Search results
Results from the WOW.Com Content Network
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
This factorization is also unique up to the choice of a sign. For example, + + + = + + + is a factorization into content and primitive part. Gauss proved that the product of two primitive polynomials is also primitive (Gauss's lemma). This implies that a primitive polynomial is irreducible over the rationals if and only if it is irreducible ...
Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in F q [x] where q = p m Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ...
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite.The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime.
Israeli strike kills 5 journalists in Gaza, hospital says. News. Reuters. Dead body found in wheel well after United flight lands in Hawaii. Weather. Weather. Associated Press.
Now the product of the factors a − mb mod n can be obtained as a square in two ways—one for each homomorphism. Thus, one can find two numbers x and y , with x 2 − y 2 divisible by n and again with probability at least one half we get a factor of n by finding the greatest common divisor of n and x − y .
(The Center Square) – The House has overwhelmingly voted against the stopgap bill presented to the House floor Thursday evening by Speaker Mike Johnson, R-La., after a last-minute scramble. With ...