On the Integration of Algebraic Functions
J. H. Davenport, "On the Integration of Algebraic Functions"
1981 | pages: 199 | ISBN: 3540102906 | PDF | 5,9 mb
1981 | pages: 199 | ISBN: 3540102906 | PDF | 5,9 mb
This work is concerned with the following question: "When is an algebraic function integrable?". We can state this question in another form which makes clearer our interpretation of integration: "If we are given an algebraic function, when can we find an expression in terms of algebraics, logarithms and exponentials whose derivative is the given function, and what is that expression?".
This question can be looked at purely mathematically, as a question in decidability theory, but our interest in this question is more practical and springs from the equirements of computer algebra. Thus our goal is "Write a program which, when given an algebraic function, will produce an expression for its integral in terms of algebraics, exponentials and logarithms, or will prove that there is no such expression".
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