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an issue of consistency

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112354] an issue of consistency
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 10 Sep 2010 05:08:08 -0400 (EDT)

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?

Andrzej Kozlowski




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