Читать книгу Mathematics for Enzyme Reaction Kinetics and Reactor Performance - F. Xavier Malcata - Страница 22

A polynomial in x refers to a sum of powers of integer exponent on x; such algebraic functions are accordingly the easiest in terms of calculation – including numerical methods, as they basically involve just multiplications and additions. In principle, any continuous function of practical interest may be expressed via a polynomial (as will be derived later); hence, algebraic operations involving polynomials are of the utmost interest for process engineering. Besides the trivial operation of addition – where terms with identical exponents of x are merely lumped, i.e.

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with

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and

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multiplication and division of polynomials appear as germane. An iterated version of the former entails the power of a polynomial, whereas the iterated version of the latter supports factorization of a polynomial – i.e. conversion from a sum to a product of simpler (usually linear) polynomials.