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Re: an issue of consistency

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112358] Re: an issue of consistency
  • From: Albert Retey <awnl at gmx-topmail.de>
  • Date: Fri, 10 Sep 2010 05:54:58 -0400 (EDT)
  • References: <i6csi4$t2m$1@smc.vnet.net>

Hi,

> This post is about a mild dispute I have been having with Wolfram's 
> technical support. It concerns behaviour that I see as inconsistent and 
> Technical Support seems to insist otherwise. I would not claim that it 
> actually represents a "bug" but I discovered it in a "real life" 
> situation, it was unexpected and took a while to see what the cause of 
> it was.
> In any case, I am not writing to "complain", but to find out if anyone 
> can justify the behaviour that I am going to describe as "consistent". 
> Technical Support thinks it is, but I can't understand their reasoning.
> 
> Consider the two "root object" numbers:
> 
> a = Root[#1^5 - # + 1 &, 1];
> b = Root[#1^5 - # + Log[2] &, 1];
> 
> The first is an algebraic number, the second is not, but they are both 
> real numbers which can be computed to arbitrary precision, e.g.
> 
>  N[{a, b}, 10]
> 
> {-1.167303978,-1.127288474}
> 
> O.K. now compare this:
> 
> Graphics[Point[{{Root[#1^5 - # + 1 &, 1], 0}}]]
> 
> and this:
> 
> Graphics[Point[{{Root[#1^5 - # + Log[2] &, 1], 0}}]]
> 
> In the first case Graphics forces N to be automatically applied while in 
> the second case one needs to do so manually:
> 
> Graphics[Point[{{Root[#1^5 - # + Log[2] &, 1], 0}}]]//N
> 
> This seems to me to be inconsistent, or at least I do not know of nay 
> obvious reason why the first number being algebraic and the second 
> number not being so should make any difference to how they are treated 
> by Graphics. Technical Support claims otherwise but is unable to provide 
> a reason that I can understand. Can anyone else?

It' hard to say since you do not provide the reasons that you don't
understand :-)

Honestly I can hardly imagine that there can be a convincing reason why
the above should be considered to be consistent. At best I could imagine
that there might be technical reasons that make a more consistent
solution impractical...

cheers,

albert


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