Re: easy(?) question on manipulating expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg38631] Re: easy(?) question on manipulating expressions
- From: carlos at colorado.edu (Carlos Felippa)
- Date: Wed, 1 Jan 2003 03:40:24 -0500 (EST)
- References: <aur8kb$8fn$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
> > Although AlgebraicRules is no longer supported one can achieve the same > effect (and more) with GroebnerBasis and PolynomialReduce. > > 2. It would be interesting to know how "optimazing compilers" from the > 1950s could do such "substitution", since in general it depends on > GroebnerBasis invented by Bruno Buchsberger in the 1970s. > > Andrzej Kozlowski > Yokohama, Japan > http://www.mimuw.edu.pl/~akoz/ > http://platon.c.u-tokyo.ac.jp/andrzej/ We are talking about two different things. Your comment concerns polynomial manipulation, a more specialized topic. Mine was regarding recognition of common algebraic subexpressions. The latter was developed by the IBM Fortran group, headed by John Backus, from 1954 through ~1964. They pioneered table-driven global flow analysis of algebraic expressions ("algebraic" in the sense of "Fortran expression", not polynomials). Reference: Part 2A of Rosen's Programming Systems and Languages, McGraw Hill, 1966, especially pp 42-45. In the early 1970s, while at the Lockheed Palo Alto Labs, I had to write a similar table-driven compiler for a CCC language. By then the technique was in textbooks. I did it by recursive descent, using a now defunct language called SNOBOL.