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How do you use Congruences in a sentence? See 8 example sentences showing how this word appears in different contexts, plus the exact meaning.

Rare word

Congruences in a sentence

Related words

Congruences | Congruence

Congruences meaning

plural of congruence

Using Congruences

  • The main meaning on this page is: plural of congruence
  • In the example corpus, congruences often appears in combinations such as: of congruences, congruences and, these congruences.

Context around Congruences

  • Average sentence length in these examples: 25.9 words
  • Position in the sentence: 0 start, 4 middle, 4 end
  • Sentence types: 8 statements, 0 questions, 0 exclamations

Often before:

monoid 1×

Often after:

using 1× swap 1×

Sentence patterns with Congruences

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

duality these congruences swap 1× explains these congruences and more 1× remainders of congruences and of 1× system of congruences 1× system of congruences and gives 1× system of congruences using the 1× theory of congruences and upon 1× to monoid congruences and then 1×

Sentence openings and endings

Common sentence openings:

computational complexity since 1× in his opuscula 1× over principal ideal 1× regular polygons are 1× the author analyzes 1× this congruence and 1×

Common sentence endings:

a ring isomorphism 1× all modular forms 1× binary quadratic forms 1× methods of solution 1× monoid as above 1× system of congruences 1×

Words around Congruences

Just before it in the word index:

congruence 39 congreve 20 congresswomen 47 congresswoman 283 congressperson 11 congresspeople 8

Just after it in the word index:

congruent 71 congruential 2 congruity 2 congruous 3 congs 2 conh 2

Similar in corpus frequency:

aargau 11 abacos 11 abboud 11 abbreviate 11 abdelkader 11 abdomens 11

Corpus analysis for Congruences

  • In this selection, "congruences" usually appears in the middle of the sentence. The average example has 25.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, monoid, using and swap stand out and add context to how "congruences" is used.
  • Recognizable usage signals include duality these congruences swap and explains these congruences and more. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "congruences" sits close to words such as aargau, abacos and abboud, which helps place it inside the broader word index.

Example types with congruences

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

In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. (19 words)

Regular polygons are geometrically self-dual: all angles are congruent, as are all edges, so under duality these congruences swap). (20 words)

One does this by extending (finite) binary relations on Σ ∗ to monoid congruences, and then constructing the quotient monoid, as above. (21 words)

Longer example sentences

This congruence (and others like it that Ramanujan proved) inspired Jean-Pierre Serre (1954 Fields Medalist) to conjecture that there is a theory of Galois representations which "explains" these congruences and more generally all modular forms. (36 words)

Each of the shares is represented in a congruence, and the solution of the system of congruences using the Chinese remainder theorem is the secret to be recovered. (28 words)

Over principal ideal domains In main, the Chinese remainder theorem has been stated in three different ways: in terms of remainders, of congruences and of a ring isomorphism. (28 words)

Example sentences (8)

Computational complexity Since modular arithmetic has such a wide range of applications, it is important to know how hard it is to solve a system of congruences.

Each of the shares is represented in a congruence, and the solution of the system of congruences using the Chinese remainder theorem is the secret to be recovered.

In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution.

One does this by extending (finite) binary relations on Σ ∗ to monoid congruences, and then constructing the quotient monoid, as above.

Over principal ideal domains In main, the Chinese remainder theorem has been stated in three different ways: in terms of remainders, of congruences and of a ring isomorphism.

Regular polygons are geometrically self-dual: all angles are congruent, as are all edges, so under duality these congruences swap).

The author analyzes with remarkable clearness and order the works of mathematicians for the preceding century upon the theory of congruences, and upon that of binary quadratic forms.

This congruence (and others like it that Ramanujan proved) inspired Jean-Pierre Serre (1954 Fields Medalist) to conjecture that there is a theory of Galois representations which "explains" these congruences and more generally all modular forms.

Common combinations with congruences

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "congruences" in a sentence?
An example: "Computational complexity Since modular arithmetic has such a wide range of applications, it is important to know how hard it is to solve a system of congruences." This page contains 8 example sentences with the word "congruences" from authentic English texts.
What does "congruences" mean?
Congruences means: plural of congruence
How many example sentences with "congruences" are there?
Voorbeeldzinnen.info contains 8 example sentences with "congruences", drawn from a database of millions of English sentences.