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D.12.7.1 nrRootsProbab

Procedure from library rootsmr.lib (see rootsmr_lib).

Return:
int: the number of real roots of the ideal I by a probabilistic 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 n<10 is given, n is the number of digits being used for constructing a random characteristic polynomial, a bigger n is more safe but slower (default: n=5).
If printlevel>0 the number of complex solutions is displayed (default: printlevel=0).

Example:
 
See also: nrRootsDeterm; nrroots; randcharpoly; solve.


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