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