Detecting Algebraic Curves in Bad Position

K. Kalorkoti

Research output: Contribution to journalArticlepeer-review


Two affine algebraic curves over the complex numbers are in bad position if they have at least two distinct common points on some vertical line, i.e. for some α ∈ C there are distinct β1 , β2 ∈ C such that (α,β1) and (α, β2) are common points of the curves. We describe a method for detecting this situation and use it to develop an algorithm for finding the common points of two algebraic curves along with their multiplicities. We also give a worst case runtime analysis for the two algorithms and include a brief comparison of the second one with an approach using Gröbner bases.
Original languageEnglish
Pages (from-to)671-690
Number of pages20
JournalJournal of Symbolic Computation
Issue number6
Publication statusPublished - Jun 2001


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