Streamlining Replace in Mathematica 8

[earth2]

Hi guys,

i have expressions of the type (X*a)(X*b). I want replace this by X^2(a*b).

So i tried building a block which does nothing but

%//.(X*a_)(X*b_)->X^2(a*b).

However, this works only if a is distinct from b. If a and b are equal if HAVE to use the replacement command

%//.(X*a_)(X*a_)->X^2(a*a).

Can I tweak the replace command s.t. Mathematica does the replacement even if a is equal to b, too, without having to write a new replacement command? That would be cool :)

Cheers,
earth2

 

[Bill Simpson]

What you see displayed in a notebook is very often different from what the internal form of the expression actually is. Pattern matching ALWAYS works on the internal form and NOT the displayed form.

Looking at the FullForm of an expression that doesn't pattern match shows you why the pattern match and what you need to match. (But that only works for simple pattern problems. For really hard pattern matching problems I have no advice for you.)

In[1]:= FullForm[(X*a)(X*b)]

Out[1]= Times[a,b,Power[X,2]]

This matches your pattern, believe it or not.

In[2]:= FullForm[(X*a)(X*a)]

Out[2]= Times[Power[a,2],Power[X,2]]

And that looks nothing like your pattern, which is why it doesn't match.

A less problematic method for this particular example that avoids all the problems with writing patterns

In[1]:= Collect[(X*a)(X*b),X]

Out[1]= a b X^2

In[2]:= Collect[(X*a)(X*a),X]

Out[2]= a^2 X^2

 

[earth2]

Hi and thanks for your answer. Ok, i just realize i have been too vague.

Acutally my expressions are of the type

MP[X,a_1]...MP[X,a_{2n}] where MP is the Minkowski scalar product. Some of the a_n might be the some. This can be replaced in my case (under an integral over X) by

X^{2n}*Symmetrized Product(MP[a_1,a_2]MP[a_2,a_3]...MP[a_{n-1},a_n]).

By hand this replacement can be easily done but how can i teach it to Mathematica? As I've said my goal is to have just one replacement rule which also takes into account if some of the a_n are not distinct.

Cheers.

EDIT: What would help me tremendously is a way to force Mathematica to write powers as products, i.e a^n as a*a*...*a (n times). :)

 

[Bill Simpson]

Hi and thanks for your answer. Ok, i just realize i have been too vague.

Acutally my expressions are of the type

MP[X,a_1]...MP[X,a_{2n}] where MP is the Minkowski scalar product. Some of the a_n might be the some. This can be replaced in my case (under an integral over X) by

X^{2n}*Symmetrized Product(MP[a_1,a_2]MP[a_2,a_3]...MP[a_{n-1},a_n]).

By hand this replacement can be easily done but how can i teach it to Mathematica? As I've said my goal is to have just one replacement rule which also takes into account if some of the a_n are not distinct.

We routinely see "how do I do this?" followed by "do this" followed by "I didn't actually want to do that, how about this?"

Post the simplest small notebook with the handful of examples that would solve all your problems if they could be done. Include what you have and exactly what you want the replacement to be that you have done by hand. Please don't include any typos.

Perhaps someone should create a really well written "READ ME" for the Math & Science Software section that encourages posters to do that. It might help streamline the process.

Reaching inside function arguments to make pattern substitutions raises the level of difficulty, sometimes substantially, but we can see what happens. Since Mathematica is an "infinite evaluation" system and evaluates things "all the way to the bottom" it is sometimes difficult to stop function evaluation until a pattern substitution can be done. It might be easier if your arguments could just be contained in a list. Then the substitutions could be done and finally the result then handed off to MP, but I don't know the specifics of your problem.

EDIT: What would help me tremendously is a way to force Mathematica to write powers as products, i.e a^n as a*a*...*a (n times). :)

General rule: Almost nobody successfully forces Mathematica to do anything. Every time you want to subvert and thwart what Mathematica wants to do you are waging an uphill battle. Trying to convince Mathematica to not do all the automatic things it does is probably going to lead you to a life of grief and failure. Get a FORTRAN compiler and write your own code and you will probably be happier.

 

[alphy]

mars

Hello earth2mars,

Thank you for sharing your question about streamlining replace in Mathematica 8. It seems like you are trying to find a more efficient way to perform a certain type of replacement in your expressions. I think there may be a couple of possible approaches to this problem.

One option could be to use the "ReplaceAll" function with a pattern that includes both a and b as distinct variables, but also allows them to be equal. For example, you could try something like this:

%//. (X*a_)(X*b_) | (X*a_)(X*a_) -> X^2(a*b)

This way, the pattern will match both cases where a and b are distinct, and where they are equal.

Another option could be to use the "ReplaceRepeated" function, which will continue to perform the replacement until the expression no longer changes. For example:

%//. (X*a_)(X*b_) -> X^2(a*b)

This way, the replacement will continue to be applied until it reaches the desired form, regardless of the values of a and b.

I hope this helps and provides some ideas for how to streamline your replacement process. Mathematica is a powerful tool for solving complex problems, and I'm sure you will be able to find a solution that works for your specific needs. Keep exploring and experimenting, and don't hesitate to reach out to the Mathematica community for more support and guidance. Best of luck in your research!