Skip to main content

output formatting - Why does Mathematica order polynomial forms in reverse from traditional order?


I could very well be missing something obvious, but this has always bugged me with Mathematica and I don't know why it does it or how to fix it.


If I enter any polynomial, say, x^2 + x - 1 for example, the output is always in the form:


-1 + x + x^2

And again:


input: Expand[(x^2 - 1) ((-3 + x)^2 - 4)]
output: -5 + 6 x + 4 x^2 - 6 x^3 + x^4

I find this much more difficult to read than the traditional way, from highest power to lowest. Is there anything I can do to change this? I'm aware that TraditionalForm prints them properly, but it is generally not recommended to do calculations with TraditionalForm so I'd like to avoid that if possible. Then again, IS IT that bad to do calculations with TraditionalForm like it warns?




Answer



As Daniel Lichtblau wrote in the comment you can use TraditionalForm


Expand[(x^2 - 1) ((-3 + x)^2 - 4)] // TraditionalForm


x4−6x3+4x2+6x−5



However, it works perfectly only with univariate polynomials


Expand[(x + y + 1)^5] // TraditionalForm



x5+5x4y+5x4+10x3y2+20x3y+10x3+10x2y3+30x2y2+30x2y+10x2+5xy4+20xy3+30xy2+20xy+5x+y5+5y4+10y3+10y2+5y+1



You can see that 5x is before y5 and so on.


My solution consist in the manual sorting of monomials


OrderedForm = HoldForm[+##] & @@ MonomialList[#][[
     Ordering[Total[#] & @@@ CoefficientRules[#], All, GreaterEqual]]] &;

Expand[(x + y + 1)^5] // OrderedForm



x^5+5 x^4 y+10 x^3 y^2+10 x^2 y^3+5 x y^4+y^5+5 x^4+20 x^3 y+30 x^2 y^2+20 x y^3+5 y^4+
10 x^3+30 x^2 y+30 x y^2+10 y^3+10 x^2+20 x y+10 y^2+5 x+5 y+1

Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more