Re: General--Exponential simplifications by default

*To*: mathgroup at smc.vnet.net*Subject*: [mg69073] Re: General--Exponential simplifications by default*From*: p-valko at tamu.edu*Date*: Tue, 29 Aug 2006 03:26:19 -0400 (EDT)*References*: <200608250935.FAA09304@smc.vnet.net> <200608270524.BAA25573@smc.vnet.net> <ecu64l$7gu$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Thanks and basically I agree. However, a funny side effect is the following: Denominator[Exp[x] /. x -> -2 ] gives E^2 but Denominator[FullForm[Exp[x]] /. x -> -2 ] gives 1 In other words, wrapping the FullForm around an expression changes its "meaning". This contradicts the statement that >>FullForm acts as a "wrapper", which affects printing, but not evaluation.<< Or am I missing something? Andrzej Kozlowski wrote: > I do not consider any of these examples "a contradiction". What needs > to be understood is the difference between certain Mathematica > expressions before and after they are evaluated. In the case of your > examples consider: > > > Numerator[Unevaluated[Exp[-x]]] > > E^(-x) > > vs > > Numerator[Exp[-x]] > > 1 > > > Numerator[Unevaluated[1/Sqrt[2]]] > > 1 > > vs > > Numerator[1/Sqrt[2]] > > Sqrt[2] > > The cause of the apparent problem is that Numerator does not hold its > argument, so whiteout Unevaluated you are getting the numerator of > the whatever your expression evaluates to, not of your actual input. > TO get the latter you simply need to use Unevaluated. This is no > different from: > > > Numerator[3/6] > > 1 > > Numerator[Unevaluated[3/6]] > > 3 > > If this is not a contradiction than neither are the other examples. > Understanding the process of evaluation is perhaps the most important > thing when using functional languages (not just Mathematica, the same > sort of things occur, perhaps in an even more striking way, in > languages like Lisp ). > > Andrzej Kozlowski > > > > On 27 Aug 2006, at 07:24, p-valko at tamu.edu wrote: > > > Daniel, > > Could you tell me why the contradiction?: > > > > In[14]:=Exp[-x]//InputForm > > Out[14]//InputForm=E^(-x) > > > > In[15]:=Numerator[Exp[-x]]//InputForm > > Out[15]//InputForm=1 > > > > Mathematica automatically turns it into Power[E, Times[-1, x]], but > > the user > > beleives that the exponent is in the numerator. > > What you see is not what you get! > > > > > > My favorite contradiction is the following: > > > > In[24]:=Numerator[1/Sqrt[2]]//InputForm > > Out[24]//InputForm=Sqrt[2] > > > > In[25]:=Denominator[1/Sqrt[2]]//InputForm > > Out[25]//InputForm=2 > > > > I think "Numerator" and "Denominator" should not be allowed to do > > whatever they want. Too much liberty here... > > > > Peter > > > > > > Daniel Lichtblau wrote: > >> guillaume_evin at yahoo.fr wrote: > >>> Hi ! > >>> > >>> I want to avoid simplifications when Mathematica integrates > >>> expressions with exponential terms. For example, I have : > >>> > >>> In[8]= Espcond[y_] = Integrate[x*Densx[x, y], {x, 0, > >>> Infinity}, Assumptions -> alpha > 0] > >>> Out[8]= E^(-2eta y)(-theta + E^(eta y)(2+theta))/(2alpha) > >>> > >>> I do not want to have a factorization by E^(-2eta y). More > >>> precisely I would like to have the following result: > >>> Out[8]= (-theta E^(-2eta y)+ E^(-eta y)(2+theta))/(2alpha) > >>> > >>> I guess there is a way to tackle this problem with > >>> "ComplexityFunction" and "Simplify", but I tried different things > >>> such as "ComplexityFunction -> (Count[{#1}, Exp_, ∞] &)" in > >>> the "Simplify" function but no change appears. > >>> > >>> Is someone could give me some tricks on how tu use the > >>> "ComplexityFunction" ? > >>> > >>> Thank you in advance. > >>> > >>> Guillaume > >>> > >>> Link to the forum page for this post: > >>> http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp? > >>> pageName=Special:Forum_ViewTopic&pid=12974#p12974 > >>> Posted through http://www.mathematica-users.org [[postId=12974]] > >> > >> > >> Could Collect with respect to powers of the exponential. > >> > >> In[59]:= ee = E^(-2eta*y)*(-theta + E^(eta*y)(2+theta))/(2*alpha); > >> > >> In[60]:= InputForm[Collect[ee, Exp[eta*y]]] > >> Out[60]//InputForm= > >> -theta/(2*alpha*E^(2*eta*y)) + (2 + theta)/(2*alpha*E^(eta*y)) > >> > >> Daniel Lichtblau > >> Wolfram Research > >

**Follow-Ups**:**Re: Re: General--Exponential simplifications by default***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**General--Exponential simplifications by default***From:*guillaume_evin@yahoo.fr

**Re: General--Exponential simplifications by default***From:*p-valko@tamu.edu