Tamazight-NLP/NLLB-Seed_Tamasheq-Latin-Script huggingface dataset:
English: As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.
Tamasheq: Daɣ ijit n ihandagan ajotnen n teɣare, anfizzak n musnat daɣ awatay wan sians eway id teɣare tijat daɣ ezaraj: illan ti amarad timad n ihandagan n matematik tolas amaskat n matematik wan uchray ewad 46 n paj
English: Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty.
Tamasheq: Matematisyen tan ajotnen issewalan fal tulaɣay n matematik, milɣaw net d tihussay net
English: G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.
Tamasheq: G.H Hardy daɣ A Apoloji n Matematisyen allaɣen medran as tamɣaren tin n milɣaw amos nat, daɣ iman nasnat, a igdahan ihuk n addalil i teɣare n matematik taqwat
English: A theorem expressed as a characterization of the object by these features is the prize.
Tamasheq: Teorem s atawan chund samal n majal s samalan win amos alqim
English: Euler (1707–1783) was responsible for many of the notations in use today.
Tamasheq: Euler (1707 har 1783) annihad i tasnif tan ti axdam nen amarad
English: Unlike natural language, where people can often equate a word (such as cow) with the physical object it corresponds to, mathematical symbols are abstract, lacking any physical analog.
Tamasheq: A izlayan id awal n batil, s addoben addinat alwaq iyyan asikdi n isim ( chund tas) amosan harat wa dar ogdah, ramis tan win matematik war ilen akayad, odanan in harat fuk dar olahan taɣissa
English: Mathematical language also includes many technical terms such as homeomorphism and integrable that have no meaning outside of mathematics.
Tamasheq: Awal wan matematik inta deɣ ahan tifir ajotnen chund homeomorfizm d ijich war n ila almaɣna s ajama n matematik
English: Mathematicians refer to this precision of language and logic as "rigor".
Tamasheq: “Matematisyen tan jan in s aqqud n awal d mantaq s “”qasawat”
English: This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.
Tamasheq: “ Awen ukdal n “”teorem tan war n oɣed, ijanen fal tinufrayen alɣibnen, s almital tan daɣ sanat ijan daɣ attarex n alɣard”
English: Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics.
Tamasheq: Iban anfham n qasawat amos addalil n erk ifahaman n matematik
English: On the other hand, proof assistants allow verifying all details that cannot be given in a hand-written proof, and provide certainty of the correctness of long proofs such as that of the Feit–Thompson theorem.
Tamasheq: Idagan iyad, iməgiha ən tamətert jarawən akayad ən ilaɣitan kul waren adobat atwəhək dǎɣ tamətert təknat as afus, izar hakən assədətu ən tidit ən timtar zəjrətnen sund tin təmkare tan Feit–Thompson .
English: In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
Tamasheq: Fal idakalan azarnen, eɣlakəd harwa tizunawen hakanen as adakal ən mertayən jar ulh ən imaɗinan ad idagan iyad: tiɣdət,musnat ən mertayən (fondations), imaɗinan… ən təmusnawen ajətnen (imaɗinan atiwəjanen) ad, təkna əntinya,almud assohen ən iban assədətu.
English: Some disagreement about the foundations of mathematics continues to the present day.
Tamasheq: Tunjiten tiyad fal tizaren ən imaɗinan tihəšulan har ešali.
English: As such, it is home to Gödel's incompleteness theorems which (informally) imply that any effective formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proved are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system).
Tamasheq: Dǎɣ sund awen, aqalnat eɣaf ən təmkarawen waren imda ən Gödel itajan (as alməɣnat waren ikna)as aratay iknan ajətan ihan imaɗinan azukatnen, as asoɣat (awa dar tidila as timkarawen adobatnen adəkəlnat atwəsəkən aqalnat tidit), eqal tahašilt waren timda (awen dar tidila as əlanəti təmkarawen adutətnen waren adobat atwəsəkən dǎɣ wen mertay.
English: Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science, as well as to category theory.
Tamasheq: Enahəji išrayan azun as tamusne ən atwəɣar, tamusne ən iritan ad tamusne ən tamatert, izar taqal tahurut anmətaf as alaɣi ən tamusne, as sund tamusne tan iritan.
English: Computability theory examines the limitations of various theoretical models of the computer, including the most well-known model—the Turing machine.
Tamasheq: Tamusne ən assedən kayad issəmda ən iritan ajətnen ən tamusne tan ordinateur, as iha iri iknan atwəzy maršin wan Turing.
English: Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity".
Tamasheq: "Tijit ən maɗinan əknanen təwayed deɣ as imaɗinan amindanen,tajanen musnat ən ""waren imədi".""
