Re: Testing for squares

*To*: mathgroup at smc.vnet.net*Subject*: [mg66260] Re: Testing for squares*From*: "Julian Aguirre" <julian.aguirre at ehu.es>*Date*: Sat, 6 May 2006 01:54:31 -0400 (EDT)*References*: <e3cimv$a3k$1@smc.vnet.net><e3f5kf$s8r$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Ray, Thank you for your message. However, most of the integers I need to test are not machine size, and test2 reverts to the uncompiled code. Julián Ray Koopman wrote: > In[1]:= test1 = IntegerQ[Sqrt[#]]&; > test2 = Compile[{{n,_Integer}},Round[Sqrt[N[n]]]^2 === n]; > v = Range[123456]; > Timing[a = test1/@v;] > Timing[b = test2/@v;] > a === b > > Out[4]= {3.49 Second,Null} > Out[5]= {0.34 Second,Null} > Out[6]= True > > Julian Aguirre wrote: > > Hi all, > > > > 1) I would like to have an efficient test to decide if an integer is a > > square. > > > > test1 = IntegerQ[Sqrt[#]]& > > > > is too slow for my needs. I am using something like > > > > test2 = Positive[#] && JacobiSymbol[#, p] && Sqrt[Round[N[#, > > precission]]]^2==# & > > > > where p is a prime (or I may use several primes). However test2 may > > return False for very large integers. How large depends on the value of > > precission. Do you know of a faster test? > > > > Thanks for any help, > > > > Julián Aguirre