Étienne Bézout ( 31 March 1730 – 27 September 1783 ) was a French mathematician who was born in Nemours, Seine-et-Marne, France, and died in Basses-Loges ( near Fontainebleau ), France.

Alexandre-Théophile Vandermonde ( 28 February 1735 – 1 January 1796 ) was a French musician, mathematician and chemist who worked with Bézout and Lavoisier ; his name is now principally associated with determinant theory in mathematics.

An integral domain is a Bézout domain if and only if any two elements in it have a gcd that is a linear combination of the two.

Actually, their forerunners were civil servant schools aimed at graduating mine supervisors ( École des mines de Paris established in 1783 ), bridge and road engineers ( École royale des ponts et chaussées established in 1747 ), shipbuilding engineers ( École des ingénieurs-constructeurs des vaisseaux royaux established in 1741 ) and five military engineering academies and graduate schools of artillery established in the 17th century in France, such as the école de l ' artillerie de Douai ( established in 1697 ) and the école du génie de Mézière ( established in 1748 ), wherein mathematics, chemistry and sciences were already a major part of the curriculum taught by first rank scientists such as Pierre-Simon de Laplace, Charles Étienne Louis Camus, Étienne Bézout, Sylvestre-François Lacroix, Siméon Denis Poisson, Gaspard Monge.

* The ring of algebraic integers A is a Bézout domain.

In general, the integral closure of a Dedekind domain in an infinite algebraic extension is a Prüfer domain ; it turns out that the ring of algebraic integers is slightly more special than this: it is a Bézout domain.

is a multiple of d. x and y are called Bézout coefficients for ( a, b ); they are not unique.

French mathematician Étienne Bézout ( 1730 – 1783 ) proved this identity for polynomials.

However there is a variation of Gauss's lemma that is valid even for polynomials over any commutative ring R, which replaces primitivity by the stronger property of co-maximality ( which is however equivalent to primitivity in the case of a Bézout domain, and in particular of a principal ideal domain ).

A Bézout domain is thus a GCD domain, and ( 4 ) gives yet another proof that a PID is a UFD.

# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.

In 1783, after leaving Mézières, he was, on the death of É. Bézout, appointed examiner of naval candidates.

Although pressed by the minister to prepare a complete course of mathematics, he declined to do so, on the grounds that this would deprive Mme Bézout of her only income, that from the sale of the textbooks written by her late husband.

In mathematics, a Bézout matrix ( or Bézoutian or Bezoutiant ) is a special square matrix associated with two polynomials, introduced by and and named after Étienne Bézout.

The Bézout matrix of order n associated with the polynomials f and g is

A pair of Bézout coefficients ( in fact the ones that are minimal in absolute value ) can be computed by the extended Euclidean algorithm.

An integral domain in which Bézout's identity holds is called a Bézout domain.

* 1730 – Étienne Bézout, French mathematician ( d. 1783 )

She also enjoyed Traité d ' Arithmétique by Étienne Bézout and Le Calcul Différential by Jacques Antoine-Joseph Cousin.

In 1758 Bézout was elected an adjoint in mechanics of the French Academy of Sciences.

Elimination theory equivalent to the wasan form was rediscovered by Étienne Bézout in 1764.

An important application of Bézout matrices can be found in control theory.

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

He went to Key West every fall and winter and was the only man in town who did not know that his title of `` Commodore '' was never used without irony.

The fact that the Americans who upheld the sovereignty of their states did this in order to keep many of their people more securely in slavery -- the antithesis of individual liberty -- made the conflict grimmer, and the greater.

On their decisive battlefield Lincoln did not distinguish between them when he paid tribute to the `` brave men, living and dead, who fought here ''.

Alexander the Great, who used runners as message carriers, did not have to worry about having every officer in his command hear what he said and having hundreds of them comment at once.

But because the governor was determined that friendship should not influence him one way or the other, he looked for a printer with a knowledge of the law ( which Woodruff did not have ), and awarded the contract to a lawyer named John Steele who had started a newspaper in Helena the year before.

`` The Germans in the fourth century were a very simple race, who comprehended little of natural laws, and who therefore referred phenomena they did not understand to supernatural intervention.

He said he was a friend of Heywood Broun who had run a free employment bureau for several months during the depression, but the generous Broun to whom I wrote did not know his name and I somehow conceived the morbid notion that the man in question was prowling round the house.

The favorite excuse of those who have now recanted their approval of communism is that they did not know how things would develop.

they found out who they were and what they could do, then within the limits of their talent they did it.

This is not to deny the existence of pogroms and ghettos, but only to assert that these horrors have had an effect on the nerves of people who did not experience them, that among the various side effects is the local hysteria of Jewish writers and intellectuals who cry out from confusion, which they call oppression and pain.

And while he had headed Batista's anti-Communist section, the Batista regime did not disturb the Communists so much as more open opponents who were alleged to be Communists.

Gloria ( surname: Ziraldo ), circa 30, who was born in Italy and once did `` chorus work '' in Toronto, has been around longer than most of the others, wistfully remembers the old days when `` we used to get the seamen from the ships, you know, with big turtleneck sweaters and handkerchiefs and all.

He was an emotional, lonely boy who spent so much time turning out drawings that he did scarcely any schoolwork.

As Sir Giles Overreach ( how often had he had to play that part, who did not believe a word of it ), he raised his arm and declaimed: `` Where is my honour now ''??

And of course the news of who the composer was did finally begin to get around among his closest friends.

How titillating it was to go among people who did not know him as the composer, but who talked in the most glowing terms of the promise of the piece after having heard the first rehearsals.

They did not know who they were or know their own worth.

Whenever the place was cleaned or a meal served it was Precious who did the work.

And the reason this could happen is clear: men of government, business men, lawyers and all who concerned themselves with the welfare of their fellow men did not let their concern to run their businesses at a profit restrict the development of freedom and opportunity.

Why did Prokofieff expand in stature and fecundity, while Stravinsky ( who leaped into fame like a young giant ) dwindled in stature and fruitfulness??

He never rested until he discovered who the culprit was, and when he did, he vowed vengeance on Viola Lake if ever the chance came his way.