The desire to use a computer to perform a mathematical computation symbolically arises naturally whenever a long and tedious sequence of manipulations is required. We have all had the experience of working out a result which required page after page of algebraic manipulation and hours (perhaps days) of our time. This computation might have been to solve a linear system of equations exactly where an approximate numerical solution would not have been appropriate. Or it might have been to work out the indefinite integral of a fairly complicated function for which it was hoped that some transformation would put the integral into one of the forms appearing in a table of integrals. In the latter case, we might have stumbled upon an appropriate transformation or we might have eventually given up without knowing whether or not the integral could be expressed in terms of elementary functions. Or it might have been any one of numerous other problems requiring symbolic manipulation.
KeywordsChebyshev Polynomial Computer Algebra Algebraic Manipulation Symbolic Computation Computer Algebra System
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