August 31, 2005
Dan writes
Hi, Thane,
The United Airlines magazine "Hemisphere" for August 2005 had a crossword puzzle in which "provide (with)" was the clue for ENDUE. I thought they had conflated two words, but the OED says it's genuine, at least through 1860. So consider ENDOW : ENDUE : IMBUE. Even better, ENDUE has a variant: INDUE.
From Eisenbud's Commutative Algebra
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Pg 310:
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This replacement of complex but constructive arguments by simple nonconstructive ones goes under the name of "elimination of elimination theory" (Weil, in his influential book [Foundations of Geometry, 1946, pg 31] says, "The device that follows..., it may be hoped, finally eliminates from algebraic geometry the last traces of Elimination-Theory...") It has been pointed out, notably by Abhyankar, that one loses interesting information if one ignores the constructive methods. He suggested in a famous poem that one should rather
Eliminate, eliminate, eliminate
Eliminate the eliminators of elimination theory
Whatever the merits of the this argument, the advent of computers has renewed interest in finding efficient algorithms for performing elimination. The most effective algorthms do not follow the older methods, but are based on the theory of Groebner bases, explained in Chapter 15.
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Pg 312:
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[Grothendieck's Generic Freeness Lemma]...
The proof is a classic example of a technique Grothendieck called dévisage (English: "unscrewing". After one application of the recursive step of the argument, we are back to the same spot but one dimension lower).
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