Please take a look at the attached file. My question refers to the last result: I get zero for the lie derivative.
It should depend on the values of v1, v2, v3, not zero. What I am missing?
Thanks for the report. You are of course right that the result shouldn't be zero.
Way, way back I made the assumption that when you are using 'natural' vectors, i.e. vectors of the form '@ x', then every thing you will be manipulating is explicitly expressed in these coordiantes. I see that this assumption is not a good one.
If you would have expressed your vector vr by
tvector x1,x2,x3;
vr := v1 * x1 + v2 * x2 + v3 * x3;
then you would have gotten the result you expected
You are right, of course; my bad.
I forgot to include the following line before the Lie derivative: f2 := d z ^ f1;
Then, I get the result I was expecting.
Daniel
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Now I would like to ask you about the style, how the result is presented:
Example f1 := x ^ d y + z ^ d z;
I get as result: f1 := d y x + d z z
I would like the result to be shown as: f1 := x d y + z d z;
as in books on the subject
Another example: f2 := d z ^ f1;
is shown as: f2 := - d y ^ d z x
I would like the result to be shown as: f2 := - x d y ^ d z
again, as in books on the subject
vr |_ f2;
I would like to be presented as (coeff1) d x ^ d y + (coeff2) d y ^ d z + (coeff3) d z ^ d x
that is, all the terms containing the same basic 2-form to be gathered together.
Is that possible?
Thanks,
Daniel
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi All,
Please take a look at the attached file. My question refers to the last result: I get zero for the lie derivative.
It should depend on the values of v1, v2, v3, not zero. What I am missing?
Thanks,
Daniel
Thanks for the report. You are of course right that the result shouldn't be zero.
Way, way back I made the assumption that when you are using 'natural' vectors, i.e. vectors of the form '@ x', then every thing you will be manipulating is explicitly expressed in these coordiantes. I see that this assumption is not a good one.
If you would have expressed your vector vr by
tvector x1,x2,x3;
vr := v1 * x1 + v2 * x2 + v3 * x3;
then you would have gotten the result you expected
I'll most likely remove the above said assumption from the code in the very near future.
Eberhard
Hi Eberhard,
Actually I was looking for the following result:
(-diff(v3,z)*x-diff(v2,y)*x-v1)*dy^dz-(diff(v2,x))*x*dx^dz+(diff(v3,x))*x*dx^dy;
Daniel
There must be something missing. You must have assigned something to f2 otherwise f2 would show up in the result you are looking for.
Eberhard
Hi Eberhard,
You are right, of course; my bad.
I forgot to include the following line before the Lie derivative:
f2 := d z ^ f1;
Then, I get the result I was expecting.
Daniel
Now I would like to ask you about the style, how the result is presented:
Example
f1 := x ^ d y + z ^ d z;
I get as result:
f1 := d y x + d z z
I would like the result to be shown as:
f1 := x d y + z d z;
as in books on the subject
Another example:
f2 := d z ^ f1;
is shown as:
f2 := - d y ^ d z x
I would like the result to be shown as:
f2 := - x d y ^ d z
again, as in books on the subject
vr |_ f2;
I would like to be presented as
(coeff1) d x ^ d y + (coeff2) d y ^ d z + (coeff3) d z ^ d x
that is, all the terms containing the same basic 2-form to be gathered together.
Is that possible?
Thanks,
Daniel