http://www.mapleprimes.com/posts/40565-A-Compendium-Of-Inequalities--How en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Sat, 13 Jun 2026 23:37:40 GMT Sat, 13 Jun 2026 23:37:40 GMT The latest comments added to the Post, A compendium of inequalities -- how can it be used? http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/40565-A-Compendium-Of-Inequalities--How http://www.mapleprimes.com/posts/40565-A-Compendium-Of-Inequalities--How?ref=Feed:MaplePrimes:A compendium of inequalities -- how can it be used?:Comments#comment74921 I wonder how many of these inequalities are true. For example, I randomly chose Theorem 21 which says if x > 0, <maple>x/(x + floor(x)) + x/(x+frac(x)) &gt;= 5/2</maple> This is wrong: the left side actually varies between 4/3 and 3/2. Moreover, Maple can be persuaded to assert this: <pre> > _EnvTry := hard: x := a + b: Q:= x/(x+b) + x/(x+a): is(Q > 3/2) assuming a >= 0, b > 0; </pre> <maple>false</maple> Note that the expression is symmetric in a and b; you can take a = frac(x) and b = floor(x) or vice versa, and at least one of these is strictly positive. I doubt that a table of inequalities would be very useful in itself, because the one you want will hardly ever be in the table (though it might be a consequence of one or more items there). I think this should be seen in the context of the need to improve Maple's ability to decide whether nonlinear inequalities are true in connection with the "assume" facilities. For example: <pre> > is(a^2 + b + 1 >= a) assuming a >= 0, b >= 0; <maple>FAIL</maple> The latest comments added to the Post, A compendium of inequalities -- how can it be used? 74921 Wed, 07 Nov 2007 00:29:27 Z Robert Israel Robert Israel http://www.mapleprimes.com/posts/40565-A-Compendium-Of-Inequalities--How?ref=Feed:MaplePrimes:A compendium of inequalities -- how can it be used?:Comments#comment74919 but in the cited example Maple can be of help to guess the correct statement: x/(x + floor(x)) + x/(x+frac(x)) -5/2; plot(%,x=0 ..6); or (the transformed one) x/(x+b) + x/(x+a)-3/2; subs(a=frac(x),b=floor(x),%); plot(%,x=-3 ..16); The latest comments added to the Post, A compendium of inequalities -- how can it be used? 74919 Wed, 07 Nov 2007 01:58:12 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/40565-A-Compendium-Of-Inequalities--How?ref=Feed:MaplePrimes:A compendium of inequalities -- how can it be used?:Comments#comment84705 The theorems seem mostly worthless. Besides the error previously mentioned, the few I checked are overly conservative. Consider theorem 1: <pre> floor(x)/(3*x+frac(x)) + frac(x)/(3*x+floor(x)) &ge; 4/15 </pre> The real limit should be 2/7, not 4/15. Similarly for theorem 6, the right side should be 4/3/x, not the conservative 1/x. Theorem 32 part 2 fails: <pre> solve(y2 := abs(cos(floor(x))) + abs(cos(frac(x))) - abs(cos(x)); fsolve(y2, x=2.9..3); 2.966118521 limit(y2, x=3, left); -cos(2) + cos(1) + cos(3) evalf(%); -0.0335433542 </pre> So does Theorem 25, at multiple locations for x &lt; 0: <pre> y := abs(sin(floor(x))) + abs(sin(frac(x))) + abs(cos(x)): plot([1,y], x=-10..4); limit(y, x=-2, left);evalf(%); sin(3) - cos(2) 0.5572668446 </pre> The latest comments added to the Post, A compendium of inequalities -- how can it be used? 84705 Mon, 12 Nov 2007 11:14:53 Z Joe Riel Joe Riel