Re: How do I create a parametric expression?

*To*: mathgroup at smc.vnet.net*Subject*: [mg68568] Re: How do I create a parametric expression?*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Wed, 9 Aug 2006 23:57:09 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 8/9/06 at 4:19 AM, axlq at spamcop.net (axlq) wrote: >I'm trying to figure out how to simplify a large expression so that >it's expressed in terms of a sub-expression that's factored into the >larger one. >My expression looks like this: >-((1 + 2*n)*((a^4*k^2 + a^2*(-1 + k^2*(q - z)^2) + 2*(q - z)^2) >*Cos[k*Sqrt[a^2 + (q - z)^2]] - k*(a^2 - 2*(q - z)^2) *Sqrt[a^2 + (q >- z)^2]*Sin[k*Sqrt[a^2 + (q - z)^2]]) *Sin[((1 + >2*n)*Pi*z)/L])/(8*Pi*w*(a^2 + (q - z)^2)^(5/2)) >Now, I *know* there are places in there were Sqrt[a^2+(q-z)^2] >occurs, either by itself or raised to various powers. If I want to >define >R:=Sqrt[a^2+(q-z)^2] >...then how can I make Mathematica re-state my expression in terms >of R? The ReplaceRepated[] function doesn't seem to do the job. ReplaceAll (./) seems to work, i.e., In[5]:= expr=-((1 + 2*n)*((a^4*k^2 + a^2*(-1 + k^2*(q - z)^2) + 2*(q - z)^2)*Cos[k*Sqrt[a^2 + (q - z)^2]] - k*(a^2 - 2*(q - z)^2)*Sqrt[a^2 + (q - z)^2]* Sin[k*Sqrt[a^2 + (q - z)^2]])* Sin[((1 + 2*n)*Pi*z)/L])/ (8*Pi*w*(a^2 + (q - z)^2)^(5/2)); In[6]:= expr /. Sqrt[a^2 + (q - z)^2] -> R Out[6]= -(((2*n + 1)*((k^2*a^4 + (k^2*(q - z)^2 - 1)*a^2 + 2*(q - z)^2)*Cos[k*R] - k*R*(a^2 - 2*(q - z)^2)* Sin[k*R])*Sin[((2*n + 1)*Pi*z)/L])/ (8*Pi*w*(a^2 + (q - z)^2)^(5/2))) Of course this doesn't replace (a^2 + (q - z)^2)^(5/2) with R^5 That could be done as by modifying the replacement rule, i.e., In[7]:= expr /. a^2 + (q - z)^2 -> R^2 Out[7]= -((1/(8*Pi*(R^2)^(5/2)*w))*((2*n + 1)* ((k^2*a^4 + (k^2*(q - z)^2 - 1)*a^2 + 2*(q - z)^2)* Cos[k*Sqrt[R^2]] - k*Sqrt[R^2]*(a^2 - 2*(q - z)^2)* Sin[k*Sqrt[R^2]])*Sin[((2*n + 1)*Pi*z)/L])) This will leave terms like Sqrt[R^2] which can be eliminated using PowerExpand. However, the transformation made by PowerExpand isn't valid for all possible values of the variables -- To reply via email subtract one hundred and four