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ass4_1

# ass4_1 - G and r is reduced with respect to G Prove that r...

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MATH 335 001 Computational Algebra Winter 2006 Assignment 4.1 Grobner Basis Solve the following problems from the notes on Grobner basis: 1) 1.5.4 (page 32). 2) 1.5.5 (page 32). 3) 1.6.1 (page 36). 4) Let G and G 0 be two Grobner bases for an ideal I k [ X ] with respect to a fixed term order. Let f k [ X ]. Assume that f * G r and f * G 0 r 0 where r is reduced with respect to
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Unformatted text preview: G and r is reduced with respect to G . Prove that r = r . 5) Find a Grobner basis for an ideal I = h x 2 y + z,xz + y i ⊆ Q [ x,y,z ] with respect to deglex with x > y > z . 6) Verify if a polynomial f = x 3 y + 3 xz + 2 x 2 y 2 + 2 yz + 2 y belongs to the ideal I above....
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