Re: Is Mathematica capable of doing this?
- To: mathgroup at smc.vnet.net
- Subject: [mg37488] Re: [mg37469] Is Mathematica capable of doing this?
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Fri, 1 Nov 2002 01:43:28 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On Thursday, October 31, 2002, at 04:42 AM, Liguo Song wrote: > Dear MathGroup, > > I am in the process of learning to use Mathematica. Here are a couple > of > questions that I want to ask the group. > > 1) Can I define a new object, Tensor, which will act like Complex? So, > two > Times[TensorA, TensorB] or TensorA*TensorB will invoke proper Times > function to > handle it. > See the examples in the help for Outer. > 2) If the answer to the above question is yes, then can I use > super/sub-scripts > to represent the indices for the Tensor, and carry out the calculation > based on > these indices? Such as, g^uv*T_vk will get T^u_k, which essentially > raises the > first index of T_vk. Another example would be g^uv*T_uv will get a > scalor T. > Unfortunately tensors in Mathematica are represented as nested lists so no information about super or subscripts is retained. You have to keep track of that information yourself, but since Outer is defined the results of computations will be correct. > I know there are couple of Tensor analysis packages, comercial and > free, out > there. But, all the free packages I looked through won't be able to do > this. > And, figuring out how to do stuff is the best to learn how to use > Mathematica. > > Maybe, I am pursuing a dragon egg here. But, I'd still like to hear > about how > well Mathematica can do to imitate this behavior. > I have little experience with Tensor Analysis. From what I can tell the tools are available in Mathematica to construct a Tensor Analysis package though. A quick search reveals the commercial package MathTensor from http://smc.vnet.net/MathTensor.html and the free package Ricci available at http://www.mathsource.com/Content/Applications/Mathematics/0204-084. Regards, Sseziwa