MaPal93

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These are questions asked by MaPal93

I want to display W__LJ as I typed it, without Maple running the calculations resulting in the output here below:

restart;

'W__LJ = 0.75 + 0.98*((1.18/Gamma)^1.9 - (1.15/Gamma)^0.98)';

W__LJ = .75+1.342152577*(1/Gamma)^1.9-1.123854165*(1/Gamma)^.98

(1)
 

NULL

Download display_formula.mw

This is important as I will place such expression in a plot like this:
textplot([2,0.9,typeset('W__LJ=0.75+0.98((1.18/Gamma)^1.9-(1.15/Gamma)^0.98)')],'font'=["helvetica","roman",35])
and I need it in the original functional form, which is easier to interpret.

I have two surfaces crossing the z=0 plane for some ranges of x and y values.

For the first surface, x=Gamma is bounded between 0 and 10 and y=rho between -1 and +1. For the second surface, x=Gamma_1 is bounded between 0 and 10 and y=Gamma_2 between 0 and 10 as well. I want to clearly identify (parametric):

  1. For which Gamma and rho ranges of values the first surface is positive (and for which negative)
  2. For which Gamma_1 and Gamma_2 ranges of values the second surface is positive (and for which negative)

Worksheet: sign_regions.mw (highlighted in yellow my two failed attempts)

I have a positive surface that I plot3d for bounded x- and y- value ranges. It reaches 1000 but it's mostly flat except almost at the edges of the x- and y-axes. Therefore, I inlcude view=[default,default,0..10] among the options of plot3d so that I can focus on the features of interest.

For coloring I use 'colorscheme'=["zgradient",["LightGray", "Gray", "Green"]]. However, this applies to the whole surface (up to 1000) and NOT exclusively to the viewed part as I would like to. 

Question: how to scale the zgradient so that it only applies to my "view" portion?

Note that I don't want to do this by using the 'markers' options to readjust the color splits manually, as I don't know the exact proportion and I don't want to randomly play around with different triplets until I achieve a visually satisfying result...

In relation to my comment below:
https://www.mapleprimes.com/questions/238277-Robustness-Of-Plotevalsomething#comment301920 (whose my worksheet rho-analysis_mmcdara_Gammapositive_MaPal.mw builds on the Sturm's analysis of @mmcdara)

I would like to better understand how to isolate/pin down the 4 real roots whose existence was confirmed by Sturm's analysis. To do so, @acer suggested to look into RootFinding:-Parametric: rho-analysis_acc(1).mw
Questions:

  1. Why the plot doesn't change if I also include -1<rho and rho<1 among the equations to solve? I understood that regions 1, 4 and 5 have 0 solutions anyway but if I add the constraints on rho I should expect 2 regions instead of 5, right?

  2. I don't understand SampleSolutions(m,2)=0.56 and SampleSolutions(m,3)=0.51 (even after reading help page). How are these numeric values found?

  3. Looking at the big picture, how to reconcile this CellPlot with A) my plot3d of Eq in https://www.mapleprimes.com/questions/238277-Robustness-Of-Plotevalsomething#comment301920 and B) @mmcdara Sturm's analysis. I am having a hard time putting all together.

    Thank you. 

    EDIT: I formulated this question by branching out from my comment 
    https://www.mapleprimes.com/questions/238277-Robustness-Of-Plotevalsomething#comment301920 in the corresponding thread. If inappropriate, please help me migrate this question as appropriate. 

I noticed that in a legend with:

  1. Three elements
  2. linestyle = [solid, longdash, dash]
  3. thickness = [4, 4, 4]

The three different linestyles are distinguishable in the plots (of course, since the curves span the whole plot area) but indistinguishable in the legend box. Since the legend box is too narrow, the symbols for a solid line, a longdash line, and a dash line are equivalent, resulting in confusion regarding which element is associated to each linestyle. Note that I don't want to use three different colors to achieve that or change my font sizes

  1. How can I "show more" of the linestyle in the legend box? "Longer" line symbols in the legend box would allow to dinstinguish a solid from a longdash from a dash even when all three are quite thick.
  2. Alternatively, can I reduce the thickness of the line symbols in the legend box (leaving unaltered the thickness of the lines in the actual plot)? "Slimmer" line symbols in the legend box would allow to dinstinguish a solid from a longdash from a dash even when all three are quite short.
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