The symmetry Lie algebra of a unirational variety equals the linear maps sending each point into its tangent space and can be recovered from the Jacobian of a parametrization in polynomial-time Monte Carlo fashion.
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Computing the continuous symmetries of a parametrized variety
The symmetry Lie algebra of a unirational variety equals the linear maps sending each point into its tangent space and can be recovered from the Jacobian of a parametrization in polynomial-time Monte Carlo fashion.