Re: Re: unable to FullSimplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg65886] Re: [mg65872] Re: unable to FullSimplify*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 21 Apr 2006 01:33:19 -0400 (EDT)*References*: <200604160545.BAA07958@smc.vnet.net> <200604181056.GAA14321@smc.vnet.net> <e24uhn$5s7$1@smc.vnet.net> <200604200914.FAA05331@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 20 Apr 2006, at 18:14, Vladimir wrote: > Andrzej Kozlowski wrote: >> Well, it seems to me that you are expecting too much. > > Well, yes, considering the internal simplification and > related code is supposedly thousands of pages long. > >> x + x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8 >> >> there are just too many different groupings and rearrangements that >> would have to be tried to get to a simpler form. > > According to documentation, "FullSimplify effectively has to try > combining every part of an expression with every other". Yes, you are right. I wrote that without giving it much thought; my only really significant point was the one about the need to use only complexity decreasing transformations and this still stands. > >> Sometimes the only >> way to transform an expression to a simpler form is by first >> transforming it to a more complex one > > I'm sure FullSimplify can be improved without the need > for such complexification steps. For example: > > In[]:= subdivide[a_ + b_] := FullSimplify[a] + FullSimplify[b]; > FullSimplify[Expand[x + (x + x^2)^4], > TransformationFunctions -> {Automatic, subdivide}] > > Out[]= x + x^4*(1 + x)^4 > Well, yes, it works nicely here but the question is, if you make this a default transformation transformation for FullSimplify how will it effect complexity? If you have a sum of n terms you will have to break it up into all possible pairs, then apply FullSimplify to each, and then keep doing this recursively. In fact it even seems hard to see how you would avoid numerous unnecessary attempts at simplifying the same expression... Obviously complexity is a very important consideration i choosing default functions for FullSimplify. Functions like subdivide should be added by users when they see the need for it. Andrzej Kozlowski

**References**:**unable to FullSimplify***From:*vladimir347@yahoo.com

**Re: unable to FullSimplify***From:*"Vladimir" <vladimir347@yahoo.com>

**Re: unable to FullSimplify***From:*"Vladimir" <vladimir347@yahoo.com>