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Since the base 1 exponential function (1x) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist). | Falas əšiɣil ebdan dǎɣ santo ən 1 (1x) eqalan harkuk ogdahan ən 1, asimililiy winan tila (eqalan asitawan logarithme dǎɣ santo ən 1 afal tila). |
Likewise, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties. | Dǎɣ olahan, əd ɣeəteurtan aqalnen agudiyan atiwasaknan dǎɣ ɣeəteurtan niyadnaɣ (atamosan ən ɣeəteurtan ən magnitude iyandǎɣ), falas awen igrawan agudiyan tabaraten ogarnen atwirh. |
It is also the first and second number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences. | Eqal awen wa dazaran əd wa sisin amaɗin nukiy ən Fibonacci (0 eqalan wala) əd eqal wadazaran amaɗin ən ajotnen iyad ən alkum ən maɗinan. |
Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all. | Mašanatnen, algèbre oɣadnen adobatnen adiqilan ašikriš dər iyadǎɣ harat, awinan eqel singleton əd winan eqel dak ayertayan. |
A binary code is a sequence of 1 and 0 that is used in computers for representing any kind of data. | Ufir nəsin eqalan tafirest ən 1 əd 0 eqalan amitkalan dǎɣ ordinateur fal adigiš əmik kul ən huktan. |
+1 is the electric charge of positrons and protons. | +1 eqalan tazayt tan électrique ən ɗositrontan əd protontan. |
The Neopythagorean philosopher Nicomachus of Gerasa affirmed that one is not a number, but the source of number. | Təmusne tan néopythagoricien Nicomaque ən Gèrasa tadutat as iyan winan eqel amapin iyan, mašan tabarat tan amapin. |
We Are Number One is a 2014 song from the children's TV show LazyTown, which gained popularity as a meme. | We Are Number One eqalan taswilt ən 2014 tan salan ən télévision fal aratan LazyTown, wa igrawan dǎɣ atwizay dǎɣ awendǎɣ. |
In association football (soccer) the number 1 is often given to the goalkeeper. | Dǎɣ football tartitan (soccer), ən numéro 1 eqalan agudiyan atiwafan dǎɣ amagaz ən but. |
1 is the lowest number permitted for use by players of the National Hockey League (NHL); the league prohibited the use of 00 and 0 in the late 1990s (the highest number permitted being 98). | Was 1 eqalan ogaran təmidrit amaɗin agrawan adiqil amitkalan fal kal balo ən Ligue tan akal ən hoəkey (NHL) ; ligue tidgal amitkal ən 00 əd 0 dǎɣ samando ən wityan 1990 (ogarnen təmɣire amaɗin igrawan adiqil was 98). |
Any random sequence of digits contains arbitrarily long subsequences that appear non-random, by the infinite monkey theorem. | Tafirest dak ən tanamašrat dǎɣ maɗinan atat ihan daw-tifirest ən tizart toɣadat zigret ta tolahat winan tanmašray, tamosat tabarat ən asikin winan itimundu. |
"Second, since no transcendental number can be constructed with compass and straightedge, it is not possible to ""square the circle""." | "Wasisin, sund wala iyan amaɗin transəendantal winan adobat adiqil aykrasan dər əomɗas əd tasasagdahat, wadadobat adiqil ""ayknan efaday ən taɣalaywat""." |
The Indian astronomer Aryabhata used a value of 3.1416 in his Āryabhaṭīya (499 AD). | Astronome wan indien Aryadhata ašiɣal ɣaleur iyan ən 3,1416 dǎɣ Āryabdhatīya nes (499 AD). |
The Persian astronomer Jamshīd al-Kāshī produced 9 sexagesimal digits, roughly the equivalent of 16 decimal digits, in 1424 using a polygon with 3×228 sides, which stood as the world record for about 180 years. | Astronome imbag Jamšīd al-Kāšī ye igi ən 9 maɗinan ən sexagésimaux, olahan ən sund wan 16 maɗinan ən décimaux, dǎɣ 1424 amitkal ən polygone ən 3×228 ən tisigwen, awa asɣaman dǎɣ agaraw wan aduniyat hawendǎɣ had ihomiši 180 nawatay. |
