4
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x = {4, 1, 2, 5, 6, 7}
y = {1, 2, 4, 5, 6, 9}

There are two lists x and y. How to find out these positions of the elements in list x are smaller than those in corresponding list y and get the following results:

{2, 3, 6}
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6
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Flatten@Position[Negative[x - y], True]

Also possible:

Flatten@Position[x - y, _?(# < 0 &)]

or, as suggested by J.M.,

Flatten[Position[x - y, _?Negative]]
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  • 1
    $\begingroup$ +1, nice use of Negative! $\endgroup$
    – corey979
    Feb 3 '20 at 13:13
  • $\begingroup$ @corey979 Thanks, I wonder why it is not called NegativeQ rather than Negative btw... ! $\endgroup$
    – anderstood
    Feb 3 '20 at 13:15
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    $\begingroup$ @anders, because Negative[] and similar functions don't have to immediately evaluate to True/False (while *Q[] functions do so), which makes them usable in assumptions like Assuming[Negative[x], Simplify[UnitStep[x]]]. (On that note, you can do your last one as Flatten[Position[x - y, _?Negative]]) $\endgroup$
    – J. M.'s torpor
    Feb 3 '20 at 13:26
  • $\begingroup$ @J.M. Thank you for the explanation! $\endgroup$
    – anderstood
    Feb 3 '20 at 13:28
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Flatten @ Position[Less @@@ Transpose[{x, y}], True]
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1
  • 2
    $\begingroup$ Equivalently: Flatten[Position[Thread[x < y], True]] $\endgroup$
    – J. M.'s torpor
    Feb 3 '20 at 13:27
6
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PositionIndex[Sign[x - y]] @ -1

{2, 3, 6}

Also

PositionIndex[UnitStep[x - y]] @ 0 (* thanks: J.M. *)

{2, 3, 6}

PositionIndex[Negative[x - y]] @ True (* thanks: anderstood *)

{2, 3, 6}

PositionIndex[Thread[x < y]]@True

{2, 3, 6}

If you prefer to have {} (rather than Missing["KeyAbsent", _]) as output when no positions satisfy the condition, you can use

Lookup[PositionIndex[Sign[x - y]], -1, {}]
Lookup[PositionIndex[UnitStep[x - y]], 0, {}]
Lookup[PositionIndex[Negative[x - y]], True, {}]
Lookup[PositionIndex[Thread[x < y]], True, {}]

for the four approaces above.

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    $\begingroup$ Another equivalent for the first: Lookup[PositionIndex[UnitStep[x - y]], 0]. $\endgroup$
    – J. M.'s torpor
    Feb 3 '20 at 13:37
  • 2
    $\begingroup$ Also: PositionIndex[Negative[x - y]][True] $\endgroup$
    – anderstood
    Feb 3 '20 at 14:04
  • 1
    $\begingroup$ Thank you both J.M. and @anderstood. I added your suggestions. $\endgroup$
    – kglr
    Feb 3 '20 at 14:09

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