English: Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra.
Tamasheq: Nadobat səlməɣa teɣare gruɗtan, iɣləlwayan, idagan ad mertayən iyad əfarnen; mertay ən təɣareten (ye təməkrusen atiwalaɣatnen as issidinən ən aɗinan) eqal edag ən aɗinan ifaran.
English: Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions.
Tamasheq: Trigonométrie taqal ašrut ən imaɗinan itajən mertayən jar išrutən ad tədnaɣen ən triangəlten ad ašəɣəlan ən trigonométriques.
English: Convex and discrete geometry were developed to solve problems in number theory and functional analysis but now are pursued with an eye on applications in optimization and computer science.
Tamasheq: Géométrie takirəmbayat as géométrie təfarat atwəsamɣarnat ye amukən ən itaraqan ən tamusne ən maɗinan ad akayad ašeɣalən, mašan aqlnat amadǎɣ alkum dǎɣ ahanay ən ijitan dǎɣ assiwəɗ ad dǎɣ alaɣi.
English: Lie groups are used to study space, structure, and change.
Tamasheq: Gruptan win Lie atiwətkal ye aləmad ən edag, taməkunt ad ašanzi.
English: Functions arise here as a central concept describing a changing quantity.
Tamasheq: Ašəɣəlan atuwənhayan diha sund musnat namas talaɣet tajute tašənzet.
English: One of many applications of functional analysis is quantum mechanics.
Tamasheq: Amukən ən harat eqal iyan ijitan ajətnen ən akayad ašeɣalan.
English: Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data becomes available).
Tamasheq: "Iməlaɣitan (ašeɣalan dǎɣ taberat ən aniyat ən umaɣ) "tajən ….lanen alaɣi "tassəbt ən assətkal ən tabaɣort ad as təmusnawen abeɣərnen; təmənhuyt ən assətkal meɣ ən tamusne taɗinat təzlay akayad ən ihukan (dat as war aqelan təlat). "
English: Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretisation broadly with special concern for rounding errors.
Tamasheq: Akayad naɗin iɣaru timkarawen ye asəbabən ən akayad dǎɣ atkul ən akayad ašeɣalan ad tamusne ən tihza; akayad ən edan ila teɣare ən ihaz ad assusəm as tənna haruwat ad aniyat ebdan ye imrəlitan awednen.
English: The Chern Medal was introduced in 2010 to recognize lifetime achievement.
Tamasheq: Tasɣəlt tan Chern təgaš ɣor 2010 ye iji nalhak ən tədawt ən ijitan.
English: This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved.
Tamasheq: Ismawən iwadən amussan maqaran jar iməssidan, ad ogdahən ad təza tarəqatan atwaqalan amukən amara.
English: The value of Pi was first calculated by him.
Tamasheq: Eqal wazaran as assedən ən migdahaw ən Pi.
English: It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins.
Tamasheq: "Aqalan Pythagoriəientan wijanen issəm ""imaɗinan"", ad dǎɣ issənta teɣare ən imaɗinan ye manassən.”
English: Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).
Tamasheq: Dǎɣ assədətu ən akənas ən fulatik, taməte tan əhrétientan ən Alexandrie tassəsnəntat, dǎɣ tənna as tartay. Dǎɣ uzif iness ad ašəšar nelam iness as fokiamən ən ɗalourdes (iyad janen tuilten).
English: Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences.
Tamasheq: Tamazilt ən alaɣi ən ikatabən amusənen dǎɣ iyad magridan tanəlkam ɣor təšəjrit ən təməniya ən kaliftan iyad, izar atwəsan as imusanən iyad aqalan imusanən dǎɣ alkad wi talaɣen izar ijrawən ɣor saɣlay nassən talilt tawedat ye ikuy ən asjət ən təmusnawen tiyad.
English: A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths.
Tamasheq: Tamezlayt maqarat ən imusanən ajətnen ašeɣalnen daw tijra tan inəsləman ɣor azaman taruwat taqal as aqalan agud inəmussanən.
English: During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer).
Tamasheq: Daɣ azzaman wen ɣur agna wan feodal d ekleziastik har wan ɣalamaniya , matematisyen tan ililan daɣ is alxidmaten tiyyad: Luca Pacioli (amaxlak n medan), Niccolo Fontana Tartaglia (injenieur maqqoran d anaɣlaf n alkittaban); Gerolamo Cardano (amaxlak wan ezzaran n ach-ak d efes n binom); Robert Recorde (fizisien) d Francois Viete (avoka)
English: British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
Tamasheq: Universiteten tin Britannique ən azaman ten dakalnat ihzawan iyad olahnen ye universiteten tin Italie ad Allemagne, mašan sund ilanət harwa tanoflayt ad tahajit tahusket, išənzitan assətan ad awatay wan ifewan, tijraten tindǎɣ assəflasnen Humboldt.
