How can one sort a list of complex numbers in increasing order with respect to their imaginary part in Maple?

I am a beginner at Maple and am attempting to use the sort function to order a list of complex numbers according to their imaginary part, however I can find no function options that help. Will I have to use a loop?

asked Oct 7, 2015 at 13:03 31 5 5 bronze badges

$\begingroup$ according to maplesoft.com/support/help/Maple/view.aspx?path=sort all you need is specifying the sorting function being something like Img(), sorry I dont know maple either $\endgroup$

Commented Oct 7, 2015 at 13:47

1 Answer 1

$\begingroup$

Maple's sort command allows you to use a custom procedure as the predicate to compare two elements.

For example, to sort a list of numeric entries according by their imaginary component:

L:=[ 3+4*I, 6-I, -3, 2, 0.4*I ]; L := [3 + 4 I, 6 - I, -3, 2, 0.4 I] sort( L, (a,b) -> Im(a)


You could also use a comparison procedure which compared the real components, in the case that the imaginary components were equal.
p := proc(a,b) if Im(a) < Im(b) then true; elif Im(a) = Im(b) then if Re(a) < Re(b) then true; else false; end if; else false; end if; end proc: L:=[ 3+4*I, 6-I, -3, 2, 0.4*I, -3+4*I, -6-I ]; sort( L, p ); [-6 - I, 6 - I, -3, 2, 0.4 I, -3 + 4 I, 3 + 4 I] 
For example, the following does not return true or false , since sqrt(2) is not of type numeric . It simply returns unevaluated.
evalb( sqrt(2) < 5 ); 1/2 2 < 5 
By utilizing the is command we can strengthen the test to also handle such quantities of type realcons . Eg,
is( sqrt(2) < 5 ); true 
This reasoning carries over to sort as well,
L := [ 3+4*I, 6-I, sqrt(2)*I, -3, 2, 0.4*I ]; 1/2 L := [3 + 4 I, 6 - I, 2 I, -3, 2, 0.4 I] sort( L, (a,b) -> Im(a) Im(a) < Im(b), must be a function that always returns true or false sort( L, (a,b) ->is(Im(a)