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The first three expressions evaluate as expected and the polynomial is displayed in what I would call "textbook" form. The last expression, however, switches the order of terms. Mathematica employs this change for two-term polynomials if it results in getting rid of the leading negative sign (at least that is the best I can deduce).

x^2 + x + 5 // TraditionalForm
(* x^2 + x + 5 *)

-x^2 + x + 5 // TraditionalForm
(* -x^2 + x + 5 *)

x^2 + x // TraditionalForm
(* x^2 + x *)

-x^2 + x // TraditionalForm
(* x - x^2 *)

These polynomials are the result of prior symbolic manipulation, so I cannot simply use HoldForm or the equivalent to maintain the desired order.

Is there a way to change this behavior in general so that the last expression displays as -x^2 + x? I can think of substitution rules to fix this particular example, but would like to find a robust solution that applies as transparently as possible across the board.

Edit

Additionally, PolynomialForm produces the same results:

PolynomialForm[-x^2 + x , TraditionalOrder -> True]
(* x - x^2 *)

PolynomialForm[-x^2 - x , TraditionalOrder -> True]
(* -x^2 - x *)

It seems that Mathematica will produce the traditional order for polynomial terms except when there are only two terms and reversing the order eliminates the leading negative sign.

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6
  • $\begingroup$ I was expecting to close this question with a reference to PolynomialForm[#, TraditionalOrder -> True] & but I see that you're going the other way. Let me think about that. $\endgroup$
    – Mr.Wizard
    Mar 5, 2013 at 23:41
  • $\begingroup$ @Mr.Wizard: Yes, I already tried PolynomialForm and that produces the same results. I will add that information to the question because that will probably be a common thought pattern. $\endgroup$
    – RandomBits
    Mar 5, 2013 at 23:45
  • $\begingroup$ Previous questions relating to this usually creates a new function to handle Plus. But would be nice with a way that lets you override the displayed order of Orderless arguments. $\endgroup$
    – ssch
    Mar 6, 2013 at 0:21
  • $\begingroup$ Previous questions: stackoverflow.com/questions/4109306/… stackoverflow.com/questions/3947071/… $\endgroup$
    – ssch
    Mar 6, 2013 at 0:22
  • $\begingroup$ @ssch I don't think those solve this one (which I assume is why you didn't post an answer.) RandomBits doesn't want to prevent ordering, he wants to control it. $\endgroup$
    – Mr.Wizard
    Mar 6, 2013 at 0:46

3 Answers 3

Reset to default
7
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Since the two other answers don't seem to do exactly what's needed, I'll try my luck:

order[poly_] := 
 Replace[Reverse@Sort[List @@ poly], List[x__] :> HoldForm[Plus[x]]]

order /@ {x^2 + x + 5, -x^2 + x + 5, x^2 + x, -x^2 - x}

$\left\{x^2+x+5,-x^2+x+5,x^2+x,-x^2- x\right\}$

Here I end up with HoldForm wrapping an expression that should have the sorted terms, and this ordering would be maintained when feeding it into TraditionalForm or TeXForm.

I avoided using Row for the output (and hence also don't use Format or MakeBoxes) so that I don't have to worry about getting things like $+\,-\,x$.

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3
  • $\begingroup$ Well I was just getting around to this method myself but you were six minutes faster so +1. :-) $\endgroup$
    – Mr.Wizard
    Aug 3, 2013 at 5:37
  • $\begingroup$ Jens, do you see anything wrong with my second method? What do you see as the advantage or disadvantage of Sort[List @@ #] versus MonomialList@#? $\endgroup$
    – Mr.Wizard
    Aug 3, 2013 at 5:50
  • $\begingroup$ @Mr.Wizard MonomialList is the right choice, I think. But using Sort seems like a cute, original twist. $\endgroup$
    – Jens
    Aug 3, 2013 at 6:09
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I hope there is a better way but here is something to build upon:

TraditionalForm @ Row[MonomialList@#, "+"] & /@
  {x^2 + x + 5, -x^2 + x + 5, x^2 + x, -x^2 + x}

Mathematica graphics

Jens pointed out a bug in my original method. Here's another:

HoldForm[+##] & @@ MonomialList@# & /@
 {x^2 + x + 5, -x^2 + x + 5, x^2 + x, -x^2 + x, -x^2 - x}

enter image description here

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  • 2
    $\begingroup$ Similar Row[MonomialList[-x^2 + x, {x}, "DegreeLexicographic"], "+"] $\endgroup$
    – ssch
    Mar 6, 2013 at 0:06
  • $\begingroup$ Is it the case that Plus@@MonomialList[expr] == expr for any expression? If so, then I can define a format: Format[xPlus[x___]] := Row[Riffle[{expr}, "+"]] and then xPlus := Plus and then use HoldForm[xPlus@@MonomialList[expr]] to the display ordering that I want while still having a valid expression when the hold is released (because the xPlus will be changed to Plus). $\endgroup$
    – RandomBits
    Mar 6, 2013 at 3:47
  • 1
    $\begingroup$ After I upvoted this, I realized it's not quite right: Try TraditionalForm@Row[MonomialList@#, "+"] &[-x^2 - x] and you get $-x^2+\,-\,x$. The same error happens with the solution by @ssch. $\endgroup$
    – Jens
    Aug 3, 2013 at 5:16
  • $\begingroup$ @Jens Okay, maybe a hybrid of the two answers will work. Let me try some stuff. $\endgroup$
    – Mr.Wizard
    Aug 3, 2013 at 5:25
1
$\begingroup$ 
poly[x_] := 
 Block[{Plus}, 
  x // Sort // Reverse // Evaluate // HoldForm // TraditionalForm]
poly[x - x^2]
(* -x^2+x *)
poly[-x^2 + x]
(* -x^2+x *)
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5
  • $\begingroup$ This is the best answer, I think (+1). But do you really need HoldFirst? $\endgroup$
    – Jens
    Aug 3, 2013 at 5:18
  • $\begingroup$ @Jens This changes the order of all the other terms, which in my understanding is not desired. I believe all but the last expression should agree with {x^2 + x + 5, -x^2 + x + 5, x^2 + x, -x^2 + x} // TraditionalForm. That is to say, it should match my answer. $\endgroup$
    – Mr.Wizard
    Aug 3, 2013 at 5:19
  • $\begingroup$ @Mr.Wizard You're right. I thought Sort on blocked Plus is a clever idea, but it doesn't quite do what's needed either. $\endgroup$
    – Jens
    Aug 3, 2013 at 5:24
  • $\begingroup$ @Jens, Mr. Wizard good catches - guess I should have done more testing. $\endgroup$
    – VF1
    Aug 3, 2013 at 5:33
  • $\begingroup$ @Jens moreover, it fails with -x + 1. $\endgroup$
    – Kuba ♦
    May 23, 2014 at 9:52

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