>
|
|
First initialize several different jet spaces over bundles , . The dimension of the base spaces are dim() =2, dim() =1, dim() =3.
>
|
|
Example 1.
Define a transformation . This transformation is a projectable transformation and therefore pullbacks by the prolongation of can be calculated directly using the Pullback command.
E3 >
|
|
| (2.1) |
E1 >
|
|
| (2.2) |
E1 >
|
|
| (2.3) |
Pullback the contact 1-form Cv[1] on to a contact form on -- this can be done with either the Pullback command or the ProjectedPullback command.
E1 >
|
|
E1 >
|
|
Example 2
Define a point transformation and prolong it to a transformation .
E1 >
|
|
| (2.6) |
E1 >
|
|
| (2.7) |
Calculate the projected pullback of the type (1, 0) form .
E1 >
|
|
Calculate the projected pullback of the type (1, 1) form .
E3 >
|
|
| (2.10) |
To illustrate the definition of the projected pullback we re-derive this result using the usual Pullback command. First convert from a bi-form to a form .
E1 >
|
|
| (2.11) |
Then pullback using
E3 >
|
|
| (2.12) |
Then convert back to a bi-form and take the type [1, 1] part.
E1 >
|
|
| (2.13) |
Example 3
Define a differential substitution and prolong it to a transformation .
E1 >
|
|
| (2.14) |
E2 >
|
|
| (2.15) |
Calculate the projected pullback of the type (1, 0) form
E2 >
|
|
Calculate the projected pullback of the type (1, 0) form
E2 >
|
|
| (2.17) |