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Example 1.
Search through the ["Winternitz", 1] library of Lie algebras and find all the Lie algebras of dimension 4 which are solvable but not nilpotent. First we use the command Query to construct the necessary procedures.
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Now narrow the search to find those Lie algebras with a 2 dimensional derived algebra.
alg_name >
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alg_name >
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Thus we conclude that there are just two 4 dimensional solvable and not nilpotent Lie algebras with 2 dimensional derived algebras in the Winternitz table. We can use the Browse command to view these Lie algebras.
alg_name >
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Example 2.
Search through the first 25 vector field systems in the Gonzalez-Lopez table to see if there is a 3 dimensional semisimple vector field system whose prolongation to the 1-jet is not transitive. (A 3 dimensional vector field system will be non-transitive on the 1-jet if there is a non-trivial isotropy subalgebra.) These are precisely the actions which will admit a first order differential invariant.
alg_name >
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M >
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M >
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M >
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M >
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M >
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M >
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M >
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