Doktorandseminarium: Gröbner bases in polynomial rings

  • Datum:
  • Plats: Ångströmlaboratoriet 2004
  • Föreläsare: Oleksandra Gasanova
  • Kontaktperson: Volodymyr Mazorchuk
  • Seminarium


Let R=K[x_1,...x_n] be a polynomial ring and let J be an ideal in this ring. A Gröbner basis of J is a specific kind of generating set of this ideal which allows us to see important properties of J and the associated algebraic variety like dimension and the number of zeros when it's finite; given a polynomial f, a Gröbner basis of J will tell us whether f belongs to J or its radical etc. Gröbner basis computation can be seen as a multivariate non-linear generalization of both Euclid's algorithm for computing polynomial greatest common divisors and Gaussian elimination for linear systems. In my talk I will introduce the notion, construction and main applications of Gröbner bases.