Re: Simplify and FullSimplify
- To: mathgroup at smc.vnet.net
- Subject: [mg58551] Re: [mg58547] Simplify and FullSimplify
- From: Andrzej Kozlowski <akozlowski at gmail.com>
- Date: Thu, 7 Jul 2005 05:35:40 -0400 (EDT)
- References: <200507060711.DAA05301@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 6 Jul 2005, at 16:11, fizzy wrote: > > A result of a calculation I was doing generated this expression.... > > q-q Exp[-a x] + c Exp[-a x] > > > naturally my next step was Simplify and I thought I'd get the Exp > [- ax] > collected.....to my complete surprize I got the following: > > Exp[-a x] (c + (-1+ Exp[a x]) q > > > How on Earth did Mathematica come up with this? I checked > FullSimplify > which did collect Exp[-a x].... > > On re-reading my question before I submitted it, I see that with > Simplify Mathematica 'collected' using Exp[- a x] q.....of course, > visually this expression seems quite complex and would seem to take > much > more 'thinking' to get ......why do Simplify and FullSimplify have > such > a vast difference in what is considered 'Simpler'? > > > Thanks....Jerry Blimbaum > > They do not differ at all in what is considered Simpler (Adam Strzebonski once published here the default ComplexityFunction which is the same for both) but FullSimplify applies a lot more transformation rules. I have no idea what transformation function in FullSimplify is responsible for this simplification. However, here is a transformation fucntion I have manufactured: f[expr_] := First[Sort[(Collect[expr, #1] & ) /@ Level[expr, {1, Infinity}], LeafCount[#1] <= LeafCount[#2] & ]] With this transformation function you will get: Simplify[(-E^((-a)*x))*q + q + c/E^(a*x), TransformationFunctions -> {Automatic, f}] (c - q)/E^(a*x) + q What f[expr] does is to try to Collect expr with respect to all subexpressions of expr at levels 1 to Infinity and then choose the form that has the least LeafCount. Obviously this is time consuming for complicated expressions. Possibly FullSimplify uses something similar. Andrzej Kozlowski
- References:
- Simplify and FullSimplify
- From: "fizzy" <fizzycist@knology.net>
- Simplify and FullSimplify