Re: Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- To: mathgroup at smc.vnet.net
- Subject: [mg104549] Re: [mg104513] Re: Wrong Simplify[] Answer for Simplify[Cos[x]^4-Sin[x]^4]?
- From: "David Park" <djmpark at comcast.net>
- Date: Wed, 4 Nov 2009 01:30:37 -0500 (EST)
- References: <hce437$r4t$1@smc.vnet.net> <hcgmni$cpe$1@smc.vnet.net> <5597513.1257237292147.JavaMail.root@n11>
Why do you use N? Mathematica is pretty smart and can handle many things symbolically and exactly. So keep things that way as long as possible. If you do use N then also use Chop. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Lawrence Teo [mailto:lawrenceteo at yahoo.com] 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... \!\({6.938893903907228`*^-17, 6.245004513516506`*^-17, 0.`, 0.`, 7.025630077706069`*^-17, 0.`, 0.`, 3.854338723185968`*^-17, 0.`, 1.1102230246251565`*^-16, 0.`, 1.1102230246251565`*^-16, 0.`, \ 3.854338723185968`*^-17, 0.`, 0.`, 7.025630077706069`*^-17, 0.`, 0.`, \ 6.245004513516506`*^-17, 6.938893903907228`*^-17}\)