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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...
\!\({6.938893903907228`*^-17, 6.245004513516506`*^-17, 0.`,
    0.`, 7.025630077706069`*^-17, 0.`, 0.`, 3.854338723185968`*^-17,
0.`,
    1.1102230246251565`*^-16, 0.`, 1.1102230246251565`*^-16, 0.`, \
3.854338723185968`*^-17, 0.`, 0.`, 7.025630077706069`*^-17, 0.`, 0.`,
\
6.245004513516506`*^-17, 6.938893903907228`*^-17}\)