बहुलिपिक इसके अंग्रेजी अर्थ का उदाहरण

The polynomials occurring in the numerator and denominator are essentially the characteristic polynomials of the map induced by f on the various homology spaces.

The characteristic polynomial of J(n,k) is given by.

The symmetric algebra on the dual of an affine space is a filtered algebra of polynomials; on a vector space, one instead obtains a graded algebra.

The associated graded algebra is the commutative algebra of smooth functions on the cotangent bundle T^*M which are polynomial along the fibers of the projection \pi\colon T^*M\rightarrow M.

Given a field k, and an algebraically closed extension K of k, an affine variety X over k is the set of common zeros in K^n of a collection of polynomials with coefficients in k:.

A projective variety X in projective space Pn over a field k can be defined by a collection of [polynomial] equations in variables x0,.

Then a k-point of X means a k-point of Pn at which the given polynomials vanish.

The theory of Diophantine equations traditionally meant the study of integral points, meaning solutions of polynomial equations in the integers Z rather than the rationals Q.

For homogeneous polynomial equations such as x3 + y3 z3, the two problems are essentially equivalent, since every rational point can be scaled to become an integral point.

In the case of the projective line, this can be proved by manipulations with the resultant of polynomials.

The above equation suffers from strong correlation between the coefficients of the first term and the polynomial terms.

Therefore, different equations using "Q-polynomials" where coefficients are orthogonal to each other are an alternative that is sometimes used.

, hk compresses the input string, and every hk can be computed within polynomial time given k, but for any probabilistic polynomial algorithm A, we have.