These avoid reliance on infinite series. | Tidgal azal ən nilkaman winan itimundu. |
As modified by Salamin and Brent, it is also referred to as the Brent–Salamin algorithm. | Awa samos as Salamin atasmatayan əd Brent, eqal deɣqanen asitawana algorithme ən Brent-Salamin. |
This is in contrast to infinite series or iterative algorithms, which retain and use all intermediate digits until the final result is produced. | Animašray əd nilkaman winan ila hadi meɣ ən algorithmetan itératif, wa itigizan əd amitkal kul ən maɗinan ən garesan hawendǎɣ har agaraw wan samando mosan animtaf. |
Such memorization aids are called mnemonics. | Tidhalen tən ən uduf aqalnen asitawana mnémoniquetan. |
The digits are large wooden characters attached to the dome-like ceiling. | Imaɗinan aqalnen magornen dǎɣ talɣa ən ešaɣer egtan dǎɣ safala nəmik wan dôme. |
"A numerical digit is a single symbol used alone (such as ""2"") or in combinations (such as ""25""), to represent numbers in a positional numeral system." | "Amaɗin ən numérique eqalan ašikel iyandǎɣ amitkalan intaɣas (atamosan ""2"") meɣ dǎɣ asirtay (atamosan ""25""), fal adisikin imaɗinan dǎɣ əmik ən numérique ən ugišawan." |
A positional number system has one unique digit for each integer from zero up to, but not including, the radix of the number system. | Əmik ən numération ən ugišawan ihan amaɗin iyandǎɣ ye hak amaɗin əmdan ən wala har, mašan dǎɣ wariha, radix ən əmik wan numération. |
The original numerals were very similar to the modern ones, even down to the glyphs used to represent digits. | Əmaɗinan wi santo aqalnen hulen olahnen dər maɗinan wi amutaynen, hawendǎɣ har glyphetan amitkalnen fal ugišawan ən maɗinan. |
The Mayas used a shell symbol to represent zero. | Mayas adakalan ašikel ən tefek fal adigiš edag ən wala. |
The Thai numeral system is identical to the Hindu–Arabic numeral system except for the symbols used to represent digits. | Əmik wan numeral ən Thaïlandais eqalan intaɣas dǎɣ əmik ən numeral hindou-arabe, dǎɣ warahen šikelan wi amitkalnen fal adigišan idagan ən maɗinan. |
They are both base 3 systems. | Aqalan windak nəsin əmikan dǎɣ santo ən 3. |
Several authors in the last 300 years have noted a facility of positional notation that amounts to a modified decimal representation. | Inumaɣan ajotnen, dǎɣ alwaq wan 300 nelan wi ilkamnen, iliɣen asirɣas ən nasiɗin ən dagan wi awadnen ugušiwan. |
For example, 1111 (one thousand, one hundred and eleven) is a repunit. | Dǎɣ olahan, 1111 (efad, temede əd maraw əd diyan) eqalan asikin. |
Besides counting ten fingers, some cultures have counted knuckles, the space between fingers, and toes as well as fingers. | Dǎɣ ugur nisiɗin ən marawat tisikaɗ, iyad itwigaz aseɗanan gar tisikaɗ, edag wa gar tisikaɗ, əd tisawen dǎɣ ogaran dǎɣ tisikaɗ. |
Stone age cultures, including ancient indigenous American groups, used tallies for gambling, personal services, and trade-goods. | Ətwigazan ən awatay wan tuhunt, dǎɣ ihan wirunen tartiten ən kalakal wi americaintan, dakalnen wi saɗanen fal adalan wi banan, əšiɣil wa manes əd miskalan ən lalan. |
Beginning about 3500 BC, clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets (originally containers for tokens) which were then baked. | Dǎɣ aywadan dǎɣ 3500 aɣ. J.-Ə. ihomiši, erkišiɣilan ən talaq aqalan anilkaman dǎɣ amiskal dǎɣ liɣitan ən numérique izgarnen dǎɣ tadhil ən əmik awilaywaynen dǎɣ tisigwen fal tisayen ən talaq (dǎɣ santo ən tisitwir fal krimkraman) wi eqalnen darat awen aygan. |
