We consider resultant-based methods for elimination of indeterminates of Ore polynomial systems in Ore algebra. We start with defining the concept of resultant for bivariate Ore polynomials then compute it by the Dieudonne determinant of the polynomial coefficients. Additionally, we apply noncommutative versions of evaluation and interpolation techniques to the computation process to improve the efficiency of the method. The implementation of the algorithms will be performed in Maple to evaluate the performance of the approaches.

中文翻译：

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矿石代数中基于结果的消除

我们考虑基于结果的方法来消除矿石代数中矿石多项式系统的不确定性。我们首先定义双变量 Ore 多项式的结果概念，然后通过多项式系数的 Dieudonne 行列式计算它。此外，我们将评估和插值技术的非交换版本应用于计算过程，以提高方法的效率。算法的实现将在 Maple 中执行，以评估方法的性能。