Skip to main content

simplifying expressions - Different outputs for Simplify


In at least one instance, the same Simplify command (without using options) produces very different results on two of my computers, one Windows 7 and the other Windows 10. Here is the code:


sf = Simplify;

r1 = (-1 + (-11 - a^2 + 2 a^4) b^2 + (8 - 3 a^2) b^3 + (-2 + a^2) b^4 - 
     b (-6 - 3 a^2 + a Sqrt[b (2 + (-2 + a^2) b)] + 
        2 a^3 Sqrt[b (2 + (-2 + a^2) b)]) - 
     a (Sqrt[b (2 + (-2 + a^2) b)] - 3 Sqrt[b^5 (2 + (-2 + a^2) b)] + Sqrt[

        b^7 (2 + (-2 + a^2) b)]))/(-1 + b - a^2 b + 
     a Sqrt[b (2 + (-2 + a^2) b)])^2;

This is what I got on one of the computers, the Windows 10 one:


Dr1 = D[r1, b] // sf 

(* (6 + 3 a^2 + 2 (-11 - a^2 + 2 a^4) b + 3 (8 - 3 a^2) b^2 + 
    4 (-2 + a^2) b^3 - (a (1 + (-2 + a^2) b))/Sqrt[b (2 + (-2 + a^2) b)] - (
    a b (1 + (-2 + a^2) b))/Sqrt[b (2 + (-2 + a^2) b)] - (
    2 a^3 b (1 + (-2 + a^2) b))/Sqrt[b (2 + (-2 + a^2) b)] - 

    a Sqrt[b (2 + (-2 + a^2) b)] - 2 a^3 Sqrt[b (2 + (-2 + a^2) b)] + (
    a b^6 (-7 - 4 (-2 + a^2) b))/Sqrt[b^7 (2 + (-2 + a^2) b)] + (
    3 a b^4 (5 + 3 (-2 + a^2) b))/Sqrt[b^5 (2 + (-2 + a^2) b)])/(-1 + b - 
    a^2 b + a Sqrt[
     b (2 + (-2 + a^2) b)])^2 - (2 (1 - a^2 + (a - 2 a b + a^3 b)/Sqrt[
      b (2 + (-2 + a^2) b)]) (-1 + (-11 - a^2 + 2 a^4) b^2 + (8 - 
         3 a^2) b^3 + (-2 + a^2) b^4 - 
      b (-6 - 3 a^2 + a Sqrt[b (2 + (-2 + a^2) b)] + 
         2 a^3 Sqrt[b (2 + (-2 + a^2) b)]) - 
      a (Sqrt[b (2 + (-2 + a^2) b)] - 3 Sqrt[b^5 (2 + (-2 + a^2) b)] + Sqrt[

         b^7 (2 + (-2 + a^2) b)])))/(-1 + b - a^2 b + 
    a Sqrt[b (2 + (-2 + a^2) b)])^3 *)

And this, much better expression is what I got on the other computer, the Windows 7 one:


D[r1, b] // sf

(* (2 (-1 + b)^2 b (4 (-2 + 9 a^2 - 8 a^4 + 2 a^6) b^4 - 
     3 a Sqrt[b (2 + (-2 + a^2) b)] - 
     b (-8 - 11 a^2 + 10 a Sqrt[b (2 + (-2 + a^2) b)] + 
        10 a^3 Sqrt[b (2 + (-2 + a^2) b)]) - 

     b^2 (24 - 14 a^2 - 14 a^4 - 29 a Sqrt[b (2 + (-2 + a^2) b)] + 
        14 a^3 Sqrt[b (2 + (-2 + a^2) b)] + 
        4 a^5 Sqrt[b (2 + (-2 + a^2) b)]) - 
     b^3 (-24 + 61 a^2 - 18 a^4 - 4 a^6 + 16 a Sqrt[b (2 + (-2 + a^2) b)] - 
        24 a^3 Sqrt[b (2 + (-2 + a^2) b)] + 
        8 a^5 Sqrt[b (2 + (-2 + a^2) b)])))/(Sqrt[
   b (2 + (-2 + a^2) b)] (-a b + Sqrt[b (2 + (-2 + a^2) b)])^3 (-1 + b - 
     a^2 b + a Sqrt[b (2 + (-2 + a^2) b)])^2) *)

Can I find the reason for this and make it the same on both computers? If so, how to do this? I may have changed global preferences for Simplify on the Windows 7 computer, but don't remember if or how or what I did concerning that. This behavior occurs both in Mathematica 11.2 and Mathematica 11.1.1.





Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...
Post a Comment
Read more