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: unable to FullSimplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65769] Re: [mg65703] unable to FullSimplify
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 17 Apr 2006 02:28:07 -0400 (EDT)
  • References: <200604160545.BAA07958@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 16 Apr 2006, at 14:45, vladimir347 at yahoo.com wrote:

> I get the following unexpected and inconsistent results:
>
> FullSimplify[Expand[b + (a + b)^4]]
>
> b + (a + b)^4
>
>
> FullSimplify[Expand[a + (a + b)^4]]
>
> a + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4
>
> Why they are different and why there is no simplification in the  
> second
> case?
>
> --
> Vladimir
>


This seems to me to be an unfortunate consequence of the fact that  
the outcome of FullSimplify (and Simplify)  depends on the ordering  
of the variables. This is because a variable order independent  
Simplify has very much higher complexity and will get stuck on a  
complicated expressions. Some time ago Adam Strzebonski of WRI sent  
the following implementation of order independent FullSimplify:

VOISimplify[vars_, expr_, assum_:True] :=
     Module[{perm, ee, best},
        perm = Permutations[vars];
        ee = (FullSimplify @@ ({expr, assum} /. Thread[vars -> #]))  
& /@ perm;
        best = Sort[Transpose[{LeafCount /@ ee, ee, perm}]][[1]];
        best[[2]] /. Thread[best[[3]] -> vars]]


With that the inconsistency disappears:


VOISimplify[{a, b}, Expand[a + (a + b)^4]]


(a + b)^4 + a


VOISimplify[{a, b}, Expand[b + (a + b)^4]]


(a + b)^4 + b

Nevertheless the example you have brought up looks unpleasant enough  
to hope that some fix can be found that does not require the full  
power (and complexity) of VOISImplify. ??

Andrzej Kozlowski 


  • Prev by Date: Calculating contradicts plotting
  • Next by Date: Re: normalization and square roots
  • Previous by thread: unable to FullSimplify
  • Next by thread: Re: unable to FullSimplify