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2. Rational mapping - Wikipedia

   en.wikipedia.org/wiki/Rational_mapping

   Formally, a rational map: between two varieties is an equivalence class of pairs (,) in which is a morphism of varieties from a non-empty open set to , and two such pairs (,) and (′ ′, ′) are considered equivalent if and ′ ′ coincide on the intersection ′ (this is, in particular, vacuously true if the intersection is empty, but since is assumed irreducible, this is impossible).

3. Rational function - Wikipedia

   en.wikipedia.org/wiki/Rational_function

   A complex rational function with degree one is a Möbius transformation. Rational functions are representative examples of meromorphic functions. [3] Iteration of rational functions on the Riemann sphere (i.e. a rational mapping) creates discrete dynamical systems. [4] Julia sets for rational maps

4. Finite field arithmetic - Wikipedia

   en.wikipedia.org/wiki/Finite_field_arithmetic

   Multiplication in a finite field is multiplication modulo an irreducible reducing polynomial used to define the finite field. (I.e., it is multiplication followed by division using the reducing polynomial as the divisor—the remainder is the product.) The symbol "•" may be used to denote multiplication in a finite field.

5. Morphism of algebraic varieties - Wikipedia

   en.wikipedia.org/wiki/Morphism_of_algebraic...

   If X is a smooth complete curve (for example, P 1) and if f is a rational map from X to a projective space P m, then f is a regular map X → P m. [5] In particular, when X is a smooth complete curve, any rational function on X may be viewed as a morphism X → P 1 and, conversely, such a morphism as a rational function on X.

6. Field (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Field_(mathematics)

   Informally, a field is a set, along with two operations defined on that set: an addition operation written as a + b, and a multiplication operation written as a ⋅ b, both of which behave similarly as they behave for rational numbers and real numbers, including the existence of an additive inverse −a for all elements a, and of a multiplicative inverse b −1 for every nonzero element b.

7. List of mathematical functions - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_functions

   Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...