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Symplectic is an English word. Below you'll find 10+ example sentences showing how it's used in practice.

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Symplectic in a sentence

Symplectic meaning

  1. Placed in or among, as if woven together.
  2. Whose characteristic abelian subgroups are cyclic.
  3. That is alternating and nondegenerate.

Using Symplectic

  • The main meaning on this page is: Placed in or among, as if woven together. | Whose characteristic abelian subgroups are cyclic. | That is alternating and nondegenerate.
  • In the example corpus, symplectic often appears in combinations such as: symplectic manifold, symplectic form, of symplectic.

Context around Symplectic

  • Average sentence length in these examples: 24.2 words
  • Position in the sentence: 6 start, 3 middle, 5 end
  • Sentence types: 13 statements, 1 questions, 0 exclamations

Often before:

almost 1× product 1×

Often after:

manifold 7× form 4× geometry 2× manifolds 2× topology 1× foliations 1×

Sentence patterns with Symplectic

These short patterns come directly from the example sentences and show how the word is often embedded:

2 a symplectic manifold is 1× an almost symplectic manifold is 1× called the symplectic form 1× close to symplectic geometry and 1× is a symplectic manifold really 1× manifolds and symplectic foliations also 1× metric or symplectic form 1× of a symplectic manifold are 1×

Sentence openings and endings

Common sentence openings:

an almost symplectic 1× ben webster what 1× by contrast with 1× differential topology differential 1× great russian encyclopedia 1× in dimension 2 1×

Common sentence endings:

a distinct discipline 1× a lagrangian immersion 1× a poisson manifold 1× also is developed 1× are locally isomorphic 1× area preserving diffeomorphism 1×

Words around Symplectic

Just before it in the word index:

symphysodon 2 symphony 779 symphonist 2 symphonisches 2 symphonique 5 symphonies 97

Just after it in the word index:

symplectomorphism 2 symplesiomorphy 2 sympodial 4 symposia 12 symposium 302 symposiums 10

Similar in corpus frequency:

aaronson 18 abai 18 abass 18 abatements 18 abdulfatah 18 abebe 18

Corpus analysis for Symplectic

  • In this selection, "symplectic" usually appears near the start of the sentence. The average example has 24.2 words, and this corpus slice is mostly made up of statements.
  • Around the word, almost, product, manifold, form and geometry stand out and add context to how "symplectic" is used.
  • Recognizable usage signals include 2 a symplectic manifold is and an almost symplectic manifold is. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "symplectic" sits close to words such as aaronson, abai and abass, which helps place it inside the broader word index.

Example types with symplectic

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Ben Webster: What is a symplectic manifold, really? (8 words)

Differential topology Differential topology is the study of (global) geometric invariants without a metric or symplectic form. (17 words)

It is close to symplectic geometry and like the latter, it originated in questions of classical mechanics. (17 words)

Longer example sentences

The introduction of a Riemannian metric or a symplectic form gives rise to a natural isomorphism between the tangent space and the cotangent space at a point, associating to any tangent covector a canonical tangent vector. (36 words)

An almost symplectic manifold is a differentiable manifold equipped with a smoothly varying non-degenerate skew-symmetric bilinear form on each tangent space, i.e., a nondegenerate 2- form ω, called the symplectic form. (34 words)

The quantization is simply where is the Lie derivative of a half-form with respect to a vector field X. Geometric quantization of Poisson manifolds and symplectic foliations also is developed. (31 words)

Question examples

Ben Webster: What is a symplectic manifold, really? (8 words)

Example sentences (14)

An almost symplectic manifold is a differentiable manifold equipped with a smoothly varying non-degenerate skew-symmetric bilinear form on each tangent space, i.e., a nondegenerate 2- form ω, called the symplectic form.

The definition of a symplectic manifold requires that the symplectic form be non-degenerate everywhere, but if this condition is violated, the manifold may still be a Poisson manifold.

The only invariants of a symplectic manifold are global in nature and topological aspects play a prominent role in symplectic geometry.

Ben Webster: What is a symplectic manifold, really?

By contrast with Riemannian geometry, where the curvature provides a local invariant of Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic.

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

Great Russian Encyclopedia (2005), Moscow : Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2. Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline.

In dimension 2, a symplectic manifold is just a surface endowed with an area form and a symplectomorphism is an area-preserving diffeomorphism.

Advertentie

It is close to symplectic geometry and like the latter, it originated in questions of classical mechanics.

Lagrangian mapping Let L be a Lagrangian submanifold of a symplectic manifold (K,ω) given by an immersion i : L ↪ K (i is called a Lagrangian immersion).

Non-degenerate skew-symmetric bilinear forms can only exist on even-dimensional vector spaces, so symplectic manifolds necessarily have even dimension.

One major example is that the graph of a symplectomorphism in the product symplectic manifold (M M, ω ω) is Lagrangian.

The introduction of a Riemannian metric or a symplectic form gives rise to a natural isomorphism between the tangent space and the cotangent space at a point, associating to any tangent covector a canonical tangent vector.

The quantization is simply where is the Lie derivative of a half-form with respect to a vector field X. Geometric quantization of Poisson manifolds and symplectic foliations also is developed.

Advertentie

Common combinations with symplectic

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "symplectic" in a sentence?
An example: "An almost symplectic manifold is a differentiable manifold equipped with a smoothly varying non-degenerate skew-symmetric bilinear form on each tangent space, i.e., a nondegenerate 2- form ω, called the symplectic form." This page contains 10+ example sentences with the word "symplectic" from authentic English texts.
What does "symplectic" mean?
Symplectic means: Placed in or among, as if woven together.
How many example sentences with "symplectic" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "symplectic", drawn from a database of millions of English sentences.