Gröbner Bases and Applications in Java - KRUM Server

Reduction
● removal of terms in a polynomial by
subtraction of multiples of a polynomial taken
from a list of polynomials
● extended reduction
R=K [ x 1 ,... , x n] , f , g ,h∈R , F ⊂R ,a∈K ,t ∈T
f g f ' , f '= f – a t g , LM a t g=m ∈ f
f F h , f = f 0 g1 f 1 ... gk f k=h , g i∈F
Lemma : f ' T f , h T f , k0
f F h , f =∑ g∈F h g gh , for some h g∈R , g∈F