Let k be a field and R=k[x, y] be a polynomial ring in two variables. Let...

 

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Let k be a field and R=k[x, y] be a polynomial ring in two variables. Let f =x*y-y+x, f = xy -x and I=< f.f,>c R be an ideal with deglex term ordering taking x<y. Find a Grobner basis of I in term of f, and f,. Let k be a field and R=k[x, y] be a polynomial ring in two variables. Let f =x*y-y+x, f = xy -x and I=< f.f,>c R be an ideal with deglex term ordering taking x<y. Find a Grobner basis of I in term of f, and f,.