http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 20:59:27 GMT Tue, 09 Jun 2026 20:59:27 GMT The latest comments added to the Post, Sorting with attributes http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes?ref=Feed:MaplePrimes:Sorting with attributes:Comments#comment80497 Joe, It is a great idea to use attributes. Replacing <code>abs(x)</code> with <code>op(1,x)^2+op(2,x)^2</code> seems to give some time improvement in all examples. It can't be applied to real x though. The latest comments added to the Post, Sorting with attributes 80497 Sat, 15 Oct 2005 01:30:18 Z alec alec http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes?ref=Feed:MaplePrimes:Sorting with attributes:Comments#comment86782 Another possibility, which works with pure reals and imaginaries, is (Re^2+Im^2)(z), or a variant. Here is a comparison of several methods for generating the magnitude (or square of magnitude). <pre> restart; use RandomTools in zs := [seq](Generate(complex(float(range=0..1,method=uniform))),i=1..10^3); end use: n := 2; time(proc() to 10^n do map(z -> z*conjugate(z),zs) od end()); time(proc() to 10^n do map(Re^2+Im^2, zs) od end()); time(proc() to 10^n do map(z -> Re(z)^2+Im(z)^2, zs) od end()); time(proc() to 10^n do map(abs,zs) od end()); time(proc() to 10^n do map(z->op(1,z)^2+op(2,z)^2,zs) od end()); time(proc() to 10^n do [seq(Re(z)^2+Im(z)^2, z=zs)] od end()); time(proc() to 10^n do [seq(op(1,z)^2+op(2,z)^2,z=zs)] od end()); 7.570 6.259 6.879 12.050 7.079 5.410 5.610 </pre> Using seq is somewhat faster than map. The fastest here, Re(z)^2+Im(z)^2, is also robust, it works for pure reals and imaginaries. The latest comments added to the Post, Sorting with attributes 86782 Sat, 15 Oct 2005 01:48:15 Z Joe Riel Joe Riel http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes?ref=Feed:MaplePrimes:Sorting with attributes:Comments#comment86781 <i>It can't be applied to real x though.</i> Nor to purely imaginary x either. The latest comments added to the Post, Sorting with attributes 86781 Sat, 15 Oct 2005 05:01:31 Z Stephen Forrest Stephen Forrest http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes?ref=Feed:MaplePrimes:Sorting with attributes:Comments#comment90356 One seq seems to be faster than map. For 2 seqs, the situation may be different - I am not sure. For example, multiple timings of the following 2 sorting procedures didn't show a significant preference of one of them, <pre>sort5 := L->map(attributes, sort([seq(setattribute(Re(z)^2+Im(z)^2,z), z=L)])); sort6 := L->[seq(attributes(i), i=sort([seq(setattribute(Re(z)^2+Im(z)^2,z), z=L)]))];</pre> The latest comments added to the Post, Sorting with attributes 90356 Sat, 15 Oct 2005 18:51:51 Z Alec Mihailovs Alec Mihailovs http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes?ref=Feed:MaplePrimes:Sorting with attributes:Comments#comment80467 It took me a while to realize just how useful this trick really is. If you want to sort integers you can write an integer n as SFloat(n,0). I think that has pretty low overhead. Needless to say, I am now using it to sort monomials by degree. It is substantially faster than accessing an element of a list. Thanks for the great technique. The latest comments added to the Post, Sorting with attributes 80467 Mon, 24 Oct 2005 10:55:48 Z roman_pearce roman_pearce http://www.mapleprimes.com/posts/43529-Sorting-With-Attributes?ref=Feed:MaplePrimes:Sorting with attributes:Comments#comment86767 Using SFloat to convert an integer into an "equivalent" software float, so that it can take an attribute, is a nice extension. Thanks for sharing it. For those wondering what Roman is doing, here is the idea (I assume), <pre> sortpolys := proc(polys,vars) local p; return map(attributes ,sort([seq](setattribute(SFloat(degree(p,vars),0),p) ,p = polys))); end proc: sortpolys([x^3+x, 1, x^2+x+1],x); 2 3 [1, x + x + 1, x + x] </pre> However, I wouldn't think that there would be much speed advantage of this compared to my method 2 (where the keys are precomputed but pairs are used for the comparison) except for fairly long lists. How many monomials do you have to sort? Is there a similar method for making any numeric quantity attributable while permitting it to be directly compared with other such numbers? SFloat can handle floats but not fractions: <pre> SFloat(2.3, 0); 2.3 SFloat(2/3, 0); Error, invalid arguments for Float constructor </pre> I'd be reluctant to use evalf because of the possibility of round-off. The latest comments added to the Post, Sorting with attributes 86767 Mon, 24 Oct 2005 19:11:03 Z Joe Riel Joe Riel