Datasets:

Tamazight-NLP

/

NLLB-Seed_Tamasheq-Latin-Script

like 0

However, at some point the quadratic formula begins to lose accuracy because of round off error, while the approximate method continues to improve.

Agudendǎɣ, dǎɣ alwaq atiwafan, təmusne tan quadratique təsinta ye agamaɗ ən asidutu nes dǎɣ tidit ən awinan ikna a imamaran, mašan as təmusne tan zahazan okaynen ən adimutiyan.

Methods of numerical approximation existed, called prosthaphaeresis, that offered shortcuts around time-consuming operations such as multiplication and taking powers and roots.

Ilanti təmusnawen ən zahazan ən numérique, asitawana ɗrosthaɗhaeresis, ta hakat tabaraten gazolnen fal aɣalay ən əšiɣilan ən chronofage Atamosnen asinimiƭif əd adakal ən azaway əd azaran.

Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics.

Algorithmetan ən tidas taganen ye agaraw ən liɣitan taganen tasaga tiknat ən algèbre anilkaman ən numérique əd itagu əšiɣil ašohen ən təmusne, ən ahanay, dǎɣ shimie, dǎɣ informatik əd dǎɣ atawar.

For solutions in an integral domain like the ring of the integers, or in other algebraic structures, other theories have been developed, see Linear equation over a ring.

Fal liɣitan dǎɣ tabarat tahat sund taɣalaywayt ən entiertan, meɣ dǎɣ iyad tabaraten ən algébrique, diyad təmusnawen asewaɗnat, anhiy Alɣisab anilkaman fal taɣalaywayt iyat.

This allows all the language and theory of vector spaces (or more generally, modules) to be brought to bear.

Awen itagu ye igitan dǎɣ alkitab dak ən magrad əd təmusne ən dagan ən vektorieltan (meɣ ogaran atamosan moduletan).

Such a system is known as an underdetermined system.

Awen əmik eqalan atiwazayan ən əmik ən daw-atiwasaknan.

The second system has a single unique solution, namely the intersection of the two lines.

Wa səsin əmik ən aliɣi iyandǎɣ, atamosan animgaš ən əsin tisirad.

Any two of these equations have a common solution.

Wi səsin winan atwasan ən alɣisaban igraw aliɣi atiwaharan.

A system of equations whose left-hand sides are linearly independent is always consistent.

Əmik ən alɣisaban əs tisigwen ən tašalmad aqalnen anilkaman ən tanhat nasan eqalan harkuk ašohen.

This yields a system of equations with one fewer equation and one fewer unknown.

Nigaraw əmik iyan ən alɣisaban dər alɣisab ən nagamaɗ əd winan atwasan dǎɣ agamaɗ.

Type 3: Add to one row a scalar multiple of another.

Əmik 3 : Asiwid ən tasiret asinimiƭif ən skalaire ən iyat tasiret.

For instance, systems with a symmetric positive definite matrix can be solved twice as fast with the Cholesky decomposition.

Dǎɣ olahan, əmikan dər ən matriəe ən namas atiwasan nayknan adobatnen adiqil ayknan əsin hadagan ogarnen urmaɗ dər təbiɗawen ən Cholesky.

A completely different approach is often taken for very large systems, which would otherwise take too much time or memory.

Ihaz imdan as azalayat eqal agud iyan atwətkal ye haratan iknanen tamvare, dakəlnen hulen səməkiyan alwəq mev təkətawt.

This leads to the class of iterative methods.

Awen itiwiy dǎɣ tabarat ən təmusnawen anelasnen.

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

Dǎɣ maɗinan, anilkaman eqal, dǎɣ hadi, iliɣitan ən tabarat taganen ye asiwid ən awinan itimundu ən təwaƭ, iyad darat iyad, ən təwaƭ ən santo atiwafan.

In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance.

Agudiyan emel harkuk ən maɗinan, inilkaman winan itimundu aqalnen deɣqanen is tihurut amitkalan dǎɣ iyad adinan haditan atamosnen awa itawanhayan, informatique, statistiquetan əd azruf.

Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning of the race, the tortoise has reached a second position; when he reaches this second position, the tortoise is at a third position, and so on.

