Re: SetPrecision vs N

*To*: mathgroup at smc.vnet.net*Subject*: [mg71714] Re: SetPrecision vs N*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 27 Nov 2006 04:04:37 -0500 (EST)*Organization*: 1&1 Internet AG*References*: <ekbmmt$f9g$1@smc.vnet.net>

Andrew Moylan schrieb: > Hi all, > > Suppose I want to evaluate an expression at a given precision. What is > the difference between using N[expr, precision] and using > SetPrecision[expr, precision]? > > I've noticed that SetPrecision seems to be equivalent even in such > situations as e.g. N[Integrate[...]] automatically calling > NIntegrate[...] when the integral can't be done exactly: > > SetPrecision[Integrate[x^x, {x, 0, 1}], 20] > and > N[Integrate[x^x, {x, 0, 1}], 20] > both give > 0.78343051071213440706 > > Are there important differences between SetPrecision and N that I > should be aware of? > > Cheers, > Andrew > Hi Andrew, the most obvious difference is: Precision[N[1.1, 1000]] --> MachinePrecision vs. Precision[SetPrecision[1.1, 1000]] -->1000. I guess, SetPrecision[#,prec]& automagically applies N[#,prec]& to an expression having greater precision than prec (especially when applied to exact expressions (which got infinite precision)). P²