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D.8.5.1 nt_solve

Procedure from library ntsolve.lib (see ntsolve_lib).

Usage:
nt_solve(gls,ini[,ipar]); gls,ini= ideals, ipar=list/intvec,
gls: contains the equations, for which a solution will be computed
ini: ideal of initial values (approximate solutions to start with),
ipar: control integers (default: ipar = [100, 10])
 
 ipar[1]: max. number of iterations
 ipar[2]: accuracy (we have the l_2-norm ||.||): accepts solution sol
          if ||gls(sol)|| < eps0*(0.1^ipar[2])
          where eps0 = ||gls(ini)|| is the initial error

Assume:
gls is a zerodimensional ideal with nvars(basering) = size(gls) (>1)

Return:
ideal, coordinates of one solution (if found), 0 else

Note:
if printlevel >0: displays comments (default =0)

Example:
 
LIB "ntsolve.lib";
ring rsq = (real,40),(x,y,z,w),lp;
ideal gls =  x2+y2+z2-10, y2+z3+w-8, xy+yz+xz+w5 - 1,w3+y;
ideal ini = 3.1,2.9,1.1,0.5;
intvec ipar = 200,0;
ideal sol = nt_solve(gls,ini,ipar);
sol;
==> sol[1]=0.8698104581550055082008024750939710335537
==> sol[2]=2.821577445750324600849626251771718236941
==> sol[3]=1.132312008466417990006094015711266871732
==> sol[4]=-1.413071026406678849397999475590194239628