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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 = {(.289845 + .132951*ii)x1  + (- .245648 + .193373*ii)x1*x2 + (- .353048
     ------------------------------------------------------------------------
                    2                                           
     + .029987*ii)x2  + (.106266 - .219808*ii)x1*x3 + (.162761 -
     ------------------------------------------------------------------------
                                                 2            
     .457592*ii)x2*x3 + (.0305787 + .212487*ii)x3 , (.129405 +
     ------------------------------------------------------------------------
                   3                             2               
     .0279011*ii)x1  + (- .153715 - .412209*ii)x1 x2 + (.440265 -
     ------------------------------------------------------------------------
                     2                             3             
     .443355*ii)x1*x2  + (- .0278132 + .30449*ii)x2  + (.186628 +
     ------------------------------------------------------------------------
                  2                                                   
     .148665*ii)x1 x3 + (.405918 - .396694*ii)x1*x2*x3 + (- .0225264 +
     ------------------------------------------------------------------------
                   2                                   2              
     .0662968*ii)x2 x3 + (- .497024 + .0451934*ii)x1*x3  + (- .18448 +
     ------------------------------------------------------------------------
                     2                           3
     .321142*ii)x2*x3  + (.14133 - .0373233*ii)x3 }

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

o3 = {{.199763-.555309*ii, -.154656+.242653*ii, .704256-.270094*ii}}

o3 : List

See also