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 Author: jcapco [ Mon Apr 24, 2017 8:49 am ] Post subject: Roots of rational polynomials Consider this code:Code:ring A=0,x,lp;poly f=(x-3/17)*(x+2/3);I don't see a straightforward way to find the exact (as rational numbers) roots of f. I looked a bit at the documentation and if I use the command laguerre(f,5,1), I obtain roots up to 5 digits (decimal) precision and not really the rational roots 3/17 and -2/3. Of course I can use factorize(f) and write a code that extracts the rational roots, but I am sure (I hope) there is a cleaner way to do this. Any hints would be much appreciated. Thanks!

 Author: jcapco [ Mon Apr 24, 2017 9:36 am ] Post subject: Re: Roots of rational polynomials So far I am using this procedure. It could exist in some library already?Code://rational roots of a rational polynomialproc Qroots(poly f) {  ideal l = factorize(f,1);  list ret;  for (int i=1;i<=size(l);i++)   {    if (deg(l[i])==1)    { //roots are rational      if (size(l[i])==1) { ret=ret+list(0);}      else { ret = ret + list(-leadcoef(l[i][2])/leadcoef(l[i][1])); }    }  } return(ret);}

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