Animašrayan ye Zenon fal Achille əd efarɣas wa aśohen ən tabarat ten tidgal-asirid ən nilkaman winan itimundu : Achille ošal darat efarɣas, mašan agud wa ɗiwaɗ edag was efarɣas dǎɣ santo ən azal, efarɣas iwaɗ edag wa səsin ; agud wa ɗiwaɗ ten əs sanatat tedagit, efarɣas eqal as edag was karad, əd dǎɣ anelasan.

This argument does not prove that the sum is equal to 2 (although it is), but it does prove that it is at most 2.

Isalan wən waradoben as hadi eqalan ogdahan ən 2 (ahuskat as atitiqil), mašan tadobat as ataqal ogaran ogdahan əd 2.

Tests for uniform convergence include the Weierstrass' M-test, Abel's uniform convergence test, Dini's test, and the Cauchy criterion.

Irum wan waykan olahan ilan irum ən M ən Weierstrass, irum wa ikan olahan ən Abel, irum ən Dini əd talɣa tan Cauchy.

The convergence is uniform on closed and bounded (that is, compact) subsets of the interior of the disc of convergence: to wit, it is uniformly convergent on compact sets.

Awaykan eqalan olahan fal daw tirtiten iganen əd idbalnen (atamosan aśuhu ən amas ən taɣaya ən aykan: dǎɣ iyad əmikan, ataqal olahnen ən aykan fal dǎɣ tirtiten ašohatnen.

The Hilbert–Poincaré series is a formal power series used to study graded algebras.

Anilkam ən Hilbert-Poincaré eqalan anilkaman ən aśahat atiwasanan dǎɣ amitkal fal teɣare ən algebretan ošwalnen.

In the 17th century, James Gregory worked in the new decimal system on infinite series and published several Maclaurin series.

Dǎɣ 17e temede nawatay, James Gregory ašiɣal dǎɣ aynayan əmik ən désimal fal nilkaman winan itimundu əd azizgar ajotnen nilkaman ən Maclaurin.

Cauchy (1821) insisted on strict tests of convergence; he showed that if two series are convergent their product is not necessarily so, and with him begins the discovery of effective criteria.

Cauchy (1821) isihušul fal iruman oɣadnen ikanen ; saknen as afal əsin nilkaman aqalan aykan anmiƭaf nasan winan eqel ayfan, əd dər diris isinta ihanayan ən talɣiwen aśohatnen.

A summability method is such an assignment of a limit to a subset of the set of divergent series which properly extends the classical notion of convergence.

Təmusne iyat ən sommabilite eqalan asimišwir iyan ən samando ən daw-tartit ən tartit ən nilkaman ikanen wi basarnen əs tihusay ən təmusne tatiwasanat ən anilkam.

Indian scholars have been using factorial formulas since at least the 12th century.

Əmusanan wi indientan adakalan tabaraten tən təzunawen harwa aywadan was 12e temede nawatay.

In functional languages, the recursive definition is often implemented directly to illustrate recursive functions.

Dǎɣ Əmigridan ən əšiɣilan, aliɣi ən manes eqalan agudiyan eqtan dǎɣ uqud fal asiknin əšiɣilan ən manes.

Other implementations (such as computer software such as spreadsheet programs) can often handle larger values.

Iyad isiqtitan (sund logiəieltan ən informatik atamosan kal tisikuyma) adoben agudiyan adikinin valeurtan ogarnen təmɣire.

Compared to the Pickover definition of the superfactorial, the hyperfactorial grows relatively slowly.

Ye sund aliɣi wan Pickover wan təzunawen iknanen, ogarnen təzunawen aɣelnat intanatedǎɣ ahin ilan.

There are, relatively speaking, no such simple solutions for factorials; no finite combination of sums, products, powers, exponential functions, or logarithms will suffice to express ; but it is possible to find a general formula for factorials using tools such as integrals and limits from calculus.

Wartilen, dǎɣ magrad ən tišdige, adabaratan deɣ raqisnen fal təzunawen; wala iyan asirtay amindan ən hadi, ən sinimitafan, ən aśuhu, əšiɣilan amutaynen meɣ ən logarithmetan war igdehan ye atan ikisan; mašan eqal adoben agaraw ən tabarat tatiwasanat fal təzunawen dǎɣ dakalan ən lalan atamosan ugišawan əd samando ən tidas.

The integrals we have discussed so far involve transcendental functions, but the gamma function also arises from integrals of purely algebraic functions.

