how to obtain the inverse series for multivariable functions using

*To*: mathgroup at smc.vnet.net*Subject*: [mg130587] how to obtain the inverse series for multivariable functions using*From*: Qi Hao <xqi.hao at gmail.com>*Date*: Wed, 24 Apr 2013 07:02:54 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hello, everyone: Now, I have a question about how to obtain the inverse series for multivariable functions. The system of nonlinear equations is like this: x = f(p,q) y = g(p,q). The inverse functions are p = h(x,y) q = r(x,y). Now, I have known the taylor expansion of x and y with respect to p and q at point(0,0), that is x = f(0,0) + df/dp(0,0)p + df/dq(0,0)q + ... y = g(0,0) + dg/dp(0,0)p + dg/dq(0,0)q + ... I want to know the taylor expansion of the inverse functions, that is p = h(0,0) + dh/dx(0,0)x + dh/dx(0,0)y + ... q = r(0,0) + dr/dx(0,0)x + dr/dy(0,0)y + ... Could you show me your mathematica codes to solve this problem ? Thank you very much! Qi Hao