Risch's decision procedure for integration, not surprisingly, uses a recursion on the number and type of the extensions from the rational functions needed to represent the integrand. Although the algorithm follows and critically depends upon the appropriate structure of the input, as in the case of multivariate factorization, we cannot claim that the algorithm is a natural one. In fact, the creator of differential algebra, Ritt, committed suicide in the early 1950's, largely, it is claimed, because few paid attention to his work. Probably he would have received more attention had he obtained the algorithm as well.
-- Joel Moses, Algorithms and Complexity, ed. J.F. Traub
Sunday, April 30, 2023
Quote of the Day
Saturday, April 29, 2023
Quote of the Day
The National Association of Theater Concessionaires reported that in 1986, 60% of all candy sold in movie theaters was sold to Roger Ebert.
-- David Letterman
Friday, April 28, 2023
Quote of the Day
I am very fond of the company of ladies. I like their beauty, I like their delicacy, I like their vivacity, and I like their silence.
-- Samuel Johnson
Thursday, April 27, 2023
Quote of the Day
The universe may have a purpose, but nothing we know suggests that, if so, this purpose has any similarity to ours.
-- Bertrand Russell
Wednesday, April 26, 2023
Quote of the Day
Without music to decorate it, time is just a bunch of boring production deadlines or dates by which bills must be paid.
-- Frank Zappa
Tuesday, April 25, 2023
Quote of the Day
Human beings are seventy percent water, and with some the rest is collagen.
-- Martin Mull
Monday, April 24, 2023
Quote of the Day
My brother sent me a postcard the other day with this big satellite photo of the entire earth on it. On the back it said: "Wish you were here".
-- Stephen Wright
Sunday, April 23, 2023
Quote of the Day
Of all the tyrannies that affect mankind, tyranny in religion is the worst.
-- Thomas Paine
Saturday, April 22, 2023
Quote of the Day
An architect's first work is apt to be spare and clean. He knows he doesn't know what he's doing, so he does it carefully and with great restraint.
As he designs the first work, frill after frill and embellishment after embellishment occur to him. These get stored away to be used "next time." Sooner or later the first system is finished, and the architect, with firm confidence and a demonstrated mastery of that class of systems, is ready to build a second system.
This second is the most dangerous system a man ever designs. When he does his third and later ones, his prior experiences will confirm each other as to the general characteristics of such systems, and their differences will identify those parts of his experience that are particular and not generalizable.
The general tendency is to over-design the second system, using all the ideas and frills that were cautiously sidetracked on the first one. The result, as Ovid says, is a "big p ile."
-- Frederick Brooks, (The Mythical Man Month)