Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Advanced Algebra: Along with a Companion Volume 'Basic Algebra'
Advanced Algebra: Along with a Companion Volume 'Basic Algebra'
Algorithms for computing triangular decompositions of polynomial systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
| Hi-index | 0.00 |
As pointed out by Fulton in his Intersection Theory, the intersection multiplicities of two plane curves V(f) and V(g) satisfy a series of 7 properties which uniquely define I(p;f,g) at each point p∈V(f,g). Moreover, the proof of this remarkable fact is constructive, which leads to an algorithm, that we call Fulton's Algorithm. This construction, however, does not generalize to n polynomials f1, …, fn. Another practical limitation, when targeting a computer implementation, is the fact that the coordinates of the point p must be in the field of the coefficients of f1, …, fn. In this paper, we adapt Fulton's Algorithm such that it can work at any point of V(f,g), rational or not. In addition, we propose algorithmic criteria for reducing the case of n variables to the bivariate one. Experimental results are also reported.