Re: How do I create a parametric expression?
- To: mathgroup at smc.vnet.net
- Subject: [mg68609] Re: How do I create a parametric expression?
- From: axlq at spamcop.net (axlq)
- Date: Fri, 11 Aug 2006 04:40:53 -0400 (EDT)
- References: <200608090819.EAA21141@smc.vnet.net> <ebebuu$lhj$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <ebebuu$lhj$1 at smc.vnet.net>, Daniel Lichtblau <danl at wolfram.com> wrote: >This is probably best done with a form of algebraic replacement. I seem >to revisit this from time to time, for example see the URLs below. But >each time the code gets a bit longer. > >http://forums.wolfram.com/mathgroup/archive/2005/Apr/msg00273.html > >http://forums.wolfram.com/mathgroup/archive/2002/Jan/msg00354.html > >The code in those threads will not go inside transcendental functions. >So below is a modification that will. Wow. Thanks. I have bookmarked the links. The function leaves instances of Sqrt[R^2] behind, and one instance of (R^2)^(5/2), but those are easy to fix. >replacementFunction[expr_,rep_,vars_] := With[ > {num=Numerator[expr],den=Denominator[expr],hed=Head[expr]}, > If [PolynomialQ[num,vars] && PolynomialQ[den,vars], > PolynomialReduce[num, rep, vars][[2]] / > PolynomialReduce[den, rep, vars][[2]] > , (* else *) > If [Head[hed]===Symbol&&MemberQ[Attributes[hed],NumericFunction], > Map[replacementFunction[#,rep,vars]&, expr] > , (* else *)expr] > ] > ] > >Your example: > >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)); > >It appears to work best here if we do not encapsulate the thing we >replace in a square root. > >In[20]:= InputForm[replacementFunction[expr, a^2+(q-z)^2-R^2, {a,q,z}]] > >Out[20]//InputForm= >-((1 + 2*n)*((-R^2 + k^2*R^4 + q^2*(3 - k^2*R^2) + > q*(-6 + 2*k^2*R^2)*z + (3 - k^2*R^2)*z^2)*Cos[k*Sqrt[R^2]] - > k*Sqrt[R^2]*(-3*q^2 + R^2 + 6*q*z - 3*z^2)*Sin[k*Sqrt[R^2]])* > Sin[((Pi + 2*n*Pi)*z)/L])/(8*Pi*(R^2)^(5/2)*w) -Alex
- References:
- How do I create a parametric expression?
- From: axlq@spamcop.net (axlq)
- How do I create a parametric expression?