next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 a unit sphere in the Bombieri-Weyl norm.
i1 : T = randomSd {2,3}

                             2                                              
o1 = {(.199286 - .15172*ii)x1  + (- .0807668 + .480646*ii)x1*x2 + (- .306795
     ------------------------------------------------------------------------
                   2                                            
     + .13281*ii)x2  + (.0181178 - .349965*ii)x1*x3 + (.444456 +
     ------------------------------------------------------------------------
                                                   2             
     .0291168*ii)x2*x3 + (.0376665 + .0480236*ii)x3 , (.0806312 +
     ------------------------------------------------------------------------
                   3                          2                 
     .0512034*ii)x1  + (.1575 - .0199892*ii)x1 x2 + (- .142047 -
     ------------------------------------------------------------------------
                     2                            3               
     .166511*ii)x1*x2  + (.116072 - .0718977*ii)x2  + (.00271222 +
     ------------------------------------------------------------------------
                   2                                                 
     .0585076*ii)x1 x3 + (.794258 + .718985*ii)x1*x2*x3 + (.0701925 -
     ------------------------------------------------------------------------
                  2                                2              
     .123431*ii)x2 x3 + (.148691 + .143182*ii)x1*x3  + (.0232708 -
     ------------------------------------------------------------------------
                     2                             3
     .433609*ii)x2*x3  + (- .440628 - .141088*ii)x3 }

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

o3 = {{{.157562+.120055*ii, .747725+.135178*ii, .583248-.207888*ii}, #steps
     ------------------------------------------------------------------------
     => 12, status  => REGULAR, last t => 1, cond#^{-1} => .346221}}

o3 : List

Ways to use randomSd :