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[Q] Implementing identities as rules
*To*: mathgroup at smc.vnet.net
*Subject*: [mg18608] [Q] Implementing identities as rules
*From*: "Kevin Jaffe" <kj0 at mailcity.com>
*Date*: Tue, 13 Jul 1999 01:01:32 -0400
*Organization*: MailCity (http://www.mailcity.lycos.com:80)
*Sender*: owner-wri-mathgroup at wolfram.com
During symbolic manipulations it often important to be able to use
both sides of an identity or definition. For example, let f be a
function defined by
In[1]:= f = Function[{x, y}, Exp[x^2 + y^2]];
Its partial derivative with respect to x is:
In[2]:= D[f[x, y], x]
2 2
x + y
Out[2]= 2 E x
Now, I want to recast this result in the form 2 x f[x, y], i.e. I want
to revert to the "left-hand side" of the original definition of f[x,
y]. How does one do this in Mathematica? I know that if I try the
rule
In[3]:= %2 /. Exp[a_^2 + b_^2] :> f[a, b]
2 2
x + y
Out[3]= 2 E x
I get the original expression, because when the pattern is replace,
f[a, b] is immediately evaluated to reproduce the original expression.
(I know that the replacement occurs because if instead I use a rule
whose right hand side cannot be evaluated further
In[4]:= %2 /. Exp[a_^2 + b_^2] :> g[a, b]
Out[4]= 2 x g[x, y]
I get the desired result.)
Is there a way to instruct Mathematica not to evaluate the expression
after the replacement has been made?
Thanks,
kj0 at mailcity.com
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