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RE: Rule parameter passing

• To: mathgroup at smc.vnet.net
• Subject: [mg34871] RE: [mg34855] Rule parameter passing
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Tue, 11 Jun 2002 05:00:37 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: TerryH [mailto:tharter at attglobal.net]
To: mathgroup at smc.vnet.net
> Sent: Sunday, June 09, 2002 11:11 AM
> Subject: [mg34871] [mg34855] Rule parameter passing
> 
> 
> Hi All:
> 
>    What is the best way in which to write a rule in which the rule's
> parameters
> may vary?  I'm trying to do some symbolic replacements in 
> various matrix
> expressions,
> in which sometimes the variables are say aA and Subscript[ \[Delta] ,
> \[aA] ], and
> at other times the variables can be dD (say).
> I have been able to do this by applying succesive rules, as in
> 
>    matrix /. aA-> aA + Subscript[ \[Delta] , \[aA] ]  /. x_Subscript->
> fcn[ /[Delta], bB]  /.aA-> bB
> 
> where the function 'fcn' is:  fcn[y_,sub_] := ysub
> 
>    However, I need to embed this code inside a Module, and 
> have not been
> able to successfully pass
> variables into the successive transformation rules listed avove.
> 
> Anybody got any ideas on how to do this efficiently?  Is the onlty way
> to do this is to write a Package?
> Unfortunately, I have no experience in writing a package.  Thanks in
> advance to all who may reply!
> ....Terry
> 
> 

Terry,

rules are no different from other Mathematica expressions. To introduce
parameters you can e.g. use them at the rhs of a definition. Perhaps this
example might help (Just copy this into a notebook, convert the cell to text
and then to input and execute; or else copy each line and execute):
 
Attributes[dsplc] = {HoldAll};
Attributes[delta] = {HoldAll};

\!\(delta[x_] := \[Delta]\_x\)

dsplc[x_] := HoldPattern[x] :> x + delta[x]

expr = Normal[Series[ArcCos[x], {x, 0, 5}]]

((expr /. dsplc[x]) - expr)/delta[x] // Expand

Series[D[ArcCos[x], {x, 1}], {x, 0, 4}]



expr = Normal[Series[Exp[y], {y, 0, 10}]]

(((expr /. dsplc[y]) - expr)/delta[y] // Expand) /. delta[y] -> 0


--
Hartmut