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Re: Unexpected failures of FullSimplify on some Root elements

• To: mathgroup at smc.vnet.net
• Subject: [mg86561] Re: Unexpected failures of FullSimplify on some Root elements
• From: "Q.E.D." <aoe at netzero.net>
• Date: Thu, 13 Mar 2008 20:52:15 -0500 (EST)
• References: <frascp$1ie$1@smc.vnet.net>

Also note that when FullSimplify is replaced with ToRadicals, as I have
shown in the updated examples here, the results are as expected (no
Root[...] elements are left unresolved).

Function[k, ToRadicals[Root[Function[x, k - (k - x^2)^2], #] & /@ Range[4]]]
/@ Prime[Range[11]]

Function[k, ToRadicals[Root[Function[x, k - (k - x^2)^2], #] & /@ Range[4]]]
/@ (Prime[Range[11]]/3)

ToRadicals[Root[Function[x, 2 - (2 - (2 - (2 - x^2)^2)^2)^2], #] & /@
Range[16]]

Trace[ToRadicals[Root[2 - 4 #1^2 + #1^4 &, 2]], TraceInternal->True,
TraceOriginal->True, TraceDepth->2]

Note that, as with FullSimplify, the result is cached, however, unlike
FullSimplify, there is very little more more Trace output if you run this
command as the first thing after restarting Mathematica.

Q.E.D.