*To*: mathgroup@smc.vnet.net*Subject*: [mg10744] Re: [mg10708] Derivative of implicit function*From*: seanross@worldnet.att.net*Date*: Mon, 2 Feb 1998 00:44:40 -0500*References*: <199801300924.EAA15409@smc.vnet.net.>

DEDONDER Philippe wrote: > > I'm a new user of Mathematica, and I would like to know if this software > can help me in solving the following problem: > > I have a function f(t,t*,x,y)=0, and I want to compute the derivative of > x (and also of y) with respect to t for t=t* and f(t,t*,x,y)=0. All I > 've managed to do till now is to give particular values to t and t* and > to Solve[f(x,y,t,t*)==0,{x,y}], which gives me particular values for x > and y (complex as well as real values). > > Can anyone help me to solve this problem? Without more information, the first thing that I think of is to change your variables. Intead of using t and t*, convert t->r Exp[j theta] and then use r and theta, so that t=t* would be when theta=0. Or -- use t->x+jy and then t=t* is when y=0. The idea of taking a derivative with respect to a complex quantity raises some questions about the best way to evaluate it. I think there may be some ambiguity in the way you decide to evaluate the derivatives. I think I would approach the derivatives by letting t*->t / Exp[2jtheta], then taking the derivative with respect to t and setting theta=0 at the end. Certainly mathematica could make the substitutions for you via transformation rules (expr/.{t->r Exp[2 I theta]}) and take the derivatives for you via D[] and even do some solving of equations for you via Solve[]. Good Luck. -- Remove the _nospam_ in the return address to respond.