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