covariant

Definitions, parts of speech, synonyms, and sentence examples for covariant.

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Editorial note

This means that `[]` is covariant, while `Relation` and `{}` are contravariant.

Examples14

Definitions4

Parts of speech2

Quick take

(algebra) The variety defined by a covariant.

Meaning at a glance

The clearest senses and uses of covariant gathered in one view.

noun

(algebra) The variety defined by a covariant.

adjective

(object-oriented programming) Using or relating to covariance.

noun

(algebra) A bihomogeneous polynomial in x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.

Definitions

Core meanings and parts of speech for covariant.

noun

(algebra) The variety defined by a covariant.

adjective

(object-oriented programming) Using or relating to covariance.

noun

(algebra) A bihomogeneous polynomial in x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.

adjective

(category theory, of a functor) Which preserves the order of morphism composition: formally, which associates each morphism f:X→Y to a morphism F(f):F(X)→F(Y).

Example sentences

This means that `[]` is covariant, while `Relation` and `{}` are contravariant.

They are saying that the variation in tests can be lowered by including covariant variables in selection criteria.

The IP you know and love contracts over the covariant and contravariant indicies of two rank-1 tensors (vectors).

You'd need to determine which factors are important, which of those are covariant, and how that relationship works.

This is the same reason why arrays should not be covariant (even though they are in Java).

Dart's type system, in particular its covariant subtyping unsoundness, outraged Andreas Rossberg of the new V8 team.

You need a metric to do this so you can raise one of the contravariant indicies to be covariant.

Since List is covariant, this value can legally be passed to a function that expects a parameter of type List[Animal].

It has a generics system that makes a lot more sense (allowing covariant/contravariant types, rather than forcing use-site variance everywhere).

In the standard notation the distinction between vector spaces and dual vector spaces manifests itself in covariant and contravariant indices of tensors.

Since these are Euclidean spaces, the difference between contravariant and covariant indices is non-existent.

Here the matrix might be regarded as a rank 1,1 tensor (one covariant, one contravariant index) that you contract with the vector.

Quote examples

However, if one were to make the replacement d^{\mu} -> d^{\mu} - I e A^{\mu}(x,t) where when v -> v e^(-I* T(x,t)) we have that A^{\mu} -> A^{\mu} - d^{\mu} T(x,t) one can show (this doesn't have to be obvious!) that then the Lagrangian ~(D^{\mu}v)* D_{\mu}v - v* v (where D is the new "covariant derivative" we described above) is now invariant under local U(1) transformations.

Ultimately, to get the fullest understanding of this we would need to talk about vector dual spaces and note that expressions like f(x, y, z, w, q) could involve two "types" of vector spaces, covariant and contravariant, which have different kinds of transformation-under-basis-change properties.