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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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