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Название: Improving exact integrals from symbolic algebras systems
Авторы: Fateman R.J., Kahan W.
Programs in symbolic algebraic manipulation systems can compute certain classes of symbolic indefinite integrals in closed form. Although these answers are ordinarily formally correct algebraic anti-derivatives, their form is often unsuitable for further numerical or even analytical processing. In particular, we address coses in which such "exact answers" when numerically evaluated may give less-accurate answers than numerical approximations from first principles! The symbolic formulas may also behave inappropriately near singularities. We discuss techniques, based in part on the calculus of divided differences, for improving the form of results of symbolic mathematics systems. In particular, computer algebra systems must take explicit account of the possibility that they are producing not "mathematics" but templates of programs consisting of sequences of arithmetic operations. In brief, mathematical correctness is not enough. Forms produced by rational integration programs are used for examples.