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D.15.8.3 getMaxPoints

Procedure from library maxlike.lib (see maxlike_lib).

Usage:
getMaxPoints(Iu, H, prec [, "nodisplay"]); ideal Iu, matrix H, int prec, int k Iu the likelihood ideal, H the (modified) Hessian of the considered algebraic statistical model, prec the precision with which to compute the maximum likelihood estimates

Return:
ring: a complex ring R in which you can find the following two lists: - MPOINTS, points in which the loglikelihood function has a local maximum, and - LHESSIANS, the (modified) Hessians at those points
also prints out the points in MPOINTS, unless a fourth argument is given

Note:
it is assumed that the likelihood ideal is 0-dimensional

Example:
 
LIB "maxlike.lib";
ring r = 0,(x,y),dp;
poly pA = -10x+2y+25;
poly pC = 8x-y+25;
poly pG = 11x-2y+25;
poly pT = -9x+y+25;
intvec u = 10,14,15,10;
ideal I = pA,pC,pG,pT;
ideal L = likeIdeal(I,u);
matrix H = logHessian(I,u);
def R = getMaxPoints(L, H, 50);
==> [1]:
==>    [1]:
==> 0.51912639453217837465463128685404418932771758896637
==>    [2]:
==> 0.21725133256396491722887792998009835426225610459149
==> 
==> // In the ring created by getmaxpoints you can find the lists
==> //   MPOINTS, containing points in which the loglikelihood function has a\
    local maximum, and
==> //   LHESSIANS, containing the (modified) Hessians at those points.
==> 
setring R;
MPOINTS;
==> [1]:
==>    [1]:
==> 0.51912639453217837465463128685404418932771758896637
==>    [2]:
==> 0.21725133256396491722887792998009835426225610459149
LHESSIANS;
==> [1]:
==>    _[1,1]=-65487950.391931360088969690060635799847590217779318
==>    _[1,2]=10577428.579689959415257134363650588464921754723022
==>    _[2,1]=10577428.579689959415257134363650588464921754723022
==>    _[2,2]=-1795635.2877514452321365400508526832132830781483598