Random word

How do you use Diophantine in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.

Rare word

Diophantine in a sentence

Diophantine meaning

Of or pertaining to Diophantus, the Greek mathematician.

Using Diophantine

  • The main meaning on this page is: Of or pertaining to Diophantus, the Greek mathematician.
  • In the example corpus, diophantine often appears in combinations such as: diophantine equations, diophantine equation, of diophantine.

Context around Diophantine

  • Average sentence length in these examples: 20.3 words
  • Position in the sentence: 6 start, 8 middle, 6 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

linear 4× exponential 2× theory 1× term 1× solve 1× polynomial 1× equations 1× solving 1×

Often after:

equations 7× equation 7× geometry 3× problems 3× approximations 1× approximation 1× inequalities 1× analysis 1×

Sentence patterns with Diophantine

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

an exponential diophantine equation is 2× a linear diophantine equation has 1× both in diophantine geometry and 1× cases of diophantine inequalities 1× diophantine problems have 1× field of diophantine approximation deals 1× given a diophantine equation with 1× given polynomial diophantine equation with 1×

Sentence openings and endings

Common sentence openings:

an exponential diophantine 2× an example of 1× arithmetic geometry on 1× bézout s identity 1× diophantine problems have 1× given a diophantine 1×

Common sentence endings:

can be unknowns 2× linear diophantine equations 2× an integer solution 1× c are constants 1× called diophantine analysis 1× equations cannot exist 1×

Words around Diophantine

Just before it in the word index:

diopecephalus 2 diop 53 dionysus 66 dionysos 6 dionysius 70 dionysiou 2

Just after it in the word index:

diophantus 15 diopter 3 dioptrique 2 dior 165 diorama 26 dioramas 15

Similar in corpus frequency:

aare 29 aarti 29 abl 29 academician 29 acquaint 29 adegboyega 29

Corpus analysis for Diophantine

  • In this selection, "diophantine" usually appears in the middle of the sentence. The average example has 20.3 words, and this corpus slice is mostly made up of statements.
  • Around the word, linear, exponential, theory, equations, equation and geometry stand out and add context to how "diophantine" is used.
  • Recognizable usage signals include an exponential diophantine equation is and a linear diophantine equation has. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "diophantine" sits close to words such as aare, aarti and abl, which helps place it inside the broader word index.

Example types with diophantine

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

Solving Diophantine equations is a very hard task. (8 words)

Bézout's identity can be used to solve Diophantine equations. (10 words)

The field of Diophantine approximation deals with the cases of Diophantine inequalities. (12 words)

Longer example sentences

Given a Diophantine equation with any number of unknown quantities and with rational integral coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers. (40 words)

Number theory Diophantine equations main A Diophantine equation is a polynomial equation in two or more unknowns for which only the integer solutions are sought (an integer solution is a solution such that all the unknowns take integer values). (39 words)

In particular, this means that, given a computably enumerable set of axioms, there are Diophantine equations for which there is no proof, starting from the axioms, of whether the set of equations has or does not have integer solutions. (39 words)

Example sentences (20)

Moreover, several concepts (especially that of height ) turn out to be crucial both in Diophantine geometry and in the study of Diophantine approximations.

Number theory Diophantine equations main A Diophantine equation is a polynomial equation in two or more unknowns for which only the integer solutions are sought (an integer solution is a solution such that all the unknowns take integer values).

The field of Diophantine approximation deals with the cases of Diophantine inequalities.

The mathematical study of Diophantine problems that Diophantus initiated is now called Diophantine analysis.

An example of linear Diophantine equation is where a, b, and c are constants.

An exponential Diophantine equation is one for which exponents of the terms of the equation can be unknowns.

An exponential Diophantine equation is one in which exponents on terms can be unknowns.

Arithmetic geometry, on the other hand, is a contemporary term for much the same domain as that covered by the term Diophantine geometry.

Advertentie

Bézout's identity can be used to solve Diophantine equations.

Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations.

Given a Diophantine equation with any number of unknown quantities and with rational integral coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers.

He had already studied Bachet 's edition of Diophantus carefully;sfn by 1643, his interests had shifted largely to Diophantine problems and sums of squaressfn (also treated by Diophantus).

Hermite normal form may also be used for solving systems of linear Diophantine equations.

Hilbert's tenth problem was to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.

In 1970, Yuri Matiyasevich solved it negatively, by proving that a general algorithm for solving all Diophantine equations cannot exist.

In general, a linear Diophantine equation has no solutions, or an infinite number of solutions.

In particular, this means that, given a computably enumerable set of axioms, there are Diophantine equations for which there is no proof, starting from the axioms, of whether the set of equations has or does not have integer solutions.

Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry ).

Nevertheless, Richard Zippel wrote that the Smith normal form "is somewhat more than is actually needed to solve linear diophantine equations.

Solving Diophantine equations is a very hard task.

Advertentie

Common combinations with diophantine

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "diophantine" in a sentence?
An example: "Moreover, several concepts (especially that of height ) turn out to be crucial both in Diophantine geometry and in the study of Diophantine approximations." This page contains 10+ example sentences with the word "diophantine" from authentic English texts.
What does "diophantine" mean?
Diophantine means: Of or pertaining to Diophantus, the Greek mathematician.
How many example sentences with "diophantine" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "diophantine", drawn from a database of millions of English sentences.