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algorithms arithmetic Arakelov divisor class group baby steps base change Bessel's inequality complexification coprime Category Theory Cauchy-Schwarz inequality Cayley-Hamliton Chinese Remainder Theorem Cramer's rule derivative determinant diagonalizable matrices discrete logarithm distributive law divisor class group double dual dual space DLP equation Euclidean domain Extended Euclidean Algorithm f-representation finite abelian group finite cyclic groups function field functional calculus fundamental theorem of algebra Faà di Bruno's formula generalized mean inequality genus giant steps global field greatest common divisor group functors group objects group structure Gibb's inequality Gram-Schmidt orthogonalization Hasse derivative Heaviside's fraction decomposition Hensel's lemma Hölder's inequality inequalities inequality inequality of arithmetic and geometric mean inequality of weighted arithmetic and geometric mean infrastructure Identity Theorem Jensen's inequality Jordan decomposition lattice determination linear system of equations log-sum inequality Leibniz rule multiplicative Maclaurin's inequality Mahler's inequality Minkowski's inequality Muirhead's inequality n-dimensional number field Newton iteration Newton's inequalities one-dimensional p-adic integers partial derivatives partial fractions partial Hasse derivatives probability of being coprime Parseval's identity Pythagorean means reduction representable functors ring Rao-Blackwell Theorem tensor product topological argument transposition triangle inequality Taylor expansion Taylor's formula universal property Yondea's lemma Young's inequality (on numbers) Zariski topology