MaplePrimes - answers and comments on Question, zaxis floating point error range is too large - can we get better resolution?

It works for me

Markiyan Hirnyk — Tue, 28 Jun 2011 18:56:15 Z

This command works well even with greed [1000,1000] on my under intermediate comp. See a nice picture in screenshot.doc .

@Christopher2222 I may be missing something,

longrob — Tue, 28 Jun 2011 21:34:34 Z

@Christopher2222 I may be missing something, but looking at those 2 plots, why is Mathematica's much better than Maple's ? Edit: I'm talking about the Zeta() plots.

FYI I've produced the plot in Maple 15 with grid = [1500, 1500] and that looks nice to me, though I don't have mathematica to compare it to..... I can post a screenshot, or try to export it and upload it, if you like ? Edit: I'm talking about the exp(1/z) plot but I could also do the zeta() plot....

A better picture

Markiyan Hirnyk — Tue, 28 Jun 2011 22:19:05 Z

with(plots):
f := exp(1/z):
complexplot3d(f, z = -.15-.15*I .. .15+.15*I, style = patchnogrid, orientation = [-90, 0], grid = [900, 900])

a finer picture is obtained: screenshot3.doc . Another question is how to export it.

range

Christopher2222 — Wed, 29 Jun 2011 00:28:09 Z

Very nice! Okay I see I didn't select a small enough range either. How do you mean export? Just right click on the plot picture and export it to jpg.

BTW. is complexplot3d the right way to go about plotting phase plots of complex functions in Maple?

How long does it take on your machine to do a grid=[900,900]?

For grid=[150,150] my comp. takes 25 minutes. You must have a faster machine. Mine is only a P4 - 3Ghz (single core) with hyperthreading technology and 2.5Gb RAM.

I see now that Maple can easily match Mathematica I just wasn't taking the grids high enough. Maybe time to get a faster machine?

In case anyone didn't realize, I was duplicating some of the figures in the article from the post why Mathematica not Maple? Here's figure 17. A phase plot of the Taylor polynomial of f(z)=1/(1-z)

Except for the colors, it's almost exactly the same. Wonder how we could match up the color scheme? Kudos to anyone who can.

f := convert(taylor(1/(1-z), z = 0, 100), polynom):
complexplot3d(f, z = -1.5-1.5*I .. 1.5+1.5*I, orientation = [-90, 180], style = patchnogrid, grid = [150, 150])

densityplot

pagan — Wed, 29 Jun 2011 01:26:34 Z

@Christopher2222 The GUI uses several hundred MB (not reported by kernelopts or the status bar). Your machine may be swapped out, and thus taking longer than optimal.

You can use densityplot for some of these things. Excepot that it doesn't accept a discont=true option and so you can get spurious bright lines where the color changes sharply, due to roundoff.

This took my machine about 5 seconds, using the commandline interface.

restart:
plotsetup(gif,plotoutput="expinv.gif");                                        

st:=time():

plots:-densityplot((a,b)->evalhf(arctan(-sin(b/(a^2+b^2)),
                                        cos(b/(a^2+b^2)))),
                   -0.25..0.25,-0.25..0.25,colorstyle=HUE,
                   style=patchnogrid,scaletorange=-Pi..Pi,
                   grid=[1500,1500],axes=none);

time()-st;

Or,

restart:
plotsetup(gif,plotoutput="expinv.gif");     

plots:-densityplot(argument(exp(1/(a+b*I))),a=-0.25..0.25,b=-0.25..0.25,
                   colorstyle=HUE, style=patchnogrid,scaletorange=-Pi..Pi,
                   grid=[1500,1500],axes=none);

Those unwanted lines don't appear with all these sorts of plots, of course. So for some things you could try it as an alternative. It seems to use less memory (combined).

The plot Markiyan showed looked nice as screenshot. But its right-click export looked dark and dull, on my Win XP

export workaround in windows and view

Christopher2222 — Wed, 29 Jun 2011 04:43:36 Z

@pagan thanks

I also experienced darkened views when it selects it to export but I've managed to circumvent it by picking a point very close to the edge of the square plot so it doesn't darken it so far I've had good luck with that method.

Also I've found that my complexplot3d Z axis out of range had the z axis into the e^33 range. If I add the view option and reduce view=[default,default,10000000] I can up my grid values. But as I reduce my z axis view the nature of the plot produces a hole for my orientation in the picture.