###### Answer: A. 3(6)-1/2(6)+1

but p( x y) is not monic as an element in R [ x ][y] since then the highest degree coefficient (i.e. the y 2 coefficient) is 2x − 1 . There is an alternative convention which may be useful e.g. in Gröbner basis contexts: a polynomial is called monic if its leading coefficient (as a multivariate polynomial) is 1 .

Wed Nov 10 2004 13:30:00 GMT-0500 (Eastern Standard Time) · Therefore let f( x ) = g( x ) = 2x + 1 . Then f( x )g( x ) = 4x 2 + 4x + 1 = 1 . Thus deg(f⋅g) = 0 which is not greater than the degrees of f and g (which each had degree 1 ). Since the norm function is not defined for the zero element of the ring we consider the degree of the polynomial f( x ) = 0 to also be undefined so that it follows the rules of a …

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The key to the proof is to note that when x ∈ L A( x ) is very large and when x ∉ L A( x ) is very small. By using bitwise parity ⊕ a set of transforms can be defined as A( x ) ⊕ t={ r ⊕ t | r ∈ A( x )}. The first main lemma of the proof shows that the union of a small finite number of these transforms will contain the entire space of …

In many occasions in physics associated Legendre polynomials in terms of angles occur where spherical symmetry is involved. The colatitude angle in spherical coordinates is the angle used above. The longitude angle appears in a multiplying factor.Together t…