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NumericalAlgebraicGeometry :: randomSd

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

                                 2                                       
o1 = {(- .0821299 - .230965*ii)x1  + (- .0515525 - .0129763*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                          
     .229274 + .196168*ii)x2  + (.30945 - .137771*ii)x1*x3 + (.018863 +
     ------------------------------------------------------------------------
                                                2              
     .138044*ii)x2*x3 + (.165776 - .133628*ii)x3 , (.00892298 +
     ------------------------------------------------------------------------
                  3                           2                 
     .331097*ii)x1  + (.452009 + .198767*ii)x1 x2 + (- .395694 +
     ------------------------------------------------------------------------
                     2                            3             
     .729709*ii)x1*x2  + (.221695 + .0248786*ii)x2  + (.567663 -
     ------------------------------------------------------------------------
                   2                                                  
     .0101901*ii)x1 x3 + (.128807 - .175454*ii)x1*x2*x3 + (- .274022 -
     ------------------------------------------------------------------------
                  2                                 2               
     .138097*ii)x2 x3 + (- .137191 - .13445*ii)x1*x3  + (- .464775 -
     ------------------------------------------------------------------------
                     2                            3
     .109222*ii)x2*x3  + (.0250332 - .170197*ii)x3 }

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

o3 = {{-.412633-.203913*ii, .481321-.0891142*ii, .739877+.033528*ii}}

o3 : List

Ways to use randomSd :