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MathGroup Archive 2005

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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


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