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Re: Decompose function into one function for each variable

• To: mathgroup at smc.vnet.net
• Subject: [mg80809] Re: Decompose function into one function for each variable
• From: Szabolcs <szhorvat at gmail.com>
• Date: Sun, 2 Sep 2007 02:58:04 -0400 (EDT)
• Organization: University of Bergen
• References: <fbaqnl$qba$1@smc.twtelecom.net>

tomfabtastic at hotmail.com wrote:
> Hello,
> 
> I have a function :
> 
> k[lgd_, pd_] := A[lgd] * B[pd] * C[pd] - D[lgd] * E[pd] * C[pd]
> 
> and I woulud like to decompose the function into :
> 
> k[lgd_, pd_] = Y[lgd] + Z[pd]
> 
> Any ideas how I can make this decomposition ?
> 
> Thanks,
> Tom

It is generally (mathematically) impossible to rewrite a function of the 
form
k(lgd, pd) = A(lgd)*B(pd)*C(pd) - D(lgd)*E(pd)*C(pd)
to
k(lgd, pd) = Y(lgd) + Z(pd)

E.g. when you change the value of pd, the change in Y(lgd) + Z(pd) does 
not depend on the value of lgd.  This is not generally true for 
A(lgd)*B(pd)*C(pd) - D(lgd)*E(pd)*C(pd).

But it is possible that I did not understand your question correctly 
(and its connection to Mathematica) ...

Szabolcs