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D.15.11.5 maxZeros
Procedure from library orbitparam.lib (see orbitparam_lib).
- Usage:
- maxZeros(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:
- matrix of constants over the basering giving an element in the orbit of v
under the action of exp(<L>) with (at least) as many zeros as the dimension of the
orbit.
- Theory:
- We apply
parametrizeOrbit to obtain a parametrization of the orbit
according to the theorem of Chevalley-Rosenlicht. By determining the parameters from bottom to top
we find an element in the orbit with (at least) as many zeros as the dimension of the
orbit.
Example:
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