# Singular          #### D.12.7.2 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; ``` 