Finding perfect squares

*To*: mathgroup at smc.vnet.net*Subject*: [mg30605] Finding perfect squares*From*: AGUIRRE ESTIBALEZ Julian <mtpagesj at lg.ehu.es>*Date*: Fri, 31 Aug 2001 04:09:30 -0400 (EDT)*Organization*: Universidad del Pais Vasco/Euskal Herriko Unibertsitatea*Sender*: owner-wri-mathgroup at wolfram.com

I need a function to determine wether a list of integers contains a square. I am using Select[mylist, SquareQ, 1] != {} where SquareQ[n] returns true if n is a perfect square. The naif choice SquareQ = IntegerQ[Sqrt[#]]& is very slow for my needs, so I define SquareQ = JacobiSymbol[#, p1] != -1 && ...&& JacobiSymbol[#, pk] !=-1 && Round[Sqrt[N[#, prec]]]^2 == # & where p1, ..., pk are odd primes. The last test may fail to recognize a square, but will never return True when applied to a non square. Increasing prec enlarges the range in which it gives correct results. Can you suggest a faster way? In my application, my list has between 10^3 and 10^5 integers with around 40 decimal digits (so that, if I understand correctly, Complile will not help). Thanks in advance. Julian Aguirre | Voice: +34 946012659 Departamento de Matematicas | Fax: +34 944648500 Universidad del Pais Vasco | Postal: Aptdo. 644, 48080 Bilbao, Spain | email: mtpagesj at lg.ehu.es