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Re: Ask Mathematica to sub for a long expression

• To: mathgroup at smc.vnet.net
• Subject: [mg71934] Re: Ask Mathematica to sub for a long expression
• From: Peter Pein <petsie at dordos.net>
• Date: Mon, 4 Dec 2006 06:39:24 -0500 (EST)
• References: <ekp4o4$2fq$1@smc.vnet.net><ekrk8s$s3q$1@smc.vnet.net> <ekuctj$82t$1@smc.vnet.net>

Hi Philipp,

Sqrt[...] is no subexpression of Power[...,3/2].

Try:
In[1]:= expressionToBeReplaced = a_^2 + b_^2 - 2*a_*b_* Cos[theta];
In[2]:= 2*Sqrt[x^2 + y^2 - 2*x*y*Cos[theta]] +
   Sqrt[x^2 + y^2 - 2*x*y*Cos[theta]]^3 /. expressionToBeReplaced -> c^2
Out[2]= 2*Sqrt[c^2] + (c^2)^(3/2)
In[3]:= Simplify[%, c >= 0]
Out[3]= c*(2 + c^2)

HTH,
Peter

Philipp schrieb:
> Mark,
> 
> You are a bit condescending in your answer. Let's test your expertise.
> How about;
> 
> In[1]:=  expressionToBeReplaced = Sqrt[a_^2 + b_^2 -
>           2*a_*b_*Cos[theta]];
> 
> In[2]:=  2 Sqrt[x^2 + y^2 - 2*x*y*Cos[theta]] + Sqrt[x^2 + y^2 -
>            2*x*y*Cos[theta]]^3 /. expressionToBeReplaced -> c
> 
> still gives
> 
> Out[2]=  2*c + (x^2 + y^2 - 2*x*y*Cos[theta])^(3/2)
> 
> Cheers,
> 
> Philipp.
> 
> Mark Westwood wrote:
>> Hi Aaron
>>
>> The simple answer is that what you want to do is very easy in
>> Mathematica.  For example, define;
>>
>> In[3]:= xpr1 = 2 Sqrt[a^2 + b^2 - 2*a*b*Cos[theta]]  (* an expression
>> involving your long expression *)
>>
>> then execute
>>
>> In[5]:= xpr1/.Sqrt[a^2 + b^2 - 2*a*b*Cos[theta]] -> c
>>
>> Out[5]:= 2c
>>
>> and now your fun begins.  Note the use of the /. which is a shorthand
>> notation for the ReplaceAll function.  Check out the on-line Help for
>> this.  As it stands this replacement rule is very inflexible, it will
>> only replace expressions which exactly match the given one.  What you
>> might want to do is replace expressions which match a more general
>> pattern.  For example, suppose you assign the expression to be replaced
>> to a variable, like this
>>
>> In[12]:= expressionToBeReplaced = Sqrt[a_^2 + b_^2 -
>> 2*a_*b_*Cos[theta]]
>>
>> (* note carefully the underscores appended to the variable names, which
>> transforms them into Patterns -- back to the Help system for further
>> info on this *)
>>
>> and now you can try things like
>>
>> In[14]:= 2 Sqrt[x^2 + y^2 - 2*x*y*Cos[theta]] /. expressionToBeReplaced
>> -> c
>>
>> Out[14]:= 2c
>>
>> Now the replacement works for any expression which has the same
>> structure as the one you are seeking to replace.  OK, over to you, post
>> again when you've mastered simple replacement rules and want more
>> guidance.
>>
>> Regards
>> Mark Westwood
>>
>> aaronfude at gmail.com wrote:
>>> Hi,
>>>
>>> Is it possible to ask Mathematica to replace a long expression, such as
>>> Sqrt[a^2+b^2-2*a*b*Cos[theta]] with "c", whenever it encounters that
>>> long expression?
>>>
>>> Thanks!
>>>
>>> Aaron Fude
>