Invariants in a sentence

The human aspect of learning is one of the few invariants.

A class also defines its invariants, and contains other properties, such as a "notes" section for documentation and metadata.

An upshot of this is that "setters" can, and normally do, implement the invariants for which Eiffel provides syntax.

Currently there are several well-known unknot recognition algorithms (not using invariants), but they are either known to be inefficient or have no efficient implementation.

Differential topology Differential topology is the study of (global) geometric invariants without a metric or symplectic form.

Due to the rich complexity of physics, many different fields possess different physical invariants.

Encapsulation of state is necessary for being able to enforce the invariants of the class.

Gibson works from the assumption that singular entities, which he calls "invariants", already exist in the real world and that all that the perception process does is to home in upon them.

Hilbert (1890) proved the theorem (for the special case of polynomial rings over a field) in the course of his proof of finite generation of rings of invariants.

Introduction of various invariants of torsion-free abelian groups has been one avenue of further progress.

Invariant expressions, particularly inner products of 4-vectors with themselves, provide equations that are useful for calculations, because one doesn't need to perform Lorentz transformations to determine the invariants.

It turns out that an arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants.

Logarithms of infinite cardinals are useful in some fields of mathematics, for example in the study of cardinal invariants of topological spaces, though they lack some of the properties that logarithms of positive real numbers possess.

Loop invariants are used to monitor specific properties of a loop during successive iterations.

Many cardinal invariants have been studied, and the relationships between them are often complex and related to axioms of set theory.

Object-oriented design uses the access specifiers in conjunction with careful design of public method implementations to enforce class invariants—constraints on the state of the objects.

Poincaré also developed a general theory of integral invariants and solutions of the variational equations.

Some programming languages, such as Eiffel contain native support for loop variants and invariants.

The automorphism group of a finite abelian group can be described directly in terms of these invariants.

The index theorem can also be run "in reverse": the index is obviously an integer, so the formula for it must also give an integer, which sometimes gives subtle integrality conditions on invariants of manifolds.