Re: Strange behaviour of Simplify
- To: mathgroup at smc.vnet.net
- Subject: [mg79075] Re: Strange behaviour of Simplify
- From: Andreas Maier <andimai at web.de>
- Date: Wed, 18 Jul 2007 02:51:08 -0400 (EDT)
- References: <f7caue$9bj$1@smc.vnet.net><f7f3k1$oi3$1@smc.vnet.net>
On Jul 16, 8:35 am, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com>
wrote:
> Andreas Maier wrote:
> > Hi,
>
> > i'm trying to simplify the following expression
>
> > In:= gamma=c Sqrt[g00])/Sqrt[c^2 g00 + g11 v^2]
>
> ------------------------^
> The above expression is syntacticly incorrect: either a parenthesis is
> missing before the 'c' or this parenthesis must be discarded.
>
>
>
> > In:=LeafCount[gamma]
> > Out:=52
>
> > using Simplify
>
> > In:= gamma2=Simplify[gamma, {Sqrt[g00] > 0, c > 0 }]
>
> > Out:=c/Sqrt[c^2 + (g11 v^2)/g00]
> > In:=LeafCount[gamma2]
> > Out:=44
>
> > Why is Mathematica (I'm using V6.0) able to cancel Sqrt[g00], but is
> > not
> > able to cancel c? I also tried ComplexityFunction->LeafCount, which
> > should work, because
>
> > In:=gamma3=1/Sqrt[1 + (g11 v^2)/(c^2 g00)]
> > In:=LeafCount[gamma3]
> > Out:=43
>
> > the LeafCount of gamma3 is smaller than gamma2, but it doesn' work.
> > Can anybody tell me, how i can transform gamma to gamma3 in
> > Mathematica?
>
> > Andreas Maier
>
> Moreover, the leaf count numbers you are reporting are fishy: I have got
> a difference of only one between the leaf count of gamma2 and of gamma3.
> You should experiment again with a fresh kernel and copy the
> input/output from the exact expressions you are working on.
>
> In[1]:= gamma = (c*Sqrt[g00])/Sqrt[c^2*g00 + g11*v^2]
> LeafCount[%]
>
> Out[1]= (c*Sqrt[g00])/Sqrt[c^2*g00 + g11*v^2]
>
> Out[2]= 22
>
> In[3]:= gamma2 = Simplify[gamma, {Sqrt[g00] > 0, c > 0}]
> LeafCount[%]
>
> Out[3]= c/Sqrt[c^2 + (g11*v^2)/g00]
>
> Out[4]= 18
>
> In[5]:= gamma3 = 1/Sqrt[1 + (g11*v^2)/(c^2*g00)]
> LeafCount[%]
>
> Out[5]= 1/Sqrt[1 + (g11*v^2)/(c^2*g00)]
>
> Out[6]= 17
>
> Regards,
> Jean-Marc
You are completely right! I wanted to simplify my problem, so i copied
only
part of it into my message. The LeafCounts i reported are from
In:=LeafCount[{{\[Gamma] -> -(c Sqrt[g00])/Sqrt[
c^2 g00 + g11 v^2]}, {\[Gamma] -> (c Sqrt[g00])/Sqrt[
c^2 g00 + g11 v^2]}}]
Out:=52
In:=LeafCount[{{\[Gamma] -> -c/Sqrt[c^2 + (g11 v^2)/g00]}, {\[Gamma] -
> c/
Sqrt[c^2 + (g11 v^2)/g00]}}]
Out:=44
In:=LeafCount[{{\[Gamma] -> -1/Sqrt[
1 + (g11 v^2)/(c^2 g00)]}, {\[Gamma] -> 1/Sqrt[
1 + (g11 v^2)/(c^2 g00)]}}]
Out:=43
Sorry for that,
Andreas