Effective Bounds for Polynomial Systems Defined Over the Rationals - Lecture 1

In this lecture, Teresa Krick explores effective bounds for polynomial systems defined over rational numbers. Learn about various tools for measuring the computational cost of solving computer algebra problems described by polynomials with rational coefficients. The presentation covers bounds for degrees and heights (bit-sizes) of outputs relative to input data, with detailed explanations of arithmetic Bézout inequality and applications to zero-dimensional polynomial systems. If time permits, the lecture also addresses the Nullstellensatz and Perron's theorem for implicitization. This 87-minute recording was captured during the "Francophone Computer Algebra Days" at the Centre International de Rencontres Mathématiques (Marseille, France) on March 13, 2025, and is available with chapter markers, keywords, abstracts, and bibliographies through CIRM's Audiovisual Mathematics Library.