Polynomials, invariants and computer algebra

Mihaela Popoviciu Draisma, Mathematical Institute Basel

My talk deals with invariants of binary forms of degree 7. Binary forms are homogeneous polynomials in two variables with complex coefficients. We denote by Rd the ring of invariants of binary forms of degree d. People studied intensively the structure of Rd in the 19th century, trying to answer the question "Is the ring Rd finitely generated over C for any d ?". David Hilbert answered this question with his two brilliant papers published in 1890 and 1893: "YES". However, until today, people were able to give a system of generators for Rd only for a few cases: for 2 ≤ d ≤ 8. The case d = 8 was solved in 1967 by Shioda. I will speak in my talk about systems of generators for R7.

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