RE: Re: SetPrecision vs N

*To*: mathgroup at smc.vnet.net*Subject*: [mg71745] RE: [mg71714] Re: SetPrecision vs N*From*: "David Park" <djmp at earthlink.net>*Date*: Tue, 28 Nov 2006 06:03:58 -0500 (EST)

The purpose of N is to convert EXACT numbers to approximate numbers with a given precision. N does nothing whatsoever on approximate numbers. So a statement like N[1.1, 1000] just leaves 1.1 unchanged. But N[Pi, 50] Precision[%] 3.1415926535897932384626433832795028841971693993751 50. does something because Pi is an exact number. But it appears that SetPrecision works on both approximate and exact numbers. SetPrecision[Pi, 50] 3.1415926535897932384626433832795028841971693993751 So if one wants to really set the precision of numbers, it is best to use SetPrecision, and just use N for converting exact to approximate numbers. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Peter Pein [mailto:petsie at dordos.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