ConseggioLigure/seed-instruct-eng-lij huggingface dataset:
What’s the Ligurian translation of this sentence?
Amerindians continue to be defined by a certain percentage of "Indian blood" (called blood quantum).
The Ligurian (Genoese) translation is:
I Amerindi van avanti à ëse definii in base à unna determinâ fraçion de «sangue indian» (ciammâ quantum de sangue).
Translate from English to Genoese:
This rule meant that those that were mixed race but with some discernible African ancestry were defined as black.
The Ligurian (Genoese) translation is:
Sta regola a voeiva dî che chi l'ea de razza mesccia ma con quarche ascendensa africaña ch'a se poesse reconosce o fïse definio möo.
What’s the Genoese translation of this sentence?
The term "Hispanic" as an ethnonym emerged in the 20th century with the rise of migration of laborers from the Spanish-speaking countries of Latin America to the United States.
The Ligurian (Genoese) translation is:
O termine «ispanico» o l'é vegnuo feua comme etnònimo do secolo XX co-o montâ da migraçion di louanti da-i paixi de lengua spagnòlla de l'America Latiña verso i Stati Unii.
What’s the Genoese translation of this sentence?
Three factors, country of academic education, discipline, and age, were found to be significant in differentiating the replies.
The Ligurian (Genoese) translation is:
Trei fattoî son stæti tegnui pe scignificativi pe-a differençiaçion de respòste: paise d'instruçion academica, discipliña e etæ.
Translate to Ligurian (Genoese):
In 2007, Ann Morning interviewed over 40 American biologists and anthropologists and found significant disagreements over the nature of race, with no one viewpoint holding a majority among either group.
The Ligurian (Genoese) translation is:
Do 2007, a Ann Morning a l'à intervistou 40 e passa biòlogi e antropòlogi americhen e a l'à attrovou de discordanse scignificative in sciâ natua da razza, sensa che nisciun ponto de vista o prevaisse tra i doî gruppi.
Translate this sentence to Ligurian:
In partial response to Gill's statement, Professor of Biological Anthropology C. Loring Brace argues that the reason laymen and biological anthropologists can determine the geographic ancestry of an individual can be explained by the fact that biological characteristics are clinally distributed across the planet, and that does not translate into the concept of race.
The Ligurian (Genoese) translation is:
Pe responde in parte a-a deciaraçion do Gill, o professô d'antropologia biològica C. Loring Brace o sostëgne che a raxon pe-a quæ di inesperti e bioantropòlogi arriëscian à determinâ l'ascendensa geografica de un individuo a peu ëse ascciæia da-o fæto che e caratteristiche biològiche an unna distribuçion clinale into pianeta, e sto chì o no se traduxe into conçetto de razza.
What’s the Genoese translation of this sentence?
Physical anthropology texts argued that biological races exist until the 1970s, when they began to argue that races do not exist.
The Ligurian (Genoese) translation is:
I testi d'antropologia fixica affermavan che e razze biològiche existan fin a-i anni '70, quande an comensou à sostegnî che e razze no existan.
Translate from English to Ligurian:
In February 2001, the editors of Archives of Pediatrics and Adolescent Medicine asked "authors to not use race and ethnicity when there is no biological, scientific, or sociological reason for doing so."
The Ligurian (Genoese) translation is:
Into frevâ do 2001, i editoî da revista Archives of Pediatrics and Adolescent Medicine an domandou a-i «autoî de no deuviâ razza e etniçitæ quande no existe unna raxon biològica, scientifica ò soçiològica pe fâlo».
Translate to Genoese:
Morning (2008) looked at high school biology textbooks during the 1952–2002 period and initially found a similar pattern with only 35% directly discussing race in the 1983–92 period from initially 92% doing so.
The Ligurian (Genoese) translation is:
O Morning (2008) o l'à examinou i testi de biologia pe-a scheua segondäia erta do periodo 1952-2002 e in scê primme o l'à attrovou un modello analogo, donde solo o 35% o discorriva sensa regii de razza into periodo 1983-92 à peto do 92% into primmo periodo.
What’s the Genoese translation of this sentence?
In general, the material on race has moved from surface traits to genetics and evolutionary history.
