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Re: Why does Mathematica change the precision of an expression to check equality?

• To: mathgroup at smc.vnet.net
• Subject: [mg69409] Re: [mg69386] Why does Mathematica change the precision of an expression to check equality?
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Mon, 11 Sep 2006 05:39:03 -0400 (EDT)
• References: <200609101119.HAA11181@smc.vnet.net>

My *guess* is that it has to do with the difficulty (impossible) of
telling wether a general expression is truly equivalent to another
expression and the balanced decision to make Mathematica practical to
use rather than absolutely correct.

On 9/10/06, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
> These thoughts come after answering a similar question in a forum
> dedicated to anther CAS. Having ran the following code, I am a little
> perplexed by the behavior of Mathematica.
>
> y = (Sqrt[5] - 2)*(Sqrt[5] + 2);
> y == 1
>
> --> N::"meprec" : "Internal precision limit $MaxExtraPrecision =
> (49.99999999999999) reached while evaluating -1 + (-2 + Sqrt[5])*(2 +
> Sqrt[5]). More...
>
> --> (-2 + Sqrt[5])*(2 + Sqrt[5]) == 1
>
> At least Mathematica returns a warning message in addition to the
> unevaluated expression
>
> I used to thought that Mathematica was not attempting to do any
> algebraic simplifications when testing, say, equality, and that one have
> to request explicitly such transformations.
>
> However, it is pretty clear that Mathematica transforms the expression
> in some way, in this case changing infinite precision -- that is exact
> numbers -- into arbitrary precision -- that is better precision that
> hardware but still not exact.
>
> So the question is, "Why, when an expression is only written with exact
> numbers, Mathematica would "downgrade" the precision to a lower and
> inexact one before attempting to answer a boolean question?"
>
> I do not see the rational behind this design choice...
>
> Best regards,
> Jean-Marc
>
> P.S. I know that one can get the correct answer by using Simplify.
>
>


-- 
http://chris.chiasson.name/

• References:
  • Why does Mathematica change the precision of an expression to check equality?
    • From: Jean-Marc Gulliet <jeanmarc.gulliet@gmail.com>