These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. | Əmikan ən numérique wən cunéiforme olahan ən əmikan wi numérique wa aɣilaywayan wa asmatayan əd itwaran asiɗin wa asiwiɗ ən ɣaleur wa əmik wa nəmikan ən numériquetan wi aɣilalwaynen. |
Sexagesimal numerals were a mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. | Əmaɗinan wi sexagesimaux aqalan əmik wan radix ertayan wa isadawan santo ən 10 əd santo ən 6 artaynen dǎɣ tafurust ən nadag əd ən šaɣeran oɣadnen ən cunéiforme. |
Unique numbers of troops and measures of rice appear as unique combinations of these tallies. | Əmaɗinan iyadǎɣ ən tartit əd akotan wi tafaɣat izgaranid sund isirtayan iyadǎɣ ən asimusuɣil neɗan. |
Conventional tallies are quite difficult to multiply and divide. | Imasaɗinan wən tiridawt aqalan andiran dǎɣ aśuhu ye ɗesan əd tuzant. |
Jews began using a similar system (Hebrew numerals), with the oldest examples known being coins from around 100 BC. | Juiftan asintan adakal əmik olahan (əmaɗinan ən hébraïque), wi ogarnen turut isiknitan atiwazaynen aqalnen aybdan ən imbešta ən harwa aywadan 100 dat. |
The Maya of Central America used a mixed base 18 and base 20 system, possibly inherited from the Olmec, including advanced features such as positional notation and a zero. | Mayas wən Amérique tanamas adakalan əmik ertayan dǎɣ santo ən 18 əd dǎɣ santo ən 20, amosan adizgaran dǎɣ Olmequetan, ahan talɣiwen azarnen atamosnen asiɗin ən dagan əd wala. |
Knowledge of the encodings of the knots and colors was suppressed by the Spanish conquistadors in the 16th century, and has not survived although simple quipu-like recording devices are still used in the Andean region. | Təmusne ən nufur ən timikras əd initan eqal aygmadan fal conquistador ən esɗagnoltan dǎɣ 16ème temede nawatay, əd wadider, ahuskat as haratan nadakal ən banan ən əmik quiɗu amosan harwa amitkalan dǎɣ akal ən andine. |
Zero was first used in India in the 7th century CE by Brahmagupta. | Wala eqal amitkalan fal wadazaran ehandag dǎɣ Inde dǎɣ 7e temede nawatay ən alwaq wananaɣ fal Brahmaguɗta. |
Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th century. | Kal maɗinan ən araban asewaɗan əmik fal adigišan fraətiontan ən déəimal, əd Muhammad ibn Mūsā al-Kwārizmī əktab alkitab iknan ye salan wən 9e temede nawatay. |
The binary system (base 2), was propagated in the 17th century by Gottfried Leibniz. | Əmik wasisin (santo 2), eqal amšaršaran dǎɣ 17ème temede nawatay fal Goƭfried Leibniz. |
The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. | Təmotayen tə amosnen alɣisab anihaga adiqil adikin aqalan intanedǎɣ asitawana awinan atwazay, əd valeurtan winan atwazay wi sagdahnen asisigdah eqalan asitawana aliɣi ən alɣisab. |
A conditional equation is only true for particular values of the variables. | Alɣisab iyan tanhat winan eqel tidit aswaden valeurtan iyad ən təmotayen. |
Very often the right-hand side of an equation is assumed to be zero. | Hulen agudiyan, tasaga tan aɣil ən alɣisab eqalan amosan agdahan ən wala. |
An equation is analogous to a scale into which weights are placed. | Alɣisab eqalan analogue iyan akot dǎɣ amosan dǎɣ itawaga azayan. |
This is the starting idea of algebraic geometry, an important area of mathematics. | Eqal anuzgum ən santo géométrie ən algébrique, ən tabarat tinfat dǎɣ maɗinan. |
