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In this lecture, Teresa Krick explores effective bounds for polynomial systems defined over rational numbers, focusing on measuring the computational cost of solving computer algebra problems. Learn about tools that help determine bounds for degrees and heights (bit-sizes) of outputs based on input data characteristics. The presentation details an arithmetic Bézout inequality with applications to zero-dimensional polynomial systems, and covers the Nullstellensatz and Perron's theorem for implicitization if time permits. This is the second lecture in a series recorded during the "Francophone Computer Algebra Days" on March 14, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this and other mathematical talks in CIRM's Audiovisual Mathematics Library, featuring helpful functionalities like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search options.
