Zero-dimensional Ideals Research Articles

On radical zero-dimensional ideals

This paper shows an algorithm to construct the Gröbner bases of radicals of zero-dimensional ideals. Computing radicals is equivalent to solving systems of algebraic equations without counting the multiplicities of solutions. We prove that the Gröbner basis of a radical zero-dimensional ideal takes a special form after a suitable transformation of coordinates.

Zero-Dimensional Valuation Ideals Associated with Plane Curve Branches

Zero-Dimensional Valuation Ideals Associated with Plane Curve Branches