English: Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content.
Tamasheq: Iməɣran adoben agay ən umaɣawən dǎɣ séminairtan meɣ ihanan numaɣ izar santen iji ən batutən ən doctorat ən amas iknan musnat.
English: Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.
Tamasheq: Iməssidan ad iməssidan janen atiwətkalən sund assin dǎɣ tahajit STEM (tamusne, amukən, temašaɣalt ad imaɗinan).
English: Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk.
Tamasheq: Inəlmadan tajan harwa assestanən ən izərfan,atamosan wi aqalnen edag ən isdawan ən tasunfat tahušalat ye iji ajaraw iyan ən tasunfat ad alməɣna was ehan ad ašəš ən haratan ye asjət ən ajaraw ən išəša iness takətawt ən mahəlat tasohet.
English: The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting.
Tamasheq: Tartit hiéroglyphique ən edanən win misratan, sund edanən win romaintan adəmalanen, azizəbat iritan ən idud atiwatkalan yeassedən.
English: Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals, and the vigesimal (base 20) system that defined Maya numerals.
Tamasheq: Tartiyen azarnen ən edanən lanen akatab azuken war aqelan déəimaux,atamosan tartit sexagésimal (ider 60) ye edan win Babylontan ad tartit ɣigésimal (ider 20) talaɣet edanən win mayas.
English: Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
Tamasheq: Dat ašəɣəlan win Euclide, ibret 300 dat. J.-C., tiɣaraten grectan dǎɣ imaɗinan timəqussən ad təflas ən məgridən ad ufaran.
English: The ancient Greeks lacked a symbol for zero until the Hellenistic period, and they used three separate sets of symbols as digits: one set for the units place, one for the tens place, and one for the hundreds.
Tamasheq: Grectan arunen warlen ešwal ye wala dat alwaq ən tanalmut, izar dakalan qarad mertayən azlaynen as ešwəlan ye edanən: mertay ye tabəde ən iyan,iyan ye tabəde tan təmərwen ad iyan ye timad.
English: Their long division algorithm was the same, and the digit-by-digit square root algorithm, popularly used as recently as the 20th century, was known to Archimedes (who may have invented it).
Tamasheq: Algorithme ən tazunt zəjret eqal iyan, ad algorithme wan racine carrée adin as adin, ajət nətwətkal əar ɣor 20e awatay, atiwazay as Archimède (as ihaməš atijan).
English: The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra.
Tamasheq: Chinoitan arunen ikrašan tiɣareten edanan okaynen assintanen as alɣayal wan Tang, imaɗinan ən azarnen as madin okayan.
English: For the hundreds place, they then reused the symbols for the units place, and so on.
Tamasheq: Ye edag ən timaɗ, dakalan harwa ešwalan ən edag ən iyan, as dǎɣ amsuɣəl.
English: The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers.
Tamasheq: Chinoitan arunen aqalan imizaran ən ajaraw, musnat ad iji ən imaɗinan atəkanen as alməɣna atiwassənan.
English: His contemporary, the Syriac bishop Severus Sebokht (650 AD) said, "Indians possess a method of calculation that no word can praise enough.
Tamasheq: "Aqalan azaran, amənokal ən Syriya Severus Sebokht (650 darat J.-C.) assilmad :" Indutan əkrašən tamkare ən assedən as wala iyat tafert wartəssen atkul".
English: The Arabs also learned this new method and called it hesab.
Tamasheq: Araban almadən deɣ tamkare taynayat izar aɣrətat as hesab.
English: The flourishing of algebra in the medieval Islamic world, and also in Renaissance Europe, was an outgrowth of the enormous simplification of computation through decimal notation.
Tamasheq: Ajət ən idan dǎɣ taməte tan inəsləman arunen, mašan deɣ dǎɣ Europe tan išray, taqal asəbab ən tamɣare təfnazat ən assedən as akatab décimale.
English: Arithmetic expressions must be evaluated according to the intended sequence of operations.
Tamasheq: Tənaten ən maɗinan adəqəlnat atwəkat as amək tazunt ən sidinən atiwəqalnen.
English: For example, digital computers can reuse existing adding-circuitry and save additional circuits for implementing a subtraction, by employing the method of two's complement for representing the additive inverses, which is extremely easy to implement in hardware (negation).
