w = superpotential B
This function uses the Koszul dual of the algebra to compute the superpotential of an m-Koszul AS regular algebra. The method is laid out in Dubois-Violette's original paper on derivation-quotient algebras. The basic algorithm is as follows: Since the algebra is m-Koszul, its homogeneous dual is isomorphic to the Ext algebra of the algebra, which is Frobenius since the algebra is AS regular. Suppose the "top form" of the Frobenius algebra is in degree m. Then given any monomial of degree m in the ambient tensor algebra of the Koszul dual, its image in the Koszul dual is a scalar multiple of this top form. This provides a functional from an appropriate tensor power, and the values of this functional are the coefficients of the superpotential.
For an easy example, the superpotential of the commutative polynomial ring is the "determinant form"; that is, it is the orbit sum over the symmetric group of the product of the variables, with coefficient given by the sign of the permutation.
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Skew polynomial rings with general skewing factors can also be considered. Here we use a field of rational functions over the rational numbers. As in the case of the rationals themselves, the default Groebner basis algorithm is not currently designed for such fields, so we include the "Naive" strategy to suppress warnings.
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As well as any quadratic AS regular algebra, such as Sklyanin algebras.
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Cubic AS-regular algebra of GK dimension three may also be considered
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The object superpotential is a method function with options.