Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the algorithmic problem of computing Cartan subalgebras in Lie algebras over finite fields and algebraic number fields.  present a deterministic polynomial time algorithm for the case when the ground fieldk is sufficiently large. Our method is based on a solution of a linear algebra problem: the task of finding a locally regular element in a subspace of linear transformations. Also,  give a polynomial time algorithm for restricted Lie algebras over arbitrary finite fields. Both methods require an auxiliary procedure for finding non-nilpotent elements in subalgebras. This problem is also treated. Computational experiences are discussed at the end of the paper.
['Willem A. de Graaf', 'Gábor Ivanyos', 'Lajos Rónyai']
I am writing a research paper on a idea Computing Cartan subalgebras of Lie algebras
[{"from": "human", "value": "I am writing a research paper on a idea Computing Cartan subalgebras of Lie algebras"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the algorithmic problem of computing Cartan subalgebras in Lie algebras over finite fields and algebraic number fields.  present a deterministic polynomial time algorithm for the case when the ground fieldk is sufficiently large. Our method is based on a solution of a linear algebra problem: the task of finding a locally regular element in a subspace of linear transformations. Also,  give a polynomial time algorithm for restricted Lie algebras over arbitrary finite fields. Both methods require an auxiliary procedure for finding non-nilpotent elements in subalgebras. This problem is also treated. Computational experiences are discussed at the end of the paper."}]