algebraic multiplicity
41Weil reciprocity law — In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K ( C ) of an algebraic curve C over an algebraically closed field K . Given functions f and g in K ( C ), i.e. rational functions on C , then: f ((… …
42Linear system of divisors — A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of… …
43Formal derivative — In mathematics, the formal derivative is an operation on elements of a polynomial ring which mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on… …
44List of commutative algebra topics — Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative… …
45Theta-divisor — In mathematics, the theta divisor Theta; is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally polarized) by the zero locus of the associated Riemann theta function. It is… …
46Newton's method — In numerical analysis, Newton s method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real valued function. The… …
47Dual curve — Curves, dual to each other; see below for properties. In projective geometry, a dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to its dual,… …
48Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 …
49Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… …
50Milnor number — In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either an… …