The Ligurian (Genoese) translation is:
Inte l'insemme, o materiale in sciâ razza o l'é passou da-i træti de feua a-a genetica e a-a stöia evolutiva.
Translate to Ligurian (Genoese):
She notes, "At best, one can conclude that biologists and anthropologists now appear equally divided in their beliefs about the nature of race."
The Ligurian (Genoese) translation is:
O nòtta: «Pe tutto ch'a vagghe ben, se peu concludde che biòlogi e antropòlogi oua pan spartii pægi inte seu convinçioin in sciâ natua da razza».
Translate this sentence to Ligurian:
33 health services researchers from differing geographic regions were interviewed in a 2008 study.
The Ligurian (Genoese) translation is:
Inte un studio do 2008 l'é stæto intervistou 33 reçercatoî de serviçi sanitäi che ne vegnivan da regioin geografiche differente.
Translate from English to Ligurian:
Many sociologists focused on African Americans, called Negroes at that time, and claimed that they were inferior to whites.
The Ligurian (Genoese) translation is:
Tanti soçiòlogi se son conçentræ in scî afroamerichen, che alantô se ghe diva möi, e an affermou ch'ean ciù grammi che i gianchi.
Translate from English to Genoese:
His solution was largely based on Al-Khwarizmi's work.
The Ligurian (Genoese) translation is:
A seu soluçion a l’ea basâ pe-o ciù in sce l’euvia de Al-Khwarizmi.
Translate from English to Genoese:
However, at some point the quadratic formula begins to lose accuracy because of round off error, while the approximate method continues to improve.
The Ligurian (Genoese) translation is:
À tutti i mòddi, à un çerto ponto a fòrmola quaddratica a comensa à perde de preçixon apreuvo à l’errô d’arriondamento, tanto che o metodo approscimativo o se fa delongo ciù bon.
Translate to Ligurian (Genoese):
Methods of numerical approximation existed, called prosthaphaeresis, that offered shortcuts around time-consuming operations such as multiplication and taking powers and roots.
The Ligurian (Genoese) translation is:
Di metodi d’approscimaçion numerica, diti prostaferexi, existeivan, e offrivan di scorsaieu pe de operaçioin che domandavan tròppo tempo, comme a moltiplicaçion e quelle in sce de potense ò de reixe.
Translate from English to Ligurian (Genoese dialect):
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.
The Ligurian (Genoese) translation is:
I algoritmi computaçionæ pe attrovâ e soluçion en unna parte importante de l’algebra lineare numerica e zeugan un ròllo importante inte l’inzegneria, inta fixica, inta chimica, inte l’informatica e inte l’econòmia.
What’s the Ligurian translation of this sentence?
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.
The Ligurian (Genoese) translation is:
Pe de soluçioin inte un dominio integrale comme l’anello di numei intreghi, ò inte de atre struttue algebriche, l’é stæto sviluppou de atre teorie (s’ammie Equaçion lineare in sce un anello).
Translate from English to Genoese:
This allows all the language and theory of vector spaces (or more generally, modules) to be brought to bear.
The Ligurian (Genoese) translation is:
Sto fæto o perette de deuviâ tutto o lenguaggio e a teoria di spaçi vettoriali (ò, ciù in generale, di mòdoli).
Translate to Ligurian:
Such a system is known as an underdetermined system.
The Ligurian (Genoese) translation is:
Un scistema comme questo o l’é dito scistema indeterminou.
What’s the Ligurian translation of this sentence?
The second system has a single unique solution, namely the intersection of the two lines.
The Ligurian (Genoese) translation is:
O segondo scistema o l’à unna scingola soluçion unica, saieiva à dî l’interseçion tra doe linie.
Translate this sentence to Genoese:
Any two of these equations have a common solution.
The Ligurian (Genoese) translation is:
Doe chechesegge de ste equaçioin an unna soluçion scompartia.
What’s the Ligurian translation of this sentence?
A system of equations whose left-hand sides are linearly independent is always consistent.
The Ligurian (Genoese) translation is:
Un scistema d’equaçioin donde i loei a-a manciña en linearmente independenti o l’é delongo coerente.
Can you translate this text to Ligurian?
This yields a system of equations with one fewer equation and one fewer unknown.
The Ligurian (Genoese) translation is:
Sto fæto o profuxe un scistema de equaçioin con unn’equaçion de meno e unn’incògnita de meno.
