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Re: Change of Variables
*To*: mathgroup at smc.vnet.net
*Subject*: [mg32512] Re: Change of Variables
*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
*Date*: Fri, 25 Jan 2002 02:57:40 -0500 (EST)
*Organization*: Universitaet Leipzig
*References*: <a2onns$5v9$1@smc.vnet.net>
*Reply-to*: kuska at informatik.uni-leipzig.de
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
what is the difference between Replace[] and ReplaceAll[] ?
??ReplaceAll
"expr /. rules applies a rule or list of rules in an attempt to
transform \
each subpart of an expression expr"
While
??Replace
"Replace[expr, rules] applies a rule or list of rules in an attempt to \
transform the entire expression expr. Replace[expr, rules, levelspec]
applies \
rules to parts of expr specified by levelspec."
And
test^2 /. v -> c*beta
gives
beta^2
and
2*Pi*c^2*h/lambda^5*(E^(h*c/(lambda*k*T)) - 1)^(-1) /.
T -> h*c/(lambda*k x)
gives
(2*c^2*h*Pi)/((-1 + E^x)*lambda^5)
Regards
Jens
John S wrote:
>
> Hello,
>
> I would greatly appreciate any help with the following problem. I am trying
> to perform a change of variable in a function/definition so that I can
> integrate it. In particular, I want to take Planck's Radiation Law:
>
> planck=2*Pi*c^2*h/lambda^5*(E^(h*c/(lambda*k*T))-1)^(-1)
>
> and substitute x=h*c/(lambda*k*T) and integrate wrt lambda from 0 to
> infinity. I tried using replace, but that does not seem to try to
> manipulate the function in terms of x, but simply seek out the replacement,
> and if it exists, perform it.
>
> An even simpler example is the following:
>
> test=v/c
> Replace[test^2,v/c -> beta]
>
> does not yield beta^2, but rather v^2/c^2.
>
> Again, any and all help would be greatly appreciated.
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