Ugišawan amosnen wi nimigrad hawendǎɣ har amaradǎɣ ikanen əšiɣilan adizubatnen, mašan əšiɣil wan gamma adifal intadǎɣ ugišawan ən əšiɣil aridan ən algébriquetan.

By taking limits, certain rational products with infinitely many factors can be evaluated in terms of the gamma function as well.

Dǎɣ adakal ən samandotan, iyad sinimitafan ən rationneltan ən fakteurtan winan iminda adobatnen deɣqanen adiqilan aykatan dǎɣ əmikan ən əšiɣil wan gamma.

Its history, notably documented by Philip J. Davis in an article that won him the 1963 Chauvenet Prize, reflects many of the major developments within mathematics since the 18th century.

Tafunft tan əšiɣil wa gamma, tiktabat atamosan fal Philip J. Dǎvis dǎɣ salan wis inta ina alhak wan Chauvenet dǎɣ 1963, saknu hadi ahusken ən ti aqalnen təwaɗen ən maɗinan harwa18e temede nawatay.

Instead of finding a specialized proof for each formula, it would be desirable to have a general method of identifying the gamma function.

Dǎɣ umaɣ ən agaraw ən tidit tatiwasanat fal hak təmusne, adiqil anihagan ye agaraw ən təmusne tatiwasanat fal asikin ən əšiɣil ən gamma.

However, the gamma function does not appear to satisfy any simple differential equation.

Ugudendǎɣ, əšiɣil ən gamma olah das warigde ye wala iyan alɣisab ən təbiɗawen ən banan.

The Bohr–Mollerup theorem is useful because it is relatively easy to prove logarithmic convexity for any of the different formulas used to define the gamma function.

Təmusne tan Bohr-Mollerup eqalan amitkalan falas eqal deɣqanen ariqisan ye asikin ən ašiśuhu ən logarithmique fal dak ən təbiɗawen ən tabaraten amitkalnen fal asiknin əšiɣil ən gamma.

As electronic computers became available for the production of tables in the 1950s, several extensive tables for the complex gamma function were published to meet the demand, including a table accurate to 12 decimal places from the U.S. National Bureau of Standards.

Ugud was ordinateurtan ən éleətroniquetan aqalnen atilan fal igitan ən təsayen dǎɣ elan wi 1950, ajotnen təsayen ibsarnen fal əšiɣil ən gamma aśohen aqalan adizgaran fal asudmir ən asistan, dǎɣ iha tasayt tatiwasanat dǎɣ 12 desimaltan ən National Bureau of Standard ən États-Unis.

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.

Dǎɣ təmusne, tabarat taqalat ašahat ən anilkaman ye azizgar ən əmik dawla, sund dǎɣ tabarat ən maɗinan meɣ ən tabarat ən shimik.

In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems.

Dǎɣ maɗinan, tabarat sakna atamosan aliɣi iyan wa itagan dǎɣ alɣisab ən salan ən mathematiquetan aɣil iyan, ogaran tənifawt eqalan təmusnawen ən maɗinan.

This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex.

Təridawt ten, ahuskat as ifnaz tanfo dǎɣ tabarat iyat intadǎɣ ən banan, tagu dǎɣ maɗinan ta wadasnen ogarnen tarmide ən tabaraten ogarnen təmɣire əd ogarnen ašuhu.

For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom.

Dǎɣ asikin, H2O eqalan tabarat ən shimiq ən aman, isaknen ye hak molékil eqalan atiwagan əs əsin atometan ən hydrogène (H) əd atome ən oxygène (O).

In empirical formulas, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound—as ratios to the key element.

Dǎɣ tabaraten ən təɣirmaten, iɣilan asintan fal harat iyan itbatan əd hakan agudiyan haditan ən atometan ən niyad haratan dǎɣ tartit - dǎɣ tumast ən salan ən harat wa atiwasanan.

Some types of ionic compounds, however, cannot be written as empirical formulas which contains only the whole numbers.

Iyad əmikan ən asirtayan ən ioniquetan waradoben agudendǎɣ adiqilan ayktaban daw tabarat ən tabaraten ən təɣirmaten winan ila haditan əmdanen.

There are several types of these formulas, including molecular formulas and condensed formulas.

Ilanti ajotnen əmikan ən tabaraten, atamosnen tabaraten ən molékilairetan əd tabaraten itamnen.

Functions were originally the idealization of how a varying quantity depends on another quantity.