Can you translate this text to Ligurian?
Type 3: Add to one row a scalar multiple of another.
The Ligurian (Genoese) translation is:
Tipo 3: Azzonze à unna riga un moltiplo scalare de unn’atra.
What’s the Ligurian translation of this sentence?
For instance, systems with a symmetric positive definite matrix can be solved twice as fast with the Cholesky decomposition.
The Ligurian (Genoese) translation is:
Pe fâ un exempio, i scistemi con unna matrixe definia poxitiva scimmetrica peuan vegnî resòlte doe vòtte ciù a-a lesta co-a decompoxiçion de Cholesky.
Translate this sentence to Ligurian:
A completely different approach is often taken for very large systems, which would otherwise take too much time or memory.
The Ligurian (Genoese) translation is:
De spesso unna metodologia do tutto despægia a ven adottâ pe di scistemi assæ grendi, che in caxo conträio domandieivan tròppo tempo ò memöia.
Translate to Genoese:
This leads to the class of iterative methods.
The Ligurian (Genoese) translation is:
Questo o pòrta a-a classe di metodi iterativi.
Translate this sentence to Genoese:
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.
The Ligurian (Genoese) translation is:
In matematica unna seria a l’é, grosso modo, a descriçion de l’operaçion d’addiçion infinia de tante quantitæ, uña apreuvo à l’atra, fin à unna quantitæ determinâ.
Translate to Ligurian:
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.
The Ligurian (Genoese) translation is:
A-o de là da seu recorrensa estrema inta matematica, e serie infinie en ben ben deuviæ ascì inte de atre discipliñe quantitative comme a fixica, l’informatica, a statistica e a finansa.
Translate to Ligurian (Genoese):
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.
The Ligurian (Genoese) translation is:
O paradòsso de Zenon d’Achille e da trattugoa o l’ascciæisce sta propietæ contraintuitiva de somme infinie: Achille o core apreuvo à unna trattugoa, ma quande o razzonze a poxiçion de quest’urtima a-o comenso da corsa, a trattugoa a l’é arrivâ à unna segonda poxiçion; quande o razzonze ascì sta segonda poxiçion, a trattugoa a n’à razzonto unna tersa, e coscì avanti.
Translate from English to Ligurian (Genoese dialect):
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.
The Ligurian (Genoese) translation is:
Sta spiegaçion a no preuva che a somma a fasse 2 (sciben ch’a l’é coscì), ma a prova che à segge a-o manco pægia a-o 2.
Translate from English to Ligurian (Genoese dialect):
Tests for uniform convergence include the Weierstrass' M-test, Abel's uniform convergence test, Dini's test, and the Cauchy criterion.
The Ligurian (Genoese) translation is:
I test pe-a convergensa uniforma compendan o test M de Weierstrass, o test de convergensa uniforme de Abel, o test de Dini e o critëio de Cauchy.
Translate this sentence to Ligurian:
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.
The Ligurian (Genoese) translation is:
A convergensa a l’é uniforme in sce di sottinsemmi serræ e delimitæ (saieiva à dî compatti) de l’interno do disco de convergensa: saieiva à dî ch’a l’é uniformemente converzente in sce di insemmi compatti.
Translate to Genoese:
The Hilbert–Poincaré series is a formal power series used to study graded algebras.
The Ligurian (Genoese) translation is:
A serie Hilbert-Poincaré a l’é unna serie formale de potensa ch’a se deuvia pe studiâ e algebre gradduæ.
Can you translate this text to Ligurian?
In the 17th century, James Gregory worked in the new decimal system on infinite series and published several Maclaurin series.
The Ligurian (Genoese) translation is:
Do secolo dïsette James Gregory o l’aiva travaggiou in sciô neuvo scistema deximâ in sce de serie infinie e o l’à pubricou tante serie de Maclaurin.
Translate from English to Ligurian:
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.
The Ligurian (Genoese) translation is:
Cauchy (1821) o l’à inscistio in sce de preuve rigorose de convergensa; o l’à demostrou che se doe serie en converzente o seu produto o no ô l’é neçessäiamente, e con lê comensa a descoverta de critëi efficaçi.
Translate to Ligurian (Genoese):
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.