To solve equations from either family, one uses algorithmic or geometric techniques that originate from linear algebra or mathematical analysis. | Fal kanan ən alɣisaban ən iyandǎɣ meɣ niyat terwe, amitkalan təmusnawen ən algorithmetan meɣ géométriquetan wi idizgarnen dǎɣ algèbre anilkaman meɣ ən akayad ən maɗinan. |
These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions. | Alɣisaban wən aqalan dǎɣ atiwasanan aśohen; nitamaɣ agudiyan ɣas ye agaraw atwimal meɣ ibanamel ən aliɣi, əd, afal atitila, ye asiɗin ən hadi ən liɣitan. |
In the illustration, x, y and z are all different quantities (in this case real numbers) represented as circular weights, and each of x, y, and z has a different weight. | Dǎɣ atwisanan, x, y əd z aqalnen daknasnat haditan abdanen (dǎɣ awen, ən haditan atiwasanen) igašnen daw almaɣna ən azayan aɣilalwayan, əd hak x, y əd z ən tazayt tabdat. |
Hence, the equation with R unspecified is the general equation for the circle. | Dǎɣ awen, alɣisab dər R winan atwasan eqalan alɣisab atiwasan ən taɣalaywayt. |
The process of finding the solutions, or, in case of parameters, expressing the unknowns in terms of the parameters, is called solving the equation. | Əšiɣil wa eqalan ye agaraw ən ləɣitan meɣ, dǎɣ əmik ən tabarat, ta saknet wiwinan atwazay dǎɣ əšiɣil ən tabarat, eqalan asitawan asikin ən alɣisab. |
Multiplying or dividing both sides of an equation by a non-zero quantity. | Asinimiƭif meɣ tazant ən winisin təsigwen ən alɣisab fal hadi winan eqel wala. |
An algebraic equation is univariate if it involves only one variable. | Alɣisab ən algébrique eqalan atimutuyan afal witugu ugiš ən iyandǎɣ tamotayt. |
In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics. | Dǎɣ maɗinan, təmusne ən əmikan anilkamnen ataqal santo əd aɣil ən atiwasan ən algèbre anilkaman, ən salan wi aqalnen amitkalan dǎɣ agudiyan ən aɣilan ən maɗinan wi amutaynen. |
This formalism allows one to determine the positions and the properties of the focuses of a conic. | Almana wən aytagu ye adisikin əmikan əd tabaraten ən kadewan ən conique. |
This point of view, outlined by Descartes, enriches and modifies the type of geometry conceived of by the ancient Greek mathematicians. | Tatbiqet ten ən nahanay, tizgarat fal Descartes, tasewaɗ əd simutuy əmik ən géométrie ihan fal wi urunen amasaɗinan ən grektan. |
An exponential Diophantine equation is one for which exponents of the terms of the equation can be unknowns. | Alɣisab ən diofantien ebdan eqalan alɣisab iyan fal atamosan wizazgarnen ən šikelan ən alɣisab adobatnen adiqilan winan atwasan. |
Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. | Géométrie algébrique amutayan eqalan ayhan fal təmusnawen ogarnen atwisan ən algèbre atiwasanan, dǎɣ aybdan ən algèbre ən asirtay, dər magrad əd asibaban ən géométrie. |
A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. | Tatbiqet iyat ən tidawt tahat alalawa ən algébrique afal əsiknitan nes sagdahnen alɣisab ən polynomial ən hukitan. |
In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions — the set of functions that satisfy the equation. | Dǎɣ maɗinan wi aridnen, alɣisab wi abdanen aqalan atiwaɣranen daw dangan ajotnen abɗanen, dǎɣ tarha atamosan ye liɣitan nasan -tartit ən əšiɣilan wi sasagdahnen alɣisab. |
Linear differential equations, which have solutions that can be added and multiplied by coefficients, are well-defined and understood, and exact closed-form solutions are obtained. | Alɣisaban wi abdanen anilkamnen, əs liɣitan adobatnen adiqilan awiɗan əd asinimiƭif fal coeffiəientan, aqalan ahusken atiwasanan əd atiwafhaman, əd liɣitan oɣadnen daw əmik iharan aqalan atiwagrawan. |
PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. | EDP adoben adiqilan amitkalan fal adalaɣen tidit maqarat ən alwaqan atamosnen anazar, takast, éleətrostatique, éleətrodynamique, tanaɣla ən aynagayan, aytimsisiran meɣ ikanan ən quantique. |
A solution is an assignment of values to the unknown variables that makes the equality in the equation true. | Aliɣi iyan eqal asimišwir ən ɣaleurtandǎɣ təmotayen winan atwazay tə taganen tigdaha ən alɣisab wa aduten. |
The set of all solutions of an equation is its solution set. | Tartit ən kul əliɣitan ən alɣisab eqalan dǎɣ tartit ən liɣitan nes. |
Depending on the context, solving an equation may consist to find either any solution (finding a single solution is enough), all solutions, or a solution that satisfies further properties, such as belonging to a given interval. | Dǎɣ maɣulat ən taberat, aliɣi ən alɣisab adobat adumas umaɣ amosan harat dak ən aliɣi (umaɣ ən iyandǎɣ aliɣi igdah), meɣ kul əliɣitan, meɣ aliɣi iyandǎɣ igdahan ye tabaraten tiyad, sund adiha agutus atiwahakan. |
In this case, the solutions cannot be listed. | Dǎɣ awen, əliɣitan wadadoben adiqilan aytawasaɗanan. |
The variety in types of equations is large, and so are the corresponding methods. | Təɗidawt ən əmikan ən alɣisaban eqal amaqaran, əd təmusnawen ihanen aqalnat intanatedǎɣ. |
This may be due to a lack of mathematical knowledge; some problems were only solved after centuries of effort. | Awen adobat adiqil aygan dǎɣ iba ən təmusnawen ən maɗinan; iyad asibaban waraqelan ayknan as darat timaɗ nelan ən irum. |
Polynomials appear in many areas of mathematics and science. | Polynômetan zagaranid dǎɣ ajotnen tabaraten ən maɗinan əd təmusnawen. |
Many authors use these two words interchangeably. | Ajotnen ənumaɣan adakalan wi nəsin tifir ən almaɣna ən təmotayen. |
Formally, the name of the polynomial is P, not P(x), but the use of the functional notation P(x) dates from a time when the distinction between a polynomial and the associated function was unclear. | Dǎɣ əmik atiwalaɣen, əsim ən polynome eqalan P, əd waden P(x), mašan amitkal ən asiɗin ən əšiɣil ən P(x) alwaq ən alɣisab ɣur təbiɗawt ən gar polynôme əd əšiɣil ihan winan eqel aridan. |
However, one may use it over any domain where addition and multiplication are defined (that is, any ring). | Agudendǎɣ, nadobat anitkil fal tabarat dak ɣur asiwiɗ əd asinimiƭif aqalan atiwasanan (atamosan dak taɣalalwayt). |
Polynomials of small degree have been given specific names. | Polynômetan ən degré wan andiran igrawan əsimawan atiwasanen. |
The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. | Polynôme 0, wa adoben adiqil atiwagan sund winan ila wala ihan əmik, eqalan asitawa polynome ən wala. |
Because the degree of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two. | Sund degré ən polynôme winan eqel wala eqalan ogaran təmɣire ən degré ən əmik iyan, polynôme wen eqalan ən degré nəsin. |
Polynomials can be classified by the number of terms with nonzero coefficients, so that a one-term polynomial is called a monomial, a two-term polynomial is called a binomial, and a three-term polynomial is called a trinomial. | Polynômetan adobatnen adiqilan akitlen dǎɣ əšiɣil ən hadi ən əmik ən koeffisientan winan eqel ba, dǎɣ almaɣna as polynôme ila əmik eqalan asitawa monomial, polynôme ən əsin əmikan eqalan asitawa binomial əd ɗolynôme ən karad əmikan eqalan asitawa trinomial. |
