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D.15.11.4 parametrizeOrbit

Procedure from library orbitparam.lib (see orbitparam_lib).

Usage:
parametrizeOrbit(L,v); L list, v matrix.

Assume:
L is a list of strictly upper triangular n x n matrices of same size. The vector space <L> genererated by the elements of L should be closed under the Lie bracket.
v is matrix of constants of size n x 1.
The basering has at least size(L) variables. However we will only use tangentGens(L,v)[1] many of them.

Return:
list, with four entries
- int, dimension of the orbit
- matrix A over the basering giving a parametrization of the orbit of v under the action of exp(<L>).
- list of integers, with the (row)-indices of entries which can be deleted by the action
- the variables of the parametrization to solve for

Theory:
We apply the theorem of Chevalley-Rosenlicht. First we determine tangent space generators, then apply matrixExp to the generators, and finally take the product to obtain the parametrization.

Example:
 


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