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searching for Euclidean division 14 found (128 total)

Polynomial long division (2,218 words) [view diff] exact match in snippet view article find links to article

method). Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend)

Polynomial remainder theorem (813 words) [view diff] exact match in snippet view article find links to article

Bézout's theorem (named after Étienne Bézout) is an application of Euclidean division of polynomials. It states that, for every number r {\displaystyle

Sturm's theorem (2,807 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \operatorname {rem} (P_{i-1},P_{i})} is the remainder of the Euclidean division of P i − 1 {\displaystyle P_{i-1}} by P i . {\displaystyle P_{i}.}

Partial fraction decomposition (7,030 words) [view diff] exact match in snippet view article find links to article

the degree of the polynomial P. This results immediately from the Euclidean division of F by G, which asserts the existence of E and F1 such that F = E

Factor theorem (1,446 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f(X)} . The theorem may be proved using Euclidean division of polynomials: Perform a Euclidean division of f ( x ) {\displaystyle f(x)} by ( x − a

Synthetic division (4,599 words) [view diff] exact match in snippet view article find links to article

In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long

Polynomial ring (8,697 words) [view diff] exact match in snippet view article find links to article

easy algorithm (such as long division) for computing the Euclidean division. The Euclidean division is the basis of the Euclidean algorithm for polynomials

Monic polynomial (1,159 words) [view diff] exact match in snippet view article find links to article

c_{n-i}} is the coefficient of the (n−i)th power of the indeterminate. Euclidean division of a polynomial by a monic polynomial does not introduce divisions

Differential operator (3,693 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X^{a}D^{b}{\text{ mod }}I} . It supports an analogue of Euclidean division of polynomials. Differential modules[clarification needed] over R

Exponentiation by squaring (3,380 words) [view diff] exact match in snippet view article find links to article

q=\left\lfloor {\frac {n_{1}}{n_{0}}}\right\rfloor } . In other words, a Euclidean division of the exponent n1 by n0 is used to return a quotient q and a rest

Asymptote (4,527 words) [view diff] exact match in snippet view article find links to article

2 3 {\displaystyle y={\frac {2}{3}}} = 1 y = the quotient of the Euclidean division of the numerator by the denominator f ( x ) = 2 x 2 + 3 x + 5 x =

Routh–Hurwitz stability criterion (3,155 words) [view diff] exact match in snippet view article find links to article

{-b}{c}}y\right)P_{2}(y),&&\implies P_{3}(y)=0,\end{aligned}}} and the Euclidean division stops. Notice that we had to suppose b different from zero in the

Hensel's lemma (9,047 words) [view diff] exact match in snippet view article find links to article

interval [ 0 , p − 1 ] . {\displaystyle [0,p-1].} ) As g is monic, the Euclidean division of a δ h {\displaystyle a\delta _{h}} by g is defined, and provides

List of editiones principes in Greek (10,824 words) [view diff] case mismatch in snippet view article find links to article

Greek Mathematics, Dover, [1921] 1981, p. 441. A. Barbera (ed.), he Euclidean Division of the Canon: Greek and Latin Sources, University of Nebraska Press