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	NationMaster - Encyclopedia: Quintic equation
		The derivative of a quintic function is a quartic function.
		A quintic is solvable using radicals if the Galois group of the quintic (which is a subgroup of the symmetric group S(5) of permutations of a five element set) is a solvable group.
		Attempting to apply it to a quintic, we seek for the equation of which the root is (a+wb+w2c+wad+w4e), w an imaginary fifth root of unity, or rather the fifth power thereof (a+wb+w2c+wad+w4e)6; this is a 24-valued function, but if we consider the four values corresponding to the roots of unity w, w2, co3, w4, viz.
	www.nationmaster.com /encyclopedia/Quintic-equation (2463 words)

	Solving the Quintic
		Finally, Ruffini (1799) and Abel (1826) showed that the solution of the general quintic cannot be written as a finite formula involving only the four arithmetic operations and the extraction of roots.
		be a branch of the inverse function of
		Galois groups of quintics are related to the symmetries of the icosahedron.
	library.wolfram.com /examples/quintic/main.html (902 words)

	Math Forum Discussions - Re: Solution to quintic wanted
		Polynomials with degree three are referred to as cubic functions.
		functions, but the general quintic function ax5 + bx4 + cx3 + dx2 + ex + f =
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.com /kb/thread.jspa?forumID=13&threadID=87137&messageID=426294 (152 words)

	Quintic equation Summary
		Quintic equations are polynomial equations with one variable, customarily denoted by x, which is never raised to a power greater than the fifth.
		The derivative of a quintic function is a quartic function.
		However, there is no formula for general quintic equations over the rationals in terms of radicals; this was first proved by the Abel-Ruffini theorem, first published in 1824, which was one of the first applications of group theory in algebra.
	www.bookrags.com /Quintic_equation (3240 words)

	Quintic function (Site not responding. Last check: )
		Quintic functions are polynomial functions in which the highest degree is five.
		Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except for the fact that they may possess an additional local maximum and minimum each.
		The derivative of a quintic function is a quartic function.
	encyclopedie-en.snyke.com /articles/quintic_function.html (72 words)

	Quintic function (Site not responding. Last check: )
		Quintic functions are polynomial functionss in which the highest degree is five.
		Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except for the fact that they possess an additional local maximum and minimum each.
		The derivative of a quintic function is a quartic function.
	publicliterature.org /en/wikipedia/q/qu/quintic_function.html (66 words)

	[No title] (Site not responding. Last check: )
		function c = cadd(a,b) c(1) = a(1) + b(1); % adds the real components c(2) = a(2) + b(2); % adds the imaginary components return; % Header: % This function treats two imaginary numbers as two 2 by 1 matrices, and % multiplies their components as two imaginary numbers would be % multiplied, using FOIL.
		function c = cmult(a,b) c(1) = a(1)b(1) - a(2)b(2); c(2) = a(1)b(2) + a(2)b(1); return; % Header: % This function treats two imaginary numbers as two 2 by 1 matrices, and % divides their components as two imaginary numbers would be divided, % using conjugate pairs and FOIL again.
		function c = cdiv(a,b); c(1) = ((a(1)b(1))+(a(2)b(2)))/((b(1)b(1))+(b(2)b(2))); c(2) = ((a(2)b(1))-(a(1)b(2)))/((b(1)b(1))+(b(2)b(2))); return; % Header: % This function treats an imaginary number as a 2 by 1 matrix and uses % the distance theorem to find its distance from 0.
	www.owlnet.rice.edu /~mlb4432/newt.m (309 words)

	libnoise: Generating coherent noise
		This quintic coherent-noise function produces vastly improved textures over the linear coherent-noise function, but one flaw remains: the light and dark areas on these textures are noticably aligned along a grid.
		A gradient coherent-noise function generates a pseudorandom gradient vector by using the integer-noise function to randomly select a vector from a pool of precomputed vectors.
		When using two- or three-dimensional versions of this gradient coherent-noise function to generate two- or three-dimensional textures, notice that the light and dark areas are no longer aligned to a grid; they are "pushed around" in some random direction by the pseudorandom gradient vectors.
	libnoise.sourceforge.net /noisegen/index.html (1529 words)

	List of mathematical functions - Wikipedia, the free encyclopedia
		A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.
		Transcendental functions are functions that are not algebraic.
		Power function: raises a variable number to a fixed power; also known as Allometric function; note: if the power is a rational number it is not strictly a transcendental function.
	en.wikipedia.org /wiki/List_of_mathematical_functions (1002 words)

	The History and Future of Special Functions
		Functions with fairly few arguments, that somehow can be used as primitives in a lot of useful calculations.
		And indeed essentially all the special functions that we use have a rather special feature in their power series: the coefficients are rational.
		To have something like a special function, and to have it be useful, there must be large "basins" of problems that are all easily reducible to that particular special function.
	www.stephenwolfram.com /publications/talks/specialfunctions (5965 words)

