     .443832*ii)x2 x3 + (.0816068 - .388874*ii)x1*x3  + (- .147195 +
     ------------------------------------------------------------------------
                     2                             3
     .454777*ii)x2*x3  + (- .387237 + .402152*ii)x3 }

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

o3 = {{-.155328-.379438*ii, -.365979-.386261*ii, .732181+.112575*ii}}

o3 : List

See also