Packet A: Tossup 17

One of these sets is most efficiently computed for a set in the graded reverse lexicographic monomial ordering. (10[1])One of these sets of an ideal I is defined as the set (10[1])of g’s (“gees”) such that the leading terms of g and I generate the same ideal; (10[1])those instances of these sets are computed using Buchberger’s (10[1])algorithm. (10[2]-5[1])These sets (10[1])name a theorem (10[1])that states the polynomial ring of a Noetherian (10[2])(“no-THEER-ee-in”) ring (10[1])is Noetherian, (10[2]-5[1])as (-5[2])proven by Hilbert. (10[3])The Legendre (10[2])polynomials (10[2])form a complete (10[1])one of these (10[1])sets (10[2])for (10[1])L2 (10[2]-5[1])(“L-two”) functions on the open (10[2])unit (-5[1])interval. (-5[1])One of these (-5[1])sets is found (10[2])by setting [read slowly] u-sub-one (10[2])to k-sub-one, (10[1])then iteratively setting (10[1])u-sub-n to k-sub-n (10[1])minus (10[1])a sum of projections (10[1])of k-sub-n (-5[1])onto u-sub-i. (10[4]-5[2])An orthonormal (10[2])one of these (10[2])sets (10[2])is constructed (10[2])using (10[1])the (10[1])Gram–Schmidt process. (10[2]-5[1])For 10 points, name these (10[1])linearly independent (-5[1])sets (10[1])that span (10[2])a vector (10[1])space. (10[2])■END■ (10[8]0[17])

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