Robert Risch

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Robert Henry Risch (* 1939 ) is an American mathematician who studies computer algebra .

Live and act

Risch received his PhD from the University of California, Berkeley in 1968 with Maxwell Rosenlicht . In his dissertation The problem of integration in finite terms , he solved the problem of the algebraic integration of elementary functions , which Joseph Liouville had already raised in the 19th century.

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

The corresponding algorithm is called the Risch algorithm, the complete implementation of which in the computer was a complex, non-trivial task. It was only achieved by Manuel Bronstein in 1990 (in the computer algebra system Axiom ).

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

Web links

Individual evidence

  1. Date of birth according to the IAS membership book 1980
  2. ^ Robert Risch: The problem of integration in finite terms . In: Transactions of the AMS . tape 139 , 1969, p. 167-189 , doi : 10.1090 / S0002-9947-1969-0237477-8 ( full text [PDF]).
  3. Robert Risch in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  4. Manuel Bronstein: Integration of elementary functions . In: Journal of Symbolic Computation . tape 9 , 1990, pp. 117-173 , doi : 10.1016 / S0747-7171 (08) 80027-2 .