#### D.12.6.2 nrRootsDeterm

Procedure from library `rootsmr.lib` (see rootsmr_lib).

Return:
  int: the number of real roots of the ideal I by a deterministic algorithm

Assume:
  If I is not a Groebner basis, then a Groebner basis will be computed by using std. If I is already a Groebner basis (i.e. if attrib(I,"isSB"); returns 1) then this Groebner basis will be used, hence it must be one w.r.t. (any) global ordering. This may be useful if the ideal is known to be a Groebner basis or if it can be computed faster by a different method.

Note:
  If printlevel>0 the number of complex solutions is displayed (default: printlevel=0). The procedure nrRootsProbab is usually faster.

Example:

    LIB "rootsmr.lib";
    ring r = 0,(x,y,z),lp;
    ideal I = (x-1)*(x-2),(y-1),(z-1)*(z-2)*(z-3)^2;
    nrRootsDeterm(I);       //no of real roots (using internally std)
    ==> 6
    I = groebner(I);        //using the hilbert driven GB computation
    int pr = printlevel;
    printlevel = 2;
    nrRootsDeterm(I);
    ==> //ideal has 8 complex solutions, counted with multiplicity
    ==> 6
    printlevel = pr;

See also: nrRootsProbab; nrroots; solve; sturmquery.

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