Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
Canonical comprehensive Gröbner bases
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Canonical comprehensive Gröbner bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Gröbner bases for families of affine or projective schemes
Journal of Symbolic Computation
Comprehensive involutive systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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In Electrical Engineering one of the most important problems to be solved for electrical networks is the load flow problem [6] [3]. Currently numerical solutions are provided by Newton's method, which involves recomputing the solution whenever the input data change. Given that this problem must be solved very often with different input data, the Gröbner basis can be an interesting approach since it can, in principle, provide a more algebraic solution of the input parameters and has to be solved completely only once, supplying formulas to compute single simulations. In this paper the basic ideas and a practical example are reported. Nevertheless, the required computations for practical network sizes are very complex and cannot yet be solved with the present algorithms.