Doktorandseminarium: Gröbner bases in polynomial rings
- Plats: Ångströmlaboratoriet 2004
- Föreläsare: Oleksandra Gasanova
- Kontaktperson: Volodymyr Mazorchuk
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.