When it is used to define a function, the domain is not so restricted. | Agud wa eqal amitkalan fal adisikin əšiɣil, ən tabarat winan eqel deɣ akuruzan. |
A polynomial in one indeterminate is called a univariate polynomial, a polynomial in more than one indeterminate is called a multivariate polynomial. | Polynôme winan ila hadi ahas itawanen polynôme itimutuyan, polynôme ən ajotnen winan ila hadi sitawana polynôme tinimtafen. |
In the case of the field of complex numbers, the irreducible factors are linear. | Dǎɣ awen ən ašikriš ən haditan aśohatnen, facteurtan winan ifiniz aqalan anilkaman. |
If the degree is higher than one, the graph does not have any asymptote. | Afal degré eqalan ogaran iyandǎɣ, alalawa winan ila asymptote. |
In elementary algebra, methods such as the quadratic formula are taught for solving all first degree and second degree polynomial equations in one variable. | Dǎɣ algèbre ən banan, təmusnawen amosnen ən tabarat ən quadratique aqalnen atiwasaɣran fal kanan kul nalɣisaban polynomialetan ən wadazaran əd wasisin degré dǎɣ tamotayt. |
However, root-finding algorithms may be used to find numerical approximations of the roots of a polynomial expression of any degree. | Agudendǎɣ, algorithmetan ən umaɣ ən azaran adobatnen adiqilan amitkalan fal agaraw ən ihomiši ən numériquetan ən azaran ən magrad polynomial ən dak degré. |
Since the 16th century, similar formulas (using cube roots in addition to square roots), but much more complicated are known for equations of degree three and four (see cubic equation and quartic equation). | Harwa dǎɣ 16e temede nawatay, ən tabaraten olahnen (dakalnen azaran ən əubiquetan dǎɣ ogaran dǎɣ azaran ogdahan), mašan ajotnen ogarnen aśuhu aqalnen atiwazayan fal alɣisab ən degré ən karad əd ikoz (anhiy alɣisab ən əubique əd alɣisab ən quartique). |
In 1830, Évariste Galois proved that most equations of degree higher than four cannot be solved by radicals, and showed that for each equation, one may decide whether it is solvable by radicals, and, if it is, solve it. | Dǎɣ 1830, Évariste Galois asikna as iyadak dǎɣ alɣisaban ən degré ogaran ikoz waradoben adiqil ayknan fal radiəautan, əd isikna as hak alɣisab, nadobat ananu as taqal aylayaman fal radikotan, əd, afal taqal, ye kanan. |
Nevertheless, formulas for solvable equations of degrees 5 and 6 have been published (see quintic function and sextic equation). | Dǎɣ awen, tabaraten ən alɣisaban salyamnen ən degré 5 əd 6 aqalan adizgaran (anhiy əšiɣil ən quintique əd alɣisab sextique). |
The most efficient algorithms allow solving easily (on a computer) polynomial equations of degree higher than 1,000 (see Root-finding algorithm). | Algorithmetan wi ogarnen aśuhu atagan ye kanan raqisnen (fal iyan ordinateur) alɣisaban polynomialetan ən degré ogaran 1000 (anhiy Root-finding algorithm). |
For a set of polynomial equations in several unknowns, there are algorithms to decide whether they have a finite number of complex solutions, and, if this number is finite, for computing the solutions. | Fal tartit ən alɣisaban polynomialetan dǎɣ ajotnen winan atwasan, ilanti algorithmetan taganen ye asikin afal ilanat hadi amidan ən aliɣi aśohen, əd, afal hadi iyan eqalan amindan, ən tidas ən liɣitan. |
A polynomial equation for which one is interested only in the solutions which are integers is called a Diophantine equation. | Alɣisab ən polynomial fal atamosan as waden atiwarhan ye liɣitan wi aqalnen aymdan eqalan asitawa alɣisab ən Diofantie. |
