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Perfect square dissection, a dissection of a geometric square into smaller squares, all of different sizes Perfect square trinomials , a method of factoring polynomials Topics referred to by the same term
Printable version; In other projects Appearance. move to sidebar hide. From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Factorization#Perfect square ...
In particular, a univariate polynomial with complex coefficients admits a unique (up to ordering) factorization into linear polynomials: this is a version of the fundamental theorem of algebra. In this case, the factorization can be done with root-finding algorithms. The case of polynomials with integer coefficients is fundamental for computer ...
Another geometric proof proceeds as follows: We start with the figure shown in the first diagram below, a large square with a smaller square removed from it. The side of the entire square is a, and the side of the small removed square is b. The area of the shaded region is . A cut is made, splitting the region into two rectangular pieces, as ...
For univariate polynomials over the rationals (or more generally over a field of characteristic zero), Yun's algorithm exploits this to efficiently factorize the polynomial into square-free factors, that is, factors that are not a multiple of a square, performing a sequence of GCD computations starting with gcd(f(x), f '(x)). To factorize the ...
square link (Ramsden's) sq lnk ≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft = 0.092 903 04 m 2: square metre (SI unit) m 2: ≡ 1 m × 1 m = 1 m 2: square mil; square thou: sq mil ≡ 1 mil × 1 mil = 6.4516 × 10 −10 m 2: square mile: sq mi ≡ 1 mi × 1 mi ≡ 2.589 988 110 336 × 10 6 m 2: square mile (US Survey) sq mi ≡ 1 mi (US) × 1 mi (US ...
A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic ...
A number of results give techniques for locating and testing primitiveness of trinomials. [4] For polynomials over GF(2), where 2 r − 1 is a Mersenne prime, a polynomial of degree r is primitive if and only if it is irreducible. (Given an irreducible polynomial, it is not primitive only if the period of x is a non-trivial factor of 2 r − 1 ...