The Ligurian (Genoese) translation is:
Un metodo de sommabilitæ a l’é l’assegnaçion de un limite à un sottinsemme de l’insemme de serie diverzente ch’a l’estende correttamente a noçion clascica de convergensa.
Translate from English to Ligurian:
Indian scholars have been using factorial formulas since at least the 12th century.
The Ligurian (Genoese) translation is:
I scensiæ indien an deuviou e formole fattoriæ fin a-o manco a-o secolo dozze.
Translate from English to Ligurian:
In functional languages, the recursive definition is often implemented directly to illustrate recursive functions.
The Ligurian (Genoese) translation is:
Inti lenguaggi fonçionali, de spesso a definiçion recorsciva a ven implementâ direttamente pe illustrâ de fonçioin ricorscive.
Can you translate this text to Ligurian?
Other implementations (such as computer software such as spreadsheet programs) can often handle larger values.
The Ligurian (Genoese) translation is:
De atre implementaçioin (comme di software pe computer, comme di programmi pe di feuggi de carcolo) de spesso peuan gestî di valoî ciù grendi.
What’s the Ligurian translation of this sentence?
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.
The Ligurian (Genoese) translation is:
No gh’é, relativamente parlando de soluçioin coscì sencie pe-i fattoriali; nisciuña combinaçion finia de somme, produti, potense, fonçioin esponençiale ò logaritmi a saià abasta pe esprimme ; ma l’é poscibile trovâ unna formola generale pe-i fattoriali pe mezo de strumenti comme integrali e limiti da-o carcolo.
Can you translate this text to Ligurian?
The integrals we have discussed so far involve transcendental functions, but the gamma function also arises from integrals of purely algebraic functions.
The Ligurian (Genoese) translation is:
I integrali di quæ emmo parlou finoua an da fâ con de fonçioin trascendentale, ma a fonçion gamma a nasce anche da di integrali de fonçioin algebriche pue.
What’s the Genoese translation of this sentence?
By taking limits, certain rational products with infinitely many factors can be evaluated in terms of the gamma function as well.
The Ligurian (Genoese) translation is:
Piggiando i limiti, çerti produti raçionali con di fattoî infinii peuan vegnî valuæ anche in termini da fonçion gamma.
What’s the Ligurian translation of this sentence?
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.
The Ligurian (Genoese) translation is:
A seu stöia, documentâ mascime da Philip J. Davis inte un articolo ch’o gh’à asseguou o premio Nobel do 1963, a reflette tanti di sviluppi prinçipæ drento da matematica da-o secolo dixeutto.
Translate this sentence to Ligurian:
Instead of finding a specialized proof for each formula, it would be desirable to have a general method of identifying the gamma function.
The Ligurian (Genoese) translation is:
Incangio de trovâ unna preuva speçializzâ pe tutte e formole, saieiva bon avei un metodo generale pe identificâ a fonçioin gamma.
What’s the Ligurian translation of this sentence?
However, the gamma function does not appear to satisfy any simple differential equation.
The Ligurian (Genoese) translation is:
À tutti i mòddi, a fonçion gamma a no pâ satisfâ nisciuña equaçion differençiale sencia.
Translate from English to Genoese:
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.
The Ligurian (Genoese) translation is:
O teorema de Bohr-Mollerup o l’é utille perché l’é relativamente façile demostrâ a convescitæ logaritmica pe uña de varie formole deuviæ pe definî a fonçion gamma.
Translate this sentence to Genoese:
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.
The Ligurian (Genoese) translation is:
Quande di anni ’50 i computer elettrònichi en stæti boin à produe de tabelle, l’é stæto pubricou varie tabelle esteise pe-a fonçion gamma complessa pe satisfâ a domanda, compreiso unna tabella accurâ fin à 12 giffre deximæ produta da-o U.S. National Bureau of Standards.
Can you translate this text to Ligurian?
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.
The Ligurian (Genoese) translation is:
Inta sciensa, unna fòrmola a l’é unna mainea curta d’esprimme unn’informaçion à livello scimbòlico, comme inte unna fòrmola matematica ò chimica.
Translate to Genoese:
In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems.
