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GF (2) GF (2) (also denoted , Z/2Z or ) is the finite field with two elements [1] (GF is the initialism of Galois field, another name for finite fields). Notations Z2 and may be encountered although they can be confused with the notation of 2 -adic integers . GF (2) is the field with the smallest possible number of elements, and is unique if ...
The polynomial is the Tutte polynomial of the bull graph. The red line shows the intersection with the plane , which is essentially equivalent to the chromatic polynomial. The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role ...
Curve fitting[ 1][ 2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [ 3] possibly subject to constraints. [ 4][ 5] Curve fitting can involve either interpolation, [ 6][ 7] where an exact fit to the data is required, or smoothing, [ 8][ 9] in which a "smooth" function is ...
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.
In mathematics, a graph polynomial is a graph invariant whose value is a polynomial. Invariants of this type are studied in algebraic graph theory. [1] Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. The chromatic polynomial, a polynomial whose values at integer arguments give the ...
The characteristic equation, also known as the determinantal equation, [1] [2] [3] is the equation obtained by equating the characteristic polynomial to zero. In spectral graph theory , the characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix .
Root-finding algorithm. In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a function cannot ...
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