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The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

The 6.1.2 equation A^6=B^6+C^6 (1) is a special case of Fermat's last theorem with n=6, and so has no solution. No 6.1.n solutions are known for n<=6 (Lander et al. 1967; Guy ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

Pre-Calculus

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...

The partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to ...

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

An algorithm that can be used to factor a polynomial f over the integers. The algorithm proceeds by first factoring f modulo a suitable prime p via Berlekamp's method and ...