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[Mathematica] Formatting output of polynomials

  1. Feb 23, 2012 #1
    Hi guys,

    I seem to still be having problems formatting polynomials in a standard way in Mathematica. I generate them randomly and would like them output using Print in a particular format. Say I have:

    theFunction=-2 + w^3 (-9 - 3 z) - 7 z + w^2 (4 + 5 z) + w (8 - 2 z^2) +
    w^4 (-5 z^2 - 5 z^3)

    I can for example use TraditionalForm to get:

    [tex]w^4 \left(-5 z^3-5 z^2\right)+w^3 (-3 z-9)+w^2 (5 z+4)+w \left(8-2 z^2\right)-7 z-2[/tex]

    but that's really not the way I want it. I'd like to output it in the form:

    [tex](-2-7z)+(8-2z^2)w+(4+5z)w^2+(-9-3z)w^3+(-5z^2-5z^3)w^4[/tex]

    with the parenthesis. I've tried CoefficientList to get the coefficients directly and then put the polynomial back together the way I want it but Mathematica changes it and doesn't keep the parenthesis around the w^0 term and will also place the w^n term first in some of the terms. Here's the code I'm using to generate the polynomials:

    Code (Text):
    degree = 5;
    bitsize = 5;
    thenumber =
      IntegerDigits[RandomInteger[{1, 2^(bitsize (degree + 1))}], 2,
       bitsize (degree + 1)];
    orderTable = Table[0, {degree + 1}];
    mylist = Table[
       aseq = Take[thenumber, {bitsize (n - 1) + 1, bitsize n}];
       atemp = Table[If[aseq[[j]] != 0,
          RandomInteger[{-9, 9}] Power[z, j - 1], "A"], {j, 1, bitsize}];
       Subscript[a, n - 1] = Plus @@ DeleteCases[atemp, _String]
       , {n, 1, degree + 1}];

    theFunction = Plus @@ Table[Subscript[a, n] w^n, {n, 0, degree}]
    TraditionalForm[theFunction]
     
    You guys have any ideas how to change it so that I can Print the output in the form I described above?
    Thanks,
    Jack
     
    Last edited: Feb 23, 2012
  2. jcsd
  3. Feb 23, 2012 #2
    Here's a quick hack

    Code (Text):
    polyForm[poly_, var_] :=
     Module[{coeffs = CoefficientRules[poly, var] // Sort},
      Interpretation[Row[Table[Row[{"(", coeff[[2]], ")", w^coeff[[1, 1]] /. 1 -> ""}],
                                         {coeff, coeffs}], "+"], poly]]
    Then

    Code (Text):
    theFunction = -2 + w^3 (-9 - 3 z) - 7 z + w^2 (4 + 5 z) +
                                  w (8 - 2 z^2) + w^4 (-5 z^2 - 5 z^3);

    polyForm[theFunction, w]
    (-2 - 7 z) + (8 - 2 z^2) w + (4 + 5 z) w^2 + (-9 - 3 z) w^3 + (-5 z^2 - 5 z^3) w^4
    It's only really for displaying the polynomial, since the `Interpretation` thing only works for cutting and pasting (that is `t = polyForm[poly, var]` does not work). If you worked at a lower level with `InterpretationBox` then you could get it working more smoothly.
     
    Last edited: Feb 23, 2012
  4. Feb 24, 2012 #3
    Ok. That works fine. I only want it for displaying. The reason is so that I can easily relate the algebra to the geometry whereas when it's not in that easy-to-recognize form sometimes I mis-interpret the geometry based on the algebra only to realize after some work that I didn't notice a term.

    Thanks!
     
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