Tamasheq: Sund, ordinatertan ən edanən adoben atkul ən taberaten ən assiwəd aɣlaknen ad assəməsədu ən taberaten awednen as sanatən ye assəkən ən imliliyan awednen, awa iknan təraɣse ən iji dǎɣ ašəɣəl dǎɣ harat (tamətki).
English: Multiplication also combines two numbers into a single number, the product.
Tamasheq: Asjət asertay deɣ assin edan as iyan dǎɣ, asənətfəs.
English: If the numbers are imagined as lying in a line, multiplication by a number greater than 1, say x, is the same as stretching everything away from 0 uniformly, in such a way that the number 1 itself is stretched to where x was.
Tamasheq: As aznazjamat awadəm as imaɗinan ilan ɣor tassaret,asjət as adin ojarən 1, nənna x, eqalid as anərkəb olahən awa itijəjan kul 0, as alməɣna as adin 1 imanes adəqəl anərkab ɣor edag ɣor ila x.
English: Any dividend divided by zero is undefined.
Tamasheq: Amazun kul azunən as wala war atwəssən.
English: The fundamental theorem of arithmetic was first proven by Carl Friedrich Gauss.
Tamasheq: Tamkare maqarat ən edan tatiwasəkna as tizarat as Carl Friedrich Gauss.
English: Positional notation (also known as "place-value notation") refers to the representation or encoding of numbers using the same symbol for the different orders of magnitude (e.g., the "ones place", "tens place", "hundreds place") and, with a radix point, using those same symbols to represent fractions (e.g., the "tenths place", "hundredths place").
Tamasheq: "Akatab ibdadən (tatiwazayat fal issəm ən ""akatab tamɣar ən edag(""itirək as assəkən meɣ aɣafal ən maɗinan dǎɣ atkul ən iyan ešwal ən mezlayən anilkamnen ən tamɣar (sund,""edag ən iyad""""edag ən təmərwen(""izar, ad edag ən radix, dǎɣ atkul ən ešwalan olahnen ye assəkən ən ikərumatan (sund,""edag ən tamara """"edagən timad".(""
English: The use of 0 as a placeholder and, therefore, the use of a positional notation is first attested to in the Jain text from India entitled the Lokavibhâga, dated 458 AD and it was only in the early 13th century that these concepts, transmitted via the scholarship of the Arabic world, were introduced into Europe by Fibonacci using the Hindu–Arabic numeral system.
Tamasheq: Atkul ən wala sund harat ən assəmutiy ad,as alkum,atkul ən akatab azuken eqal taguhe ye tizarat dǎɣ akatab jaïn ən Inde atiwəɣran as Lokaɣibhâga, intan ɣor 458 darat J.-C. izar ɣor sənto ən 13e awatay as muziyaten, atiwəfanen as torhajət ən musnat ən adunya ən tarabt,agašən ɣor Europe as Fibonacci dǎɣ atkul ən mertay ən adin hindu-tarabt.
English: The result is calculated by the repeated addition of single digits from each number that occupies the same position, proceeding from right to left.
Tamasheq: Agaraw atiwassedan as assiwad amissaɣalan ən adinan iyadǎɣ ən maɗin kul ikrašən edag iyan ,as atkul ɣor aɣil as tašalje.
English: The rightmost digit is the value for the current position, and the result for the subsequent addition of the digits to the left increases by the value of the second (leftmost) digit, which is always one (if not zero).
Tamasheq: Adin iknan ugiš ən aɣil edagar ən edaj namaradǎɣ, ad agaraw ən assiwad adimalan ən edanan dǎɣ tašalje tiwadan as talət ən edan wasəsin (ihan tašalje),ogdahən harkuk ad iyan (as warogdeh as wala).
English: A multiplication table with ten rows and ten columns lists the results for each pair of digits.
Tamasheq: Tabalt ən assənətfəs təlat maraw laytan ad marawat təzunawen issakna igarawən ən assin edanən kul.
English: Similar techniques exist for subtraction and division.
Tamasheq: Timkarawen olahnen aɣlaknat ye afanaz ad tazunt .
English: In mathematical terminology, this characteristic is defined as closure, and the previous list is described as .
Tamasheq: Dǎɣ saməndo ən maɗin, tamezlayt tatiwatkal sund aɣəfal, akatab okayan tatiwalaɣat sund.
English: The total in the pence column is 25.
Tamasheq: Amsədu ən tazunt ən pence taqal 25.
English: This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column.
Tamasheq: Assedən wen amissaɣəl dǎɣ atkul edan ən ehan ən šillings, ad ašrut awedan təfat asiwad ən adin izjarən ihan wan pennies.
