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April 12th, 2011, 08:00 AM   #1
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Reduced Monomials

Can someone please explain how to compute a set of grobner basis-reduced monomials, for example,

Let J denote the ideal in R[x,y,x];

J:=<x^2+y^2+z^2,x*y*z,x+y+z>

then a Grobner basis with respect to the ordering x>y>z is

GB:=(z^3,y^2+z^2+y*z,x+y+z)

and the set of Grobner basis-reduced monomials is:

rM(GB):={1,y,z,z^2,zy,y*z^2}

I'm not entirely sure how these sets are generated, could someone please exaplain?

Thanks.
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