More questions about Maxima's tensor functions

Hi Viktor,

Viktor T. Toth wrote:
> I also need to call your attention to the fact that
> 
> 	EQ:Q([],[])=b[ff]*(E([f,f],[]))^2
> 
> is not a valid itensor expression. You cannot have the same index (f) occur
> twice in a covariant position. I think what you are trying to say here
> should be expressed as
> 
> 	EQ:Q([],[])=b[ff]*(E([f],[f]))^2
> 
> where the same index occurring once in a covariant and once in a
> contravariant position implies summation. But this expression also will not
> work very well, since it is not linear in E([f],[f]), and itensor (and
> specifically, ic_convert()) loses track of indices.

As you can see I'm still in the learning stage here. I'm a bit confused 
by this because most texts eg YC Fung, "Foundations of Solid Mechanics", 
write the formulae using only covariant indices.
Another example is 
<http://www.engin.umich.edu/class/bme456/ch1mathprelim/bme456mathprelim.htm>;

Other texts avoid the issue by only working in orthonormal bases. 
Luckily I have one text by Sokilnokoff that expresses it in way that 
makes more sense to me in this context.

I think the part that I'm missing is that the tensor expressions I'm 
getting from the texts aren't referred to a basis so whenever one needs 
to generate components of that expression then the metric must appear.

So I think that I need to contract the E tensor with one of the metric 
tensors before I try to work with the components and that will raise one 
of the indices. Still trying to figure out exactly how to do that though.

Guessing...

The strain tensor is defined as

strain([i,j],[]) = (1/2)*(g([i,j],[]) - h([i,j],[]))

where g is the metric in the deformed configuration and h is the metric 
in the reference configuration.

The tensor I'm trying to work with is Greens strain which I think is 
E([i],[j]) = h([],[i,j])*strain([i,k],[]) or something like that.

> Lastly, I thank you for your patience as you're trying to put the tensor
> packages to good use. I am using these exchanges to gather information to
> find out what needs to be done to make the packages more usable. I think
> it's obvious that they were originally designed to assist with conventional
> gravity theories, 

:-) If you haven't studied that field then it's not obvious.

> but the design seems flexible enough to accommodate other
> needs... I've already taken care of a number of issues, and based on
> feedback like yours, I hope to be able to improve the packages more.

Can I suggest that the documentation might be updated to be make it 
clearer what the intended use of the ctensor package is?

Also a few more simple examples might help, perhaps some that don't make 
too many assumptions about the user's level of knowledge.

I got lost at the 2nd line of demo 1, where it says
"As an example, consider a conformally flat metric:"

Was kind of expecting the initial demos to follow along with the sorts 
of examples you might find in an introductory tensor analysis text. This 
is usually showing how to express and manipulate vector equations in 
tensorial notation eg dot and cross products.

I think a good start might be to take the text and examples from the 
introduction of your paper "Tensor Manipulation in GPL Maxima" and turn 
that into a demo.

If you think that's a good idea then once I have figured out how to 
drive it I may be able to help out with some of this.

Regards
Glenn

-- 
Glenn Ramsey  07 8627077
http://www.componic.co.nz