English: One typical booklet that ran to 150 pages tabulated multiples "from one to ten thousand at the various prices from one farthing to one pound".
Tamasheq: "Alkad olahan ilan 150 ɗageten issakna tijutawen ""ɣor iyan as maraw efdan ɣor hebutan abdanen əlanen ɣor farthing as alkad"".
English: This study is sometimes known as algorism.
Tamasheq: Aləmad wen atiwəssan agud iyan fal issəm ən algorisme.
English: Also, arithmetic was used by Islamic Scholars in order to teach application of the rulings related to Zakat and Irth.
Tamasheq: Edanən atiwətkal deɣ as imusanən ən inəsləman ye assaɣar ən iji tənaten adəkalen Tanaqast ad Irth.
English: Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.
Tamasheq: Assiwad (atiwətkal as ešwal ən assiwad) taqal iyan dǎɣ akoz sidinən ən amas ən madin, karad wiyadnen aqalan afanaz, assənətfəs ad tazunt.
English: In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Tamasheq: Dǎɣ assedin, edag iyan ən imaɗinan, assiwəd adobat atwəj fal haratan əfarnen sund ɣeəteurtan, matrices, tidəgaten ad təmsədawen.
English: Using the gerundive suffix -nd results in "addend", "thing to be added".
Tamasheq: Atkul ən səmdo gérondif -nd ihaku edag ye ""addenadde”", “”harat ən assiwad""."
English: """Sum"" and ""summand"" derive from the Latin noun summa ""the highest, the top"" and associated verb summare."
Tamasheq: ""Sum"ad ""Summand""izjarənid issəm latin summa ""iknan azaway,afəla""ad magrad ertayan summare".
English: The later Middle English terms "adden" and "adding" were popularized by Chaucer.
Tamasheq: "Tənaten ən tədabit-təglizit təknat tahajit "adden"ad “"adding"”atwəzayan as Chaucer."
English: As an example, should the expression a + b + c be defined to mean (a + b) + c or a + (b + c)?
Tamasheq: As təlat ən milhaw,akatab a + b + c as atwətkəl sund adərtidila ( a + b) + c meɣ a + (b + c)?
English: Even some nonhuman animals show a limited ability to add, particularly primates.
Tamasheq: Iyad imudaran imanes waren eqel adinat saknen assahat ən assiwad ibdadən, atamosən aytedim.
English: With additional experience, children learn to add more quickly by exploiting the commutativity of addition by counting up from the larger number, in this case, starting with three and counting "four, five."
Tamasheq: Ad aləmad, aratən lamədan assiwəd šikanen as dakalan asəmələliy ən assiwad as sadanən ɣor maɗin wa iknan təmɣare,dǎɣ edag wen, dǎɣ assənt as karad as isadan "akoz, səmos."
English: Zero: Since zero is the additive identity, adding zero is trivial.
Tamasheq: Wala: falas wala eqal muzyat tawedat, assiwad ən wala eqal raqis.
English: One aligns two decimal fractions above each other, with the decimal point in the same location.
Tamasheq: Nəzimzizer assin ikərumatən decimales iyan fal iyan, ad edag décimal ɣor iyan edag.
English: If the addends are the rotation speeds of two shafts, they can be added with a differential.
Tamasheq: As issiwedan aqalan azalən ən ɣalayan ən assin ihəškan, nadobat assərtay ad ebadi.
English: It made use of a gravity-assisted carry mechanism.
Tamasheq: Exdm s mekaniz idhal gravite
English: To subtract, the operator had to use the Pascal's calculator's complement, which required as many steps as an addition.
Tamasheq: Fal agamad, adabara anihaga adamatkal talɣa ən əaləulatriəe wan Pascal, awa amosan hadi ən hadagan ən asiwid.
English: Both XOR and AND gates are straightforward to realize in digital logic allowing the realization of full adder circuits which in turn may be combined into more complex logical operations.
Tamasheq: Išar wi XOR əd AND aqalan fal asinanesan banan ye aritwigin dǎɣ oɣadan ən numérique dǎɣ adabaratan oɣadnen ogarnen aśuhu.
English: Many implementations are, in fact, hybrids of these last three designs.
Tamasheq: Ajotnen isiqtitan aqalan, dǎɣ aygan, abdanen əd wi karad ilkamnen təmoɣgrazen.
English: Unanticipated arithmetic overflow is a fairly common cause of program errors.
Tamasheq: Isusukayan ən arithmétique fal iba nigi eqal harat amosan atiwazayan dǎɣ qaɣadan ən asinihigi.