	Luboš Motl's reference frame: Modular functions & elliptic genus
		The hyperplane is the intersection of the quintic hypersurface and a CP^3 given by a linear equation inside the CP^4.
		This trace is a function of "q=exp(2.pi.i.tau)" where "tau" is the complex structure of the torus.
		Recall that the holomorphic modular functions (without singularities) are polynomials of the modular functions of weight 4 and 6, respectively.
	motls.blogspot.com /2006/09/modular-functions-elliptic-genus.html (1210 words)

	mx.effects.easing.Quintic (Flex™ 2 Language Reference)
		The Quintic class defines three easing functions to implement motion with Flex effect classes.
		The acceleration of motion for a Quintic easing equation is greater than for a Quadratic, Cubic, or Quartic easing equation.
		A reference to the class object or constructor function for a given object instance.
	livedocs.macromedia.com /flex/2/langref/mx/effects/easing/Quintic.html (335 words)

	Narrow wavelength polarizing beamsplitter - Patent 5828489
		Polarizing beamsplitters of the present invention may be fabricated with multiple reflection bands (limited only by the upper and lower refractive indices of the materials used to form the rugate filter) and with reflection band(s) in other spectral regions besides the visible spectrum.
		With respect to the present invention, the incident medium is the embedding medium (e.g., fused silica prism) and the transmitted medium is the rugate filter.
		The quintic function is used to minimize the refractive index discontinuity between the rugate filter and embedding medium.
	www.freepatentsonline.com /5828489.html (3613 words)

	spaps (Spline Toolbox)
		Further, the distance of the function f from the given data is measured by
		-vector-valued) function f from the data are the sum of the componentwise measures.
		Reinsch's approach [1] is used (including his clever way of choosing the equation for the optimal smoothing parameter in such a way that a good initial guess is available and Newton's method is guaranteed to converge and to converge fast).
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/splines/spaps.html (264 words)

	Quintic Equation -- from Wolfram MathWorld
		The general quintic can be solved in terms of Jacobi theta functions, as was first done by Hermite in 1858.
		is the inverse nome, which is expressible as a ratio of Jacobi theta functions.
		By solving a quartic, a quintic can be algebraically reduced to the Bring quintic form, as was first done by Jerrard.
	mathworld.wolfram.com /QuinticEquation.html (702 words)

	Appendix.
		This algorithm is based on Klein's theory of the connection between the general quintic and the icosahedral equation, described in his famous lectures on the icosahedron [8].
		According to this view, the reduction of the quintic to the icosahedral equation is inadmissible.
		The Brioschi resolvent is a one parameter family of quintics, to which the general quintic may be reduced; it is this equation we will actually solve.
	math.dartmouth.edu /~doyle/docs/icos/icos/node6.html (2228 words)

	Quintic equation - Wikipedia, the free encyclopedia
		In mathematics, a quintic equation is a polynomial equation in which the greatest exponent on the independent variable is five.
		However, there is no formula for general quintic equations over the rationals in terms of radicals; this is known as the Abel-Ruffini theorem, first published in 1824, which was one of the first applications of group theory in algebra.
		In 1858 Charles Hermite showed that the Bring radical could be characterized in terms of the Jacobi theta functions and their associated elliptic modular functions, using an approach similar to the more familiar approach of solving cubic equations by means of trigonometric functions.
	en.wikipedia.org /wiki/Quintic_equation (900 words)

	Steps to the Quintic
		Ruffini (1799) and Abel (1826) proved that it is not possible to give an explicit solution for the general quintic equation with symbolic coefficients in terms of square roots, cube roots, and so on.
		However, it was necessary to go beyond the extraction of roots and to use elliptic and hypergeometric functions.
		Here is a complete implementation of Hermite's solution of the quintic in Mathematica in terms of elliptic functions.
	library.wolfram.com /examples/quintic/steps.html (615 words)

	Cartesians, Polynomials, Quadratics
		A function is a relation for which there is exactly one value of the dependent variable for each value of the independent variable.
		Degree four polynomials are quartic functions and degree five polynomials are quintic functions.
		Functions with only even or odd exponents are termed even or odd and relate to its symmetry when graphed.
	www.andrews.edu /~calkins/math/webtexts/numb12.htm (1609 words)

	GRIDDATA
		The GRIDDATA function interpolates scattered data values on a plane or a sphere to a regular grid, an irregular grid, a specified set of interpolates, or scattered data points.
		The effects of data points are weighted by a function of their radial distance from a grid point.
		The function fit to each interpolant corresponding to the POWER keyword set equal to 1, 2 (the default), and 3 respectively is as follows:
	idlastro.gsfc.nasa.gov /idl_html_help/GRIDDATA.html (5048 words)