Əšiɣilan aqalnen ən santo ən nuzguman ən əmik atamosan ən təwaƭ tabdat aswaden iyan haditan.

"This definition of ""graph"" refers to a set of pairs of objects."

""Aliɣi wen ən ""graphe"" itagan isiknitan ən tartit ən əsin haratan."

When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.

Agud was tabarat əd zaboten aqalnat ayertayan ən haditan atiwasanen, hak wa səsin adobat adiqil atiwagan sund koordonnéetan ən kartésien ən tatbiqet dǎɣ atiwanan.

Occasionally, it may be identified with the function, but this hides the usual interpretation of a function as a process.

Agudiyan, nadobat aniziy əšiɣil, mašan awen itafar iliɣitan atiwasanen ən əšiɣil sund atiwasanagan.

A map can have any set as its codomain, while, in some contexts, typically in older books, the codomain of a function is specifically the set of real or complex numbers.

Tesayt tadobat atigriw dak asirtay sund zaboten, indele, dǎɣ iyad tabaraten, atamosnen dǎɣ alkitaban ogarnen tərut, ən zabo ən əšiɣil eqalan atiwasanan dǎɣ tartit ən haditan atiwasanen meɣ ašohatnen.

Another common example is the error function.

Iyan asikin atiwasanan eqalan əšiɣil ən ayšlayan.

Power series can be used to define functions on the domain in which they converge.

Inalkimən ən assahat adoben adəqəlan iji ye aləɣi ən ashəɣəlan fal edag wa dǎɣ galant.

Then, the power series can be used to enlarge the domain of the function.

Darat awen, inalkimən ən assahat adoben adəqəlan iji ye assəhraw ən edag wan ashəɣəl.

Parts of this may create a plot that represents (parts of) the function.

Tishruten ən edag wen adobatnat adəjinat tassəret saknet (tishruten ən) ashəɣəl.

This is the canonical factorization of .

Awen amoss afənazat tolahat ən.

At that time, only real-valued functions of a real variable were considered, and all functions were assumed to be smooth.

Ɣor azaman,ashəɣəlan ɣas win təmɣar tadutet ən tamətuyt taduten aqalan atwətkal, izar ashəɣəlan kul aqalan amossan ashiləlaken.

Functions are now used throughout all areas of mathematics.

Ashəɣəlan aqalan darat awa ayjan dǎɣ dəgan kul win maɗinan.

This is how inverse trigonometric functions are defined in terms of trigonometric functions, where the trigonometric functions are monotonic.

Awen dǎɣ as ashəɣəlan ən maɗinan amləlaynen aqalan atwən dǎɣ ashəɣəlan ən maɗinan, agud was ashəɣəlan ən maɗinan aqalan awaren itəmətuy.

Usefulness of the concept of multi-valued functions is clearer when considering complex functions, typically analytic functions.

Enəfi ən tənna ən ashəɣəlan ən təmɣəren ajotnen taqal aduten agud wad nəssəmɣar ashəɣəlan əmdanen, milhaw ən ashəɣəlan anizjamen.

Such a function is called the principal value of the function.

Ashəɣəl wen atiwəɣra as təmɣər tazarat ən ashəɣəl.

Functional programming is the programming paradigm consisting of building programs by using only subroutines that behave like mathematical functions.

Taqan tajət taqal mənhuy ən taqan tənfat akarass ən taqanen dǎɣ iji ɣas ən daw tahajit teməshaɣəlt sund ashəɣəlan ən maɗinan.

"Except for computer-language terminology, ""function"" has the usual mathematical meaning in computer science."

Dǎɣ azajor ən samədo ən magrad ən səslo,"" ashəɣəl ""ila tənna ən maɗin atiwəzayan dəɣ tənna."

Terms are manipulated through some rules, (the -equivalence, the -reduction, and the -conversion), which are the axioms of the theory and may be interpreted as rules of computation.

Tənaten aqalnat atiwədassən as tənaten, (tigdəhawt, afənazət, ad assəməliliy), aqalnen inəhəja ən tamusne izar adoben atwələɣi sund tənaten ən maɗin.

Nicolas Chuquet used a form of exponential notation in the 15th century, which was later used by Henricus Grammateus and Michael Stifel in the 16th century.

Nicolas Chuquet itkəl iri ən assəkən idwalən ɣor 15e awatay, atiwəjan darat awen as Henricus Grammateus ad Michael Stifel ɣor 16e awatay.

