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

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has and equal chance of reaching any of the solutions of the target system T.
i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                 2                                           
o2 = ({(.0524999 + .0807136*ii)x1  + (.121222 - .322846*ii)x1*x2 + (- .139293
     ------------------------------------------------------------------------
                     2                                              
     + .0739784*ii)x2  + (.51794 - .354317*ii)x1*x3 + (- .00577795 +
     ------------------------------------------------------------------------
                                                 2              
     .402161*ii)x2*x3 + (.0377007 - .308661*ii)x3 , (- .168162 +
     ------------------------------------------------------------------------
                   3                            2                 
     .0525416*ii)x1  + (.489167 + .0327356*ii)x1 x2 + (- .257447 -
     ------------------------------------------------------------------------
                      2                           3              
     .0375813*ii)x1*x2  + (.105164 + .077897*ii)x2  + (.0778296 +
     ------------------------------------------------------------------------
                  2                                                    
     .335657*ii)x1 x3 + (- .250418 - .513779*ii)x1*x2*x3 + (- .125977 +
     ------------------------------------------------------------------------
                  2                                  2             
     .381752*ii)x2 x3 + (- .176749 - .128786*ii)x1*x3  + (.404584 -
     ------------------------------------------------------------------------
                     2                            3
     .537832*ii)x2*x3  + (.198122 - .0166276*ii)x3 }, {{.220119+.881806*ii,
     ------------------------------------------------------------------------
     .192574+.354482*ii, -.0693751-.0800718*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{{.073864+.792452*ii, -.142382-.403763*ii, .422373-.0697697*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .403353}}

o3 : List

Ways to use randomInitialPair :