The Ligurian (Genoese) translation is:
Inta matematica, unna fòrmola pe-o sòlito a fa referensa à unn’identitæ ch’a definisce l’egualiansa tra unn’esprescion matematica e unn’atra; e ciù importante son i teoremi da matematica.
What’s the Genoese translation of this sentence?
This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex.
The Ligurian (Genoese) translation is:
Sta covençion, sciben che meno importante inte unna formula relativamente sencia, a scignifica che i studioxi da matematica peuan manipolâ ciù a-a lesta de formole ciù grende e complesse.
Translate to Ligurian:
For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom.
The Ligurian (Genoese) translation is:
Pe fâ un exempio, H2O a l’é a formola chimica de l’ægua, donde se dixe che tutte e seu molecole comprendan doî atomi d’idrògeno e un d’oscigeno.
Translate this sentence to Ligurian:
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.
The Ligurian (Genoese) translation is:
Inte formole empiriche, ste proporçioin comensan con un elemento ciave e dapeu assegnan di numei d’atomi di atri elementi into compòsto (comme rappòrti à l’elemento ciave).
Translate from English to Genoese:
Some types of ionic compounds, however, cannot be written as empirical formulas which contains only the whole numbers.
The Ligurian (Genoese) translation is:
À tutte e mainee, çerte qualitæ de compòsti chimichi no peuan vegnî scrite comme formole empiriche che contëgnan solo di numei intreghi.
Translate to Ligurian:
There are several types of these formulas, including molecular formulas and condensed formulas.
The Ligurian (Genoese) translation is:
Gh’é tante qualitæ de ste formole, compreiso quelle molecolare e condensæ.
What’s the Genoese translation of this sentence?
Functions were originally the idealization of how a varying quantity depends on another quantity.
The Ligurian (Genoese) translation is:
In origine e fonçioin ean l’idealizzaçion de unna unna quantitæ variabile a depende da unn’atra quantitæ.
Translate from English to Ligurian:
This definition of "graph" refers to a set of pairs of objects.
The Ligurian (Genoese) translation is:
Sta definiçioin de «grafico» a fa referensa à un insemme de cobbie d’oggetti.
Translate from English to Ligurian (Genoese dialect):
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.
The Ligurian (Genoese) translation is:
Quande o dominio e o codominio son insemmi de numei reali, tutte e cobbie peuan vegnî pensæ comme e coordinæ cartexañe de un ponto in sciô cian.
Translate to Ligurian:
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.
The Ligurian (Genoese) translation is:
Unna mappa a peu avei un insemme chesesegge comme codominio, mentre inte çerti contesti (tipicamente inti libbri ciù vegi) o codominio de unna fonçion o l’é speçificamente l’insemme di numei reali ò complesci.
What’s the Ligurian translation of this sentence?
Another common example is the error function.
The Ligurian (Genoese) translation is:
Un atro exempio commun a l’é a fonçion d’errô.
Translate to Genoese:
Then, the power series can be used to enlarge the domain of the function.
The Ligurian (Genoese) translation is:
Dapeu se peu deuviâ a serie de potensa pe allargâ o dominio da fonçion.
Translate this sentence to Genoese:
Parts of this may create a plot that represents (parts of) the function.
The Ligurian (Genoese) translation is:
De parte de questo peuan creâ un grafico ch’o representa (parte de) unna fonçion.
Translate from English to Ligurian:
This is the canonical factorization of .
The Ligurian (Genoese) translation is:
Sta chì a l’é a fattorizzaçion canònica de .
Translate from English to Genoese:
At that time, only real-valued functions of a real variable were considered, and all functions were assumed to be smooth.
The Ligurian (Genoese) translation is:
À quelli tempi se consciderava solo de fonçioin con di valoî reali de unna variabile, e se supponeiva che tutte e fonçioin fïsan lisce.
Translate this sentence to Genoese:
Functions are now used throughout all areas of mathematics.
The Ligurian (Genoese) translation is:
E fonçioin oua se deuvian inte tutti i campi da matematica.
Translate to Ligurian (Genoese):
This is how inverse trigonometric functions are defined in terms of trigonometric functions, where the trigonometric functions are monotonic.
The Ligurian (Genoese) translation is:
Coscì l’é comme se definisce e fonçioin trigonometriche inverse in termini de fonçion trigonometriche, donde e fonçioin trigonometriche en monòtone.