Thus they would write polynomials, for example, as .

Darat awen, ikatəb timərtay, ad assistant, sund.

The result is always a positive real number, and the identities and properties shown above for integer exponents remain true with these definitions for real exponents.

Alkum eqal harkuk amaɗin aduten maqar,izar milhawen ad təlaten atiwəsaknanen safəla ye imijaran əmdanen aqalan tidit dəɣ ilaɣitan ye imijaran adutətnen.

This function equals the usual th root for positive real radicands.

Ashəɣəl ogdah ad aɗɗin th harkuk ye aɗɗinən adutatnen maqornen.

This is the starting point of the mathematical theory of semigroups.

Eqal edag wan tekle ən musnat ən maɗin ən aɣil ən jənəj.

We can again replace the set N with a cardinal number n to get Vn, although without choosing a specific standard set with cardinality n, this is defined only up to isomorphism.

Nadobat dǎɣ ishray assəməskəl ən mertay N as maɗin azaran n ye ajaraw ən Ɣn, harwa dǎɣ iban assənəfrən ən mertay agidahən ikna ən təzart n, wadǎɣ war eqel tebəde as ɣor migdəhaw.

Nicolas Bourbaki, Elements of Mathematics, Theory of Sets, Springer-Verlag, 2004, III.§3.5.

Nicolas Bourbaki, Elements of Mathematics, Theory of Sets, Springer-Verlag, 2004, III.§3.5.

Iterating tetration leads to another operation, and so on, a concept named hyperoperation.

Amsoɣəl ən təkazen iwayd as asseɗən iyan, as dǎɣ alkum, tamusne tatiwəɣrət asseɗən maqarən.

In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (that is, percentage increase or decrease) in the dependent variable.

Dǎɣ tidəgaten atiwəjanen, ashəɣəlan adwalnen sasahaɣən tartit tadǎɣ as assəmətuy azuken ən assəmətuy ogdahən (adar tidila ugdah dəɣ timaɗ ən assiwaɗ meɣ afənaz)

This function property leads to exponential growth or exponential decay.

Takrəsht ten ən ashəɣəl təway as assiwəɗ ən tadəwla meɣ afənaz ən tadəwla.

Similarly, the composition of onto (surjective) functions is always onto.

Harat iyan, tartit ən ashəɣəlan onto (ugishan) eqal harkuk onto.

Then one can form chains of transformations composed together, such as .

Nadobat deɣ iji ən inəlkam ən imliliyan artaynen kul, sund.

This alternative notation is called postfix notation.

Assəkən wen ən tənməshayt issəm iness assəkən darat tabəde.

The category of sets with functions as morphisms is the prototypical category.

Iri ən tədawen dǎɣ ashəɣəlan sund iji eqal iri atiwassəknan.

For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example).

Sund,emekət (dB) eqal tajute təjat fal iji ən inəhəjan olahnen ad maɗinan ən təzart ye assuhu ad təmɣare ən aləɣitan (as arurəd amutəyan eqal sund atilan).

They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting.

Alilan as aləɣi ən inəhəja ən amsuɣəl ən tuzunawen ən nəzarən,izjarənid dǎɣ tənawen ən assedən ən maɗinan azarnen meɣ tihzawt ən issənətfass, taləɣen iritan iyad dǎɣ anyat nawadəm izar adoben tilalt as assedən ogdahən.

The next integer is 4, which is the number of digits of 1430.

Amadin niyan ilkamən eqal 4, mamos amadin ən aɗɗinan ən 1430.

Prior to Napier's invention, there had been other techniques of similar scopes, such as the prosthaphaeresis or the use of tables of progressions, extensively developed by Jost Bürgi around 1600.

Dat iji ən Naɗier, əlanəti təmkarawen tiyad ən taləsse tolahət, sund ɗrosthaɗhaeresis meɣ iji ən tabəlen ən tikiya, təknat təmɣare as Jost Bürgi ibret ən 1600.

Speaking of a number as requiring so many figures is a rough allusion to common logarithm, and was referred to by Archimedes as the “order of a number”.

Magrad ən maɗin sund ahushəl ajit ən adinən eqal ishəbaj makərən ən maɗin iyan, izar eqal atwətkəl as Archimède sund "təzart ən maɗin".

Such methods are called prosthaphaeresis.

Timkarawen tin atiwəɣranat as prosthaphaeresis.

