Risch algorithm

Robert Henry Risch ( born 1939 ) is an American mathematician, who deals with computer algebra.

Life and work

Risch received his doctorate in 1968 at the University of California, Berkeley with Maxwell Rose light. In his dissertation, The problem of integration in finite terms ( Transactions of the AMS, Bd.139, 1969, pp. 167-189 ), he solved the problem of the algebraic integration of elementary functions, which had Joseph Liouville raised in the 19th century.

It is asked for an algorithm which can decide the one hand, whether the indefinite integral of an elementary function with other elementary functions can be expressed, and on the other hand is to find this expression. " Elementary " functions, which ( with inverse functions ), the logarithm and the exponential function can be formed in finite terms with elementary arithmetic operations, including the concatenation of root expressions, trigonometric functions.

The corresponding algorithm is called the Risch algorithm, its implementation in the computer is a non- trivial task as before, which could previously be solved only partially.

After his doctorate, he worked at the IBM Thomas Watson Research Center, from 1970 to 1972 at the Institute for Advanced Study.