GradPack v1.1

*To*: mathgroup at smc.vnet.net*Subject*: [mg61473] GradPack v1.1*From*: "Ofek Shilon" <ofek at simbionix.com>*Date*: Wed, 19 Oct 2005 23:07:21 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi dear Mathgroup. I just submitted to the MathSource a notebook called GradPack v1.1, that personally made my life a lot easier - The original task it addressed was formulating gradients and hessians of complex potentials in R^n (i.e., real smooth functions on R^n). It evolved into a symbolic abstract-differentiation system, which enables computation of gradients of scalar fields and jacobiabs of vector fields. Both input and output are given at a coordinate-free abstract level - e.g., once the symbol v is declared as a vector, (using the appropriate syntax), you can immediately obtain results such as Grad[ ||v|| ^ 14 ] = 14 (||v||^12) Transpose[Jacobian[v]].v , and of course - variants up to arbitrary complexity. Elaborate examples are contained in the notebook. (this isn't the exact notation the notebook uses - it can't pass as ASCII text). The main design emphasis was on ease of use and intuitive notations. The notebook is available at - http://library.wolfram.com/infocenter/MathSource/5901/ I'd much appreciate any feedback & comments. Ofek Shilon