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While tinkering with How to get a list of monomials of a polynomial without coefficients? on a whim I tried a fourth argument in Collect and found:

Collect[(x + y + z + 1)^2, {x, y}, foo, bar]

bar[bar[foo[1 + 2 z + z^2], y foo[2 + 2 z], y^2 foo[1]],
  x bar[foo[2 + 2 z], y foo[2]], x^2 bar[foo[1]]]

It seems that in addition to a third parameter that applies to coefficients the fourth parameter takes the place of Plus to reassemble the expression. I also note that this functionality has been present since at least version 7.0.1.

  • Is this understanding correct?

  • When was this introduced and has it changed any since then?

  • Has this been discussed here before?

  • What uses might this be put to?

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    $\begingroup$ It's been around since at least V5.2 (2006) and seems unchanged since then. That's as much as I know. $\endgroup$
    – Stefan R
    Jul 21, 2015 at 20:17
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    $\begingroup$ Introduced in either version 3 or 4, I forget which. Not sure if it has changed since then. $\endgroup$
    – Daniel Lichtblau
    Jul 22, 2015 at 3:11
  • $\begingroup$ @Daniel Since this is a longstanding feature is there a reason it has not been documented? $\endgroup$
    – Mr.Wizard
    Jul 22, 2015 at 5:54
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    $\begingroup$ It is not really the most carefully designed of features. (Or so claims the developer who put it in 20 or so years ago.) $\endgroup$
    – Daniel Lichtblau
    Jul 22, 2015 at 14:36

1 Answer 1

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This is an answer generated from the comments.

D. Lichtblau:

Introduced in either version 3 or 4, I forget which. Not sure if it has changed since then.

Mr.Wizard:

Since this is a longstanding feature is there a reason it has not been documented?

D. Lichtblau:

It is not really the most carefully designed of features. (Or so claims the developer who put it in 20 or so years ago.)

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