We propose a new framework for discussing computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represente...
In this work, we employ a complex representation for an algebraic curve, and illustrate how the algebraic transformation which relates two Euclidean equivalent curves can be deter...
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations o...
Changbo Chen, James H. Davenport, John P. May, Mar...
This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional non-autonomous differential equations: those with the r...
Let f be a univariate polynomial with real coefficients, f ∈ R[X]. Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for is...