Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2011

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

Search the Archive

Re: Full simplify problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122272] Re: Full simplify problem
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sun, 23 Oct 2011 06:22:52 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j7u59t$u$1@smc.vnet.net>

On Oct 22, 1:18 pm, "A. Lapraitis" <ffcita... at gmail.com> wrote:
> Hello,
>
> Could anyone explain why the following does not give zero?
>
> In[72]:= Assuming[
>  x == y + z,
>  FullSimplify[
>   E^x - E^(y + z)
>   ]
>  ]
>
> Out[72]= E^x - E^(y + z)
>
> Thanks!

Wow! This is rather strange! Here is some similar examples

In[31]:= Assuming[x - y == 0, FullSimplify[E^x - E^(y + z)]] (*works*)

Out[31]= E^y*(1 - E^z)

In[36]:= Assuming[x - y == 2, FullSimplify[E^x - E^(y + z)]](*not
works*)

Out[36]= E^x - E^(y + z)

In[37]:= Assuming[x == y, FullSimplify[E^x - E^(y + z)]] (*works*)

Out[37]= E^y*(1 - E^z)

In[30]:= Assuming[x == 2*y, FullSimplify[E^x - E^(y + z)]] (*not
works*)

Out[30]= E^x - E^(y + z)

Somehow FullSimplify need some push in order to simplify your
expression and similar ones.
I don't claim this is a normal behavior, I don't have any explanation
for it, I don't know what
I would do if I didn't have some knowledge of Mathematica but I found
the following
workaround (not trivial indeed)  for your example:

In[69]:= Assuming[x == y + z, FullSimplify[E^x - E^(y + z),
ComplexityFunction -> (If[Head[#1] === Power, 1, 0] & )]]

Out[69]= 0

This does the same

In[70]:= Assuming[x == y + z, FullSimplify[E^x - E^(y + z),
ComplexityFunction -> (Count[{#1}, _Power, Infinity] & )]]

Out[70]= 0

(You can use the option ComplexityFunction to specify different
simplicity criteria. Here the goal is to avoid Power if possible.
Remember that Head[Exp[z]] is Power and FullForm[Exp[z]] is
Power[E,z].)

I would also add that for my similar examples mentioned above a
workaround could be:

In[80]:= TrigToExp[Assuming[x == 2*y, FullSimplify[E^x - E^(y + z),
ComplexityFunction -> (Count[{#1}, _Power, Infinity] & )]]]

Out[80]= E^(2*y) - E^(y + z)

In[82]:= TrigToExp[Assuming[x - y == 2, FullSimplify[E^x - E^(y + z),
ComplexityFunction -> (Count[{#1}, _Power, Infinity] & )]]]

Out[82]= E^(2 + y) - E^(y + z)

Best Regards
Dimitris





  • Prev by Date: AbsoluteTime[] runs slowly?
  • Next by Date: Re: Ticks without labels
  • Previous by thread: Re: Full simplify problem
  • Next by thread: Re: Full simplify problem