D.7.4.2 triMNewton
..................
Procedure from library ntsolve.lib (see ntsolve_lib).

Usage:
triMNewton(G,a[,ipar]); G,a= ideals, ipar=list/intvec

Assume:
G: g1,..,gn, a triangular system of n equations in n vars, i.e.
gi=gi(var(n-i+1),..,var(n)),

a: ideal of numbers, coordinates of an approximation of a common
zero of G to start with (with a[i] to be substituted in var(i)),

ipar: control integer vector (default: ipar = 100,10)
    ipar[1]: max. number of iterations
  ipar[2]: accuracy (we have as norm |.| absolute value ):
           accept solution sol if |G(sol)| < |G(a)|*(0.1^ipar[2]).
  

Return:
an ideal, coordinates of a better approximation of a zero of G

Example:
LIB "ntsolve.lib";
ring r = (real,30),(z,y,x),(lp);
ideal i = x^2-1,y^2+x4-3,z2-y4+x-1;
ideal a = 2,3,4;
intvec e = 20,10;
ideal l = triMNewton(i,a,e);
l;
==> l[1]=-2.000000000042265738880279143423
==> l[2]=1.41421356237309504880168872421
==> l[3]=1
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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