Re: Derivatives of user-defined control-flow functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg51090] Re: Derivatives of user-defined control-flow functions*From*: pein <petsie at arcor.de>*Date*: Mon, 4 Oct 2004 06:18:01 -0400 (EDT)*References*: <cjoiel$al2$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Maxim A. Dubinnyi schrieb: > Can anyone correctly define derivatives of > user-defined control-flow functions? > > The derivative of build-in control function 'If' is evaluated as: > > In[]= D[If[f[x], g[x], h[x]], x] > Out[]= If[f[x],g'[x],h'[x]] > > Which is perfectly correct answer. I wish to introduce my own > control flow function MyIf and define it's derivatives with > properties identical to ones in build-in If function. > Usually derivatives are defined via properties of > symbol 'Derivative' by setting > > Derivative[order...][function_name]:= (derivative definition) > > but this method fails in case of control-flow expressions. > The problem origin is in the rule for derivatives of > composite functions: > > In[]= D[f[g[x]], x] > Out[]= f'[g[x]]g'[x] > > This rule should not be applied if 'f' is control-flow function such > as 'If', 'Which', etc, and it is really so for build-in control-flow > expressions. But how can I suppress this deepely build-in rule for > some user-defined symbols? > > I am experienced user of Mathematica, and I use widely symbolic > and functional programming in my applications, > but can't find any solution of this problem. > > Is it the task which can't be solved by means of Mathematica > symbolic programming language? > > > Maxim A. Dubinnyi > That is what TagSet has been made for: MyIf /: D[MyIf[cond_, yes_, no_], x_] := MyIf[cond, D[yes, x], D[no, x]] -- Peter Pein, Berlin

**Follow-Ups**:**Re: Re: Derivatives of user-defined control-flow functions***From:*"Maxim A. Dubinnyi" <maxim@nmr.ru>