The coefficients may be taken as real numbers, for real-valued functions. | Coefficientan adobatnen adiqilan amitkalan sund haditan wi itbanen, fal əšiɣilan ən valeurtan itbatnen. |
This equivalence explains why linear combinations are called polynomials. | Tigdaha ten asakna awa fal isirtayan anilkamnen aqalan asitawana polynômetan. |
"In the case of coefficients in a ring, ""non-constant"" must be replaced by ""non-constant or non-unit"" (both definitions agree in the case of coefficients in a field)." | "Dǎɣ awen koeffisientan ən taɣalalwayt, anihaga adisimutiy ""babo-winan itimutuy"" fal ""babo-winan atwasan meɣ babo-iyandǎɣ"". (Wi nəsin əsiknitan iglanen dǎɣ awen ən koeffisientan dǎɣ ašikriš iyan)." |
When the coefficients belong to integers, rational numbers or a finite field, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials (see Factorization of polynomials). | Agud wa koeffisientan ahan dǎɣ entiertan, əmaɗinan ən rationneltan meɣ taɣisa timindat, ilanti algorithmetan taganen tirimnen ifanazan əd tidas ən fanazan dǎɣ polynômetan winan ifiniz (anhiy əšiɣil wa polynômetan). |
The characteristic polynomial of a matrix or linear operator contains information about the operator's eigenvalues. | Polynôme wa talɣa ən matris meɣ emag ilkaman iahan salan fal valeurtan aridnen ən emag. |
However, the elegant and practical notation we use today only developed beginning in the 15th century. | Agudendǎɣ, asiɗin ən ayknan əd aytawagen was itamatkalan ešalidǎɣ winan eqel awiɗan dǎɣ ugud ən 15ème temede nawatay. |
"This ""completes the square"", converting the left side into a perfect square." | "Awen ""isawaɗ wa ogdahan"", simliliyan tasaga tan tašalmad dǎɣ wa ogdahan." |
Descartes' theorem states that for every four kissing (mutually tangent) circles, their radii satisfy a particular quadratic equation. | Təmusne tan Descartes stipule ye fal kul wi tinukoz tiɣalalwayen tə tatafnen (təmotayen ən tangent), izarazaran nasan gadahan ye alɣisab quadratique ebdan. |
Babylonian mathematicians from circa 400 BC and Chinese mathematicians from circa 200 BC used geometric methods of dissection to solve quadratic equations with positive roots. | Imasaɗinan ən babylonientan ihomiši 400 dat J.-C. əd imasaɗinan wi əhinoistan ihomiši 200 dat J.-C. atkalan təmusnawen ən géométriquetan ən təbiɗawt fal kanan ən alɣisaban quadratique ən azaran wi awiɗnen. |
Euclid, the Greek mathematician, produced a more abstract geometrical method around 300 BC. | Euclide, amaɗin wa greə, iga dǎɣ edag ən təmusne ən géométrique ogaran 300 atwinhay ibret dat Jésus-Christ. |
Al-Khwarizmi goes further in providing a full solution to the general quadratic equation, accepting one or two numerical answers for every quadratic equation, while providing geometric proofs in the process. | Al-Kwārizmī ika ogaran igig dǎɣ agay ən aliɣi imdan ən alɣisab quadratique atiwasanan, erɗan iyan meɣ əsin əsiknitan ən numérique fal hak alɣisab quadratique, dak dǎɣ agay ən sidutitan ən géométriquetan dǎɣ tabarat. |
Abū Kāmil Shujā ibn Aslam (Egypt, 10th century) in particular was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. | Abū Kāmil Šujā ibn Aslam (Misra, 10e temede nawatay) dǎɣ təbiɗawt eqal wadazaran ye tiridawt ən maɗinan ən irrationnel (agudiyan daw əmik ən azar ogdahan, ən azar ən əubique meɣ ən azar wasikoz) sund əliɣitan ɣur alɣisaban quadratiquetan meɣ sund koeffisientan dǎɣ alɣisab iyan. |
His solution was largely based on Al-Khwarizmi's work. | Aliɣi nes eqal hulen ayhan fal əšiɣilan ən Al-Khwarizmi. |