Singular Manual: randcharpoly

| #### D.12.7.9 randcharpoly Procedure from library `rootsmr.lib` (see rootsmr_lib). Usage: randcharpoly(b,i); randcharpoly(b,i,n); b,i ideal; n int Return: poly: the characteristic polynomial of a pseudorandom rational univariate projection having one zero per zero of i. If n<10 is given, it is the number of digits being used for the pseudorandom coefficients (default: n=5) Assume: i is a Groebner basis and b is an ordered monomial basis of r/i, r = basering Note: shows a warning if printlevel>0 (default: printlevel=0) Example:
    LIB "rootsmr.lib";
    ring r = 0,(x,y,z),dp;
    ideal i = (x-1)*(x-2),(y-1),(z-1)*(z-2)*(z-3)^2;
    i = std(i);
    ideal b = qbase(i);
    poly p = randcharpoly(b,i);
    p;
    ==> z8-1989306z7+1720335326522z6-844575738768293508z5+25739857498506957597394\
       5z4-49855396253842786126599566442z3+5991506449298102407845582886576172z2-\
       408335865183407651473343362162998177144z+12078261759575784323866334900781\
       464660123776
    nrroots(p); // See nrroots in urrcount.lib
    ==> 6
    int pr = printlevel;
    printlevel = pr+2;
    p = randcharpoly(b,i,5);
    ==> // poly, 9 monomial(s)
    ==> z8-2923964*z7+3712323518934*z6-2671920147197312780*z5+1191863249059288760\
       005489*z4-337242235263204293461543939056*z3+59079952041382728808956425746\
       100736*z2-5855367303472484622963975143953858560000*z+25120629313761950033\
       6395930918610534400000000
    ==> *********************************************************************
    ==> * WARNING: This polynomial was obtained using  pseudorandom numbers.*
    ==> * If you want to verify the result, please use the command          *
    ==> *                                                                   *
    ==> * verify(p,b,i)                                                     *
    ==> *                                                                   *
    ==> * where p is the polynomial I returned, b is the monomial basis     *
    ==> * used, and i the Groebner basis of the ideal                       *
    ==> *********************************************************************
    nrroots(p);
    ==> 6
    printlevel = pr;

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