LYCOS RETRIEVER 
Polynomial
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Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, Mathematica has the world's broadest and deepest integrated web of polynomial algorithms. Carefully tuned strategies automatically select optimal algorithms, allowing large-scale polynomial algebra to become a routine part of many types of computations.
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Polynomial functions are nothing more than a sum of power functions. As a result, certain properties of polynomials are very "power-like." When many different power functions are added together... polynomials begin to take on unique behaviors.
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Polynomial models have poor asymptotic properties. By their nature, polynomials have a finite response for finite values and have an infinite response if and only if the value is infinite. Thus polynomials may not model asympototic phenomena very well.
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Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable progress has been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this paper the structure and design of the software package PHC is described. The main program operates in several modes, is menu-driven and file-oriented. This package features a great variety of root-counting methods among its tools.
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The Polynomial people were distinctive in their appearence, characterised by their finite sums of monomial terms and being differentiable at every point. In this respect they had much in common with the exponentials of Asia Minor, leading to the traditional view that their origins cam be found there.
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To a mathematician, polynomial models are very special. Strictly speaking, polynomial models are not 'nonlinear'. Even though a graph of X vs. Y is curved (in all but some special cases), the derivative of Y with respect to the parameters is linear.
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Polynomial