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I have this list with some duplicate elements and I want to delete duplicate ones.

mylist = {ConditionalExpression[1, -1 <= x <= 0], 
   ConditionalExpression[-x, x <= -1], 
   ConditionalExpression[-x, x <= -1], 
   ConditionalExpression[Abs[x], x <= -1]};

Now I tried to delete duplicate elements with this.

DeleteDuplicates[mylist]

Code output

This doesn't work. I expected that two of these three elements {ConditionalExpression[-x, x <= -1], ConditionalExpression[-x, x <= -1], ConditionalExpression[Abs[x], x <= -1]} should be deleted.

Then I thought probably that was due to Mathematica thinking that x is complex, so I added the assumption that x is real, but this didn't work either.

Assuming[x \[Element] Reals, DeleteDuplicates[mylist]]

results from assumptions code; no difference in result

How can I delete duplicate elements so the three elements above are considered duplicate?

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4 Answers 4

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DeleteDuplicates[Refine[mylist, Assumptions -> x ∈ Reals]]

gives what you want

res

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Try this:

DeleteDuplicates[Refine[Map[LogicalExpand, mylist], Assumptions -> x \[Element] Reals]]

enter image description here

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  • $\begingroup$ This one is a bit longer than bmf's answer. I wonder if there is any case this works but bmf's answer or vice versa. $\endgroup$
    – hana
    Apr 18, 2022 at 15:55
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Assuming you do want to keep one of the equivalent ConditionalExpressions

DeleteDuplicatesBy[mylist, Refine[#, #[[2]]] &]

{ConditionalExpression[1, -1 <= x <= 0], ConditionalExpression[-x, x <= -1]}

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  • $\begingroup$ I think this would consider {ConditionalExpression[1 - x, 0 <= x <= 1/2], ConditionalExpression[1 - x, x <= 1/2]} duplicates while they aren't. $\endgroup$
    – hana
    Apr 17, 2022 at 23:08
  • $\begingroup$ DeleteDuplicatesBy[mylist, Refine] seems sufficient. $\endgroup$
    – Roman
    May 3 at 19:51
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list =
  {ConditionalExpression[1, -1 <= x <= 0],
   ConditionalExpression[-x, x <= -1],
   ConditionalExpression[-x, x <= -1],
   ConditionalExpression[Abs[x], x <= -1]};

In this case we only need

DeleteDuplicates @ Refine @ list

enter image description here

From the documentation:

"Refine[expr] uses default assumptions ..."

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