| #### D.8.7.11 num_radical_via_decom Procedure from library `recover.lib` (see recover_lib). Usage: num_radical_via_decom(I,D); ideal I, int D D a bound to the degree of the elements of the components. Return: ideal: the radical of I Remarks: Uses Bertini. This procedure merely calls num_prime_decom with the same input and then intersects the returned components. Note: Should only be called from a ring over the rational numbers. Example:
    LIB "recover.lib";
    //First, we attempt to compute the radical via the hybrid algorithm.
    ring R=0,(x,y,z),dp;
    ideal I=(x+y)^2*(y+2z)^3, (x+y)^3*(x-3z)^2;
    int D=2;
    int Prec=300;
    ideal numRad=num_radical_via_decom(I,D,Prec);
    numRad;
    //Then we compute the radical symbolically and compare the results.
    ideal Rad=radical(I);
    Rad;
    reduce(Rad,std(numRad));
    reduce(numRad,std(Rad));
See also: num_prime_decom; num_radical_via_randlincom.

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