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functions when graphed, except they may possess one additional local maximum and one additional local minimum. The derivative of a quintic function is a...

For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of...

subgroup of the symmetric group on five letters. Since the Galois group of the general quintic equation is isomorphic to the symmetric group on five letters...

degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree...

⁠ are symmetric polynomials in ⁠ α {\displaystyle \alpha } ⁠ and ⁠ β {\displaystyle \beta } ⁠. Specifically, they are the elementary symmetric polynomials...

have an odd degree, septic functions appear similar to quintic and cubic functions when graphed, except they may possess additional local maxima and local...

symmetric functions of the roots (exchanging x1 and x2 exchanges also s1 and s2), but some simple symmetric functions of s1 and s2 are also symmetric...

squares) Polynomial family Quadratic function Cubic function Quartic function Quintic function Sextic function Septic function Octic function Completing the...

implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x. With a curve given...

{c}{a}}=0.} The first Vieta's formula is useful for graphing a quadratic function. Since the graph is symmetric with respect to a vertical line through the vertex...

Galois group. For example, S5, the symmetric group in 5 elements, is not solvable which implies that the general quintic equation cannot be solved by radicals...

Arnold). Dickson, Leonard E. (1959), "XIII: Groups of the Regular Solids; Quintic Equations", Algebraic Theories, New York: Dover Publications Hazewinkel...

available for quintic and higher-order equations, beyond trivial or special cases. Linear equation Quadratic equation Cubic equation Quintic equation Polynomial...

is replaced by the symmetric one (or, what amounts to the same thing, if each of the three square roots is replaced by the symmetric one). This argument...

encodes the number of rational curves of any fixed degree in a general quintic hypersurface of four-dimensional complex projective space. Bong Lian, Kefeng...

symmetry in geometry is nearly as old as the science of geometry itself. Symmetric shapes such as the circle, regular polygons and platonic solids held deep...

Generalizing this problem, one can ask how many lines can be drawn on a quintic Calabi–Yau manifold, such as the one illustrated above, which is defined...

that is symmetric with respect to double-duality for abelian varieties and for which the pullback of the Poincaré bundle along the associated graph morphism...

{10}{16}}N_{5}(2x-3)+{\frac {5}{16}}N_{5}(2x-4)+{\frac {1}{16}}N_{5}(2x-5)} The quintic B-spline is the cardinal B-spline of order 6 denoted by N 6 ( x ) {\displaystyle...

R. B. King, E. R. Canfield (1992-08-01), "Icosahedral symmetry and the quintic equation", Computers & Mathematics with Applications, vol. 24, no. 3, pp...