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Roots of rational polynomials http://www.singular.unikl.de/forum/viewtopic.php?f=10&t=2597 
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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=(x3/17)*(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 polynomial
proc 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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