Deciding if a variety forms an algebraic group

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Let n be a positive integer and let f₁,, fᵣ be polynomials in n² indeterminates over an algebraically closed field K. We describe an algorithm to decide if the invertible matrices contained in the variety of f₁,, fᵣ form a subgroup of GL(n,K); that is, we show how to decide if the polynomials f₁,, fᵣ define a linear algebraic group.