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7 g V V P 9 g V P 9 V 6 g V 6 g V sl 7 V 4 g V 6 V sl 5 u V 6 F b sus4 V sl 4 e from MUS 290 at Urbana University Smash Mouth Cant Get Enough OfIf v = f(x)=g(x) 2K(x) (with f(x);g(x) 6= 0 and (f(x);g(x)) = 1) is algebraic over K then let p(x) = a 0 a 1x a nxn 2Kx be its minimal polynomial Since p(x) is irreducible it follows that a 0 and a n are both nonzero Since p(v) = 0 it follows that a 0g(x)n a 1f(x)g(x)n 1 a nf(x)n = g(x)np(v) = 0 The previous equality implies12 3 V 11 g V 6 V 14 V 6 F b sus4 V P 12 V 2 g V 11 e V 4 g V sl 14 g V 4 V 2 g V 4 k V 4 G b m7add11 V 19 u V 4 g V M Full O 18 g V 4 g V 4 V u V 2 g V 18 e V 4 V 16 V 4 ALWAYS WITH ME, ALWAYS WITH YOU Joe Satriani Page 4 of 15 Generated using 1 Vroegop g.f.b.v