For example, each chamber of the shell of a nautilus is an approximate copy of the next one, scaled by a constant factor.

Sund, edag kul ən afrənki ən tilmat eqal milhaw tohazət tatəlkamət, təgashət tadəwla as adin ibdadən.

Logarithms are also linked to self-similarity.

Amaɗin eqal deɣ ayertayan as tigozst ən milhaw.

It is used to quantify the loss of voltage levels in transmitting electrical signals, to describe power levels of sounds in acoustics, and the absorbance of light in the fields of spectrometry and optics.

Atiwətkal ye eket ən ajmod idagan ən assahat dǎɣ ihuk ən laɣitan ən loran, ye timla ən idagan ən assahat ən inazarən dǎɣ maslat, ad assugish ən efew dǎɣ dəgan ən tamusne ən fewən ad mənhuy.

Vinegar typically has a pH of about 3.

Aman səməmnen ilan pH iwaɗan 3.

"This ""law"", however, is less realistic than more recent models, such as Stevens's power law.)"

Ten""tahashilt"", aguden, war tadutət as iritan iknanen tinya, sund tahashilt ən assahat wan Stevens".

When the logarithm of a random variable has a normal distribution, the variable is said to have a log-normal distribution.

Agud maɗin ən ashanzi ən təbaɣort təla ihukan aknanen, nəjan as ashanzi ila ihuk ən eket iknan.

For such a model, the likelihood function depends on at least one parameter that must be estimated.

Ye sund iri, ashəɣəl ən təlat ən təjute torhajət ən ɣas ad ashrut admaren aqəl atwəshbaj.

Similarly, the merge sort algorithm sorts an unsorted list by dividing the list into halves and sorting these first before merging the results.

Sund, musnat ən aɗɗin ən azalay as assəlyam ən lay waren anəfrən as tazunt ən lay as assin ad assənəfrən izar nastnat dat assərtay ən jarawən.

Lyapunov exponents use logarithms to gauge the degree of chaoticity of a dynamical system.

Tidəwla tin Lyapunov itkalnat imaɗinan ye eket ən təmɣar ən taɣshət ən harət ifranən.

The Sierpinski triangle (pictured) can be covered by three copies of itself, each having sides half the original length.

Triangle tan Sierpinski (asura) tadobat ataqəl abrəbəki as karadət milhawen iness, iyat dak təla ishrutan ən tazune ən təzəjrət waren təjət.

Another example is the p-adic logarithm, the inverse function of the p-adic exponential.

Milhaw iyan eqal maɗɗin tənaten ən eɗan, ashəɣəl ebdən ən təzəjrət tənaten ən eɗan.

Carrying out the exponentiation can be done efficiently, but the discrete logarithm is believed to be very hard to calculate in some groups.

Iji ən təzəjrət adobat iji səsahat, mashan aɗin ifarən eqal sund ikna assuhu ən asseɗən dǎɣ tartiten tiyad.

Square roots of negative numbers can be discussed within the framework of complex numbers.

Racines carrées ən maɗinan ədarətnen adoben adəqəlan tamədasht dǎɣ edag wan maɗinan əmdanen.

In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the Sulba Sutras, dated around 800–500 BC (possibly much earlier).

Dǎɣ Inde təruwat, tamusne initan təmusnawen ad ijitan ən migdəhaw ad raəine carréeeqal deɣ harwa aruwən as Sulba Sutras, təlat aylan 800-500 dat J.-C.(ihaməsh ajen as atrub).

The letter jīm resembles the present square root shape.

Tassəsawit jim tolah ad iri wan amaradəɣ ən racine carrée.

It defines an important concept of standard deviation used in probability theory and statistics.

Taleɣat anyat iknan ən ijij-niri ijan dǎɣ tamusne ən təbɣar ad tənaten.

Most pocket calculators have a square root key.

Ajət ən titəkalkanen as ihaz ikanat tassəkat ən racine carrée.

The time complexity for computing a square root with n digits of precision is equivalent to that of multiplying two n-digit numbers.

Assuhu nəlwaq wan asseɗən ən raəine əarrée ad n aɗinən ən adətu ogdah ad tan assənətfəs ən assin maɗinan ən n aɗin.

Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.

Itarəqan win Hilbert aqalan sanatət təmərwen ad karad ən tarəqan ən maɗinan izjarnen as massis ən maɗin ən allemand David Hilbert ɣor 1900.