	Quintic’s GUI Design Projects - GUI Consultancy, Style Council, Style Guides, Icon Design
		As a result of Quintic’s recommendations in respect of product design and usability, Flowmaster Ltd commissioned our experts to design and develop a set of icons for their latest product release.
		Flowmaster Ltd also commissioned Quintic's GUI team to redesign its set of 218 symbols, used in its fluid flow analysis software to represent the components of systems to be analysed.
		To find out more about Quintic's GUI consultancy and development expertise, click here, or contact us today to discuss how we can help with your GUI requirements.
	www.quintic.co.uk /solutions/cad/projects/ui.html (335 words)

	Finite Elements (Site not responding. Last check: )
		Coefficients at the three red points at each vertex of the macrotriangle are obtained by interpolating to function values and gradients at the vertices of the triangle.
		The green points in the minimal determining set are obtained similarly as in the quintic element, either by interpolating to perpendicular CBDs at the centers of the edges, or by requiring that the perpendicular CBDs be linear along each edge.
		The result is a schemed that's piecewise cubic, it requires only function and first order derivative values, and it reproduces quadratic or linear functions exactly.
	www.math.utah.edu /~alfeld/MDS/felm.html (555 words)

	1_2_3a_update
		A function, in the mathematical sense used here, is, "An association of exactly one object from one set (the range) with each object from another set (the domain).", according to James and James(1968).
		A spline function is a piecewise polynomial function that has one less continuous value at its break points than it does within each of its panels.
		The primary spline functions in use in approximation are the linear and cubic splines.
	il.water.usgs.gov /proj/feq/fequtl98.i2h/1_2_3a_update.html (5508 words)

	mx.effects.easing.Quintic (Flex™ 2 Language Reference)
		The Quintic class defines three easing functions to implement motion with Flex effect classes.
		The acceleration of motion for a Quintic easing equation is greater than for a Quadratic, Cubic, or Quartic easing equation.
		A reference to the class object or constructor function for a given object instance.
	livedocs.adobe.com /flex/2/langref/mx/effects/easing/Quintic.html (335 words)

	The inverse of a quintic function
		I would like to know if there is a easier method to find the zeros of the inverse of this quintic equation.
		Finding the zeros of the inverse function is much easier than what we have been attempting to do.
		This point has coordinates (z,0) for some number z, and this number z is the zero of the inverse function.
	mathcentral.uregina.ca /QQ/database/QQ.09.03/chana1.html (378 words)

	BioMath: Polynomial Functions
		We have already seen degree 0, 1, and 2 polynomials which were the constant, linear, and quadratic functions, respectively.
		A turning point is a point at which the function changes from increasing to decreasing or decreasing to increasing as seen in the figure below.
		In general, it is not possible to analytically determine the maxima or minima of polynomials.
	www.biology.arizona.edu /BioMath/tutorials/polynomial/Polynomialbasics.html (782 words)

	Quintic equation solution - applet
		When you use the button to search for a start value, the idea is to go through a sequence of values, e.g.
		If you are interested in the numerical values, these solutions are often as accurate on a computer as the exact solutions obtained using sqrt etc even when such solutions are available.
		That's because of the tiny rounding errors involved in evaluating mathematical functions on a computer using the normal level of precision.
	tunesmithy.netfirms.com /japplets/iterative_solution_of_quintic.htm (455 words)

	TSpline5
		Quintic natural spline creator given an array of arbitrary function values on equidistant n abscissa values from xmin to xmax and possibly end point conditions
		Quintic natural spline creator given a function to be evaluated on n equidistand abscissa points between xmin and xmax and possibly end point conditions
		TSpline5 computes the coefficients of a quintic natural quintic spli s(x) with knots x(i) interpolating there to given function values: s(x(i)) = y(i) for i = 1,2,..., n.
	root.cern.ch /root/html404/TSpline5.html (989 words)

	Object (Flex™ 2 Language Reference)
		A constructor function is a Function object used to create objects, and is an alternative to using the
		A reference to the prototype object of a class or function object.
		This property is static in that it is specific to the class or function that you create.
	livedocs.macromedia.com /flex/2/langref/Object.html (1751 words)

	Elliptic Curves - Cambridge University Press
		It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic.
		This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves.
		Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521582288 (239 words)

	Polynomial and Polynomial Functions classification and solutions, Cubic, Quartic, Quintic, nth-degree polynomial
		Thus, any polynomial f(x) with real coefficients can be expressed in the translatable form of its source function that is, using shown method we can put every polynomial function back to the origin.
		Before we proceed to analyze the conditions for the existence of the real roots or the zeroes of the higher degree polynomials let us mention that both, the function-theoretic and the formal algebraic approach to the concept of a polynomial, will be equivalent using the shown method.
		Thus, the classification defines; three types of the cubic functions, ten types of quartic functions, and hundred and sixteen types of quintic polynomial functions, that means, defined are the necessary and the sufficient conditions for each type.
	www.nabla.hr /Index.htm (337 words)

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