Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
System of polynomial equationsA system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers, K is generally assumed to be the field of complex numbers, because each solution belongs to a field extension of k, which is isomorphic to a subfield of the complex numbers.
Roadrunner (supercomputer)Roadrunner was a supercomputer built by IBM for the Los Alamos National Laboratory in New Mexico, USA. The US$100-million Roadrunner was designed for a peak performance of 1.7 petaflops. It achieved 1.026 petaflops on May 25, 2008, to become the world's first TOP500 LINPACK sustained 1.0 petaflops system. In November 2008, it reached a top performance of 1.456 petaFLOPS, retaining its top spot in the TOP500 list. It was also the fourth-most energy-efficient supercomputer in the world on the Supermicro Green500 list, with an operational rate of 444.
Jordan normal formIn linear algebra, a Jordan normal form, also known as a Jordan canonical form (JCF), is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them. Let V be a vector space over a field K.
