Algebraic in a sentence

Algebraic geometry has traditionally meant the understanding of geometric objects, such as algebraic curves and surfaces, through the study of the algebraic equations for those objects.

Figurine algebraic notation Figurine algebraic notation (or FAN) is a widely used variation of algebraic notation which substitutes a piece symbol for the letter representing a piece, for example: ♞c6 in place of Nc6.

It follows that real algebraic geometry is not only the study of the real algebraic varieties, but has been generalized to the study of the semi-algebraic sets, which are the solutions of systems of polynomial equations and polynomial inequalities.

The name algebraic integer comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers.

Topological spaces with algebraic structure For any algebraic objects we can introduce the discrete topology, under which the algebraic operations are continuous functions.

Algebraic and transcendental numbers main An algebraic number is a number that is a root of a non-zero polynomial equation in one variable with rational coefficients (or equivalently — by clearing denominators — with integer coefficients).

Algebraic combinatorics is continuously expanding its scope, in both topics and techniques, and can be seen as the area of mathematics where the interaction of combinatorial and algebraic methods is particularly strong and significant.

Algebraic logic Algebraic logic uses the methods of abstract algebra to study the semantics of formal logics.

Algebraic notation" in citation Abbreviated (or short) algebraic notation generally records moves in the format "abbreviation of the piece moved – file where it moved – rank where it moved".

Algebraic properties When many partially transparent layers need to be composited together, it is worthwhile to consider the algebraic properties of compositing operators used.

Algebraic structure and the word problem There are a number of results that relate solvability of the word problem and algebraic structure.

Algebra In general, for an algebraic category C, an embedding between two C-algebraic structures X and Y is a C-morphism e:X→Y which is injective.

All rational numbers are algebraic, and all constructible numbers are algebraic.

An algebraic set is called irreducible if it cannot be written as the union of two smaller algebraic sets.

A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud (1995), which uses "h A " to mean the covariant hom-functor.

Another formal generalization is possible to Universal algebraic geometry in which every variety of algebras has its own algebraic geometry.

Applications of algebraic topology Classic applications of algebraic topology include: * The Brouwer fixed point theorem : every continuous map from the unit n-disk to itself has a fixed point.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

Further, the geometric structure of the spectrum of the ring (equivalently, the algebraic structure of the module) captures the behavior of the spectrum of the operator, such as algebraic multiplicity and geometric multiplicity.

General algebraic framework on semirings: the algebraic path problem Many problems can be framed as a form of the shortest path for some suitably substituted notions of addition along a path and taking the minimum.