Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69529] Re: Why does Mathematica change the precision of an expression to check equality?
  • From: "Nasser Abbasi" <nma at 12000.org>
  • Date: Thu, 14 Sep 2006 06:57:26 -0400 (EDT)
  • References: <ee0spn$b3f$1@smc.vnet.net>
  • Reply-to: "Nasser Abbasi" <nma at 12000.org>

"Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com> wrote in message 
news:ee0spn$b3f$1 at smc.vnet.net...
> 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://support.wolfram.com/mathematica/kernel/features/simplifynumerical.html

Nasser


  • Prev by Date: Re: Known recursion link to Hermite polynomials not solved in Mathematica
  • Next by Date: Re: Derivative of a function with multiple variables
  • Previous by thread: Re: Why does Mathematica change the precision of an expression to check equality?
  • Next by thread: Why does Simplify often get stuck?