Re: Re: Wrong Simplify[] Answer for

*To*: mathgroup at smc.vnet.net*Subject*: [mg104570] Re: [mg104513] Re: Wrong Simplify[] Answer for*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Wed, 4 Nov 2009 01:34:33 -0500 (EST)*Reply-to*: hanlonr at cox.net

a = Cos[x]^2 - Sin[x]^2; b = Cos[x]^4 - Sin[x]^4; Table[a - b, {x, -10, 10}] // Simplify {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} Note what happens when you use precision greater than machine precision Off[N::meprec] Table[a - b, {x, -10, 10}] // N[#, 20] & {0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-250,0.*10^-250,0.*10^-250,0,0.*10^-250,0.*10^-250,0.*10^-250,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249,0.*10^-249} Bob Hanlon ---- Lawrence Teo <lawrenceteo at yahoo.com> wrote: ============= Hi all, Thanks for the insight. So Simplify[] in Mathematica is right. But why I observe small delta if I subtract the two expressions with // N? Is it because of machine precision related limitation? a = Cos[x]^2 - Sin[x]^2 b = Cos[x]^4 - Sin[x]^4 Table[a - b, {x, -10, 10}] // N Return small delta... \!\({6.938893903907228`*^-17, 6.245004513516506`*^-17, 0.`, 0.`, 7.025630077706069`*^-17, 0.`, 0.`, 3.854338723185968`*^-17, 0.`, 1.1102230246251565`*^-16, 0.`, 1.1102230246251565`*^-16, 0.`, \ 3.854338723185968`*^-17, 0.`, 0.`, 7.025630077706069`*^-17, 0.`, 0.`, \ 6.245004513516506`*^-17, 6.938893903907228`*^-17}\) On Oct 31, 2:50 pm, Peter Breitfeld <ph... at t-online.de> wrote: > Lawrence Teo wrote: > > We know that Simplify[Cos[x]^2-Sin[x]^2] -> Cos[2 x] > > But why Simplify[Cos[x]^4-Sin[x]^4] -> Cos[2 x] too? > > > Doing subtraction between the two expressions will give small delta. > > This is enough to prove that the two expression shouldn't be the same. > > > Can anyone give me any insight? Thanks. > > it's simply true, because: > > cos^4 x - sin^4 x = (cos^2 x - sin^2 x)(cos^2 x + sin^2 x) > = (cos^2 x - sin^2 x) * 1 = cos 2x > > -- > _________________________________________________________________ > Peter Breitfeld, Bad Saulgau, Germany --http://www.pBreitfeld.de