Good to see changes happening.

Rarely do I visit anywhere on mapleprimes but the recent tab.  I would like to see a tree structure implimented there. 

I just visitied the posts and saw the available categories and I would like to suggest another category ...

... how about one called... Ideas for maple projects ... you know, like ideas people come up with that they would like to see done in maple but don't have the time or knowledge for example to do it in Maple themselves. 

I was thinking collaborative projects but I see it probably won't work well here.  Most people like to present completed projects rather than part projects and only get part credit for the work.  Not only that, but everyone has different styles of programming and someone elses style of programming may not mesh with anothers, or trying to decipher what someone has already done can present difficulties in itself.

I'll mention here and start off here an example for Ideas for maple projects.  I was filling up buckets of water to water the plants outside and had an empty yogurt container floating in the bucket.  Initially it mostly all floats, then the water slowly enters the open end until the container sits a certain angle in equilibrium.  ...

... well maybe it's a silly example but I wondered without trying of course, how one would present such a problem with maybe an animation in Maple.  At least I thought it could be interesting. 

Okay yes.  It was a bit fuzzy when you said it had roots but didn't explicitly imply complex roots which for some reason I was oblivious to at the time.

In which case Maple should respond to No real roots but an infinte number of complex roots exist.

Okay yes.  It was a bit fuzzy when you said it had roots but didn't explicitly imply complex roots which for some reason I was oblivious to at the time.

In which case Maple should respond to No real roots but an infinte number of complex roots exist.

No real roots anyways.  At no point will it cross the x-axis

The max of cos(x) as x approaches infinity will never be above 1, and the min will never be below -1. 

Hence 2^(of a number approaching 1) approaches 2 from below
and    2^(of a number approaching -1) approaches 0.5 from above

So even 2^(cos(x)) - an infinitely oscillating value between 0.5 and 2, that doesn't cross the x-axis ever.  So I am sorry I can't see why it should have any roots at all.

No real roots anyways.  At no point will it cross the x-axis

The max of cos(x) as x approaches infinity will never be above 1, and the min will never be below -1. 

Hence 2^(of a number approaching 1) approaches 2 from below
and    2^(of a number approaching -1) approaches 0.5 from above

So even 2^(cos(x)) - an infinitely oscillating value between 0.5 and 2, that doesn't cross the x-axis ever.  So I am sorry I can't see why it should have any roots at all.

Yes, sadly, I have fallen into a trap and expected the default to work all the time (without realizing it was 10 from the help page, oops)

It's almost as if Maple should automatically scan lower range chunks say base 10 scale to be sure it didn't miss any.  Then again that begs someone to question me ... "So how far do you go with that?" and "It still could miss some Roots"  Of course my answer is not permanent nor is it exact, just a suggestion without limits. 

A side question...

Are there any proofs, theorems or conjectures one could use here, to know without a doubt that a certain type of polynomial contains n roots? 

Yes, sadly, I have fallen into a trap and expected the default to work all the time (without realizing it was 10 from the help page, oops)

It's almost as if Maple should automatically scan lower range chunks say base 10 scale to be sure it didn't miss any.  Then again that begs someone to question me ... "So how far do you go with that?" and "It still could miss some Roots"  Of course my answer is not permanent nor is it exact, just a suggestion without limits. 

A side question...

Are there any proofs, theorems or conjectures one could use here, to know without a doubt that a certain type of polynomial contains n roots? 

I agree that some categories may contain overlap but I think users would post to areas they would see fit.  I suppose what I meant was. if it was a question that was fairly basic it could be posted to the getting started section.  The tips and techniques could contain advanced techniques not suitable in a beginner category.  And stickies would stay on top and should be posted (in my view) in the getting started section and not get in the way when users were surfing other categories.  I don't suggest the category be named getting started but maybe beginning or some similar name but I think the name getting started is suitable.

The news section is just another category where users could go, and immediately see what the last news update was.  Rather than to scour the myriad of posts/questions that may have otherwise shuffled it far out of view in the posts listings and difficult to find. 

Now to the point situation.  As you mentioned, points are awarded as a reputation.  But it wouldn't seem fair that someone who is encouraging conversation (by posting) among mapleprimes users be awarded nothing.  This is why I suggested only a single point so it wouldn't increase as much.  Take for example an imaginary mapleprimes user "Iprime" for example.  let's say he has asked 100 questions, good or bad and he has not recieved a single vote for his posts or questions but yet he has contributed to mapleprimes in someway.  And maybe it is a low quality post (but why?  I don't see why anyone would, on purpose at least anyway) but the most he could ever get is 1 point (that being if no one gave him a vote for his question). Sure he'll get the prolific poster badge but his points ( 0 ) will not reflect his involvement in the community rarely if at all do I look at what badges someone has.  If a question wasn't deemed appropriate (spam for example) his deleted post would remove the point he gained. 

Another example:
Let's take 2 advanced users, for example, both having 2000 points each.   One hasn't answered/posted anything for 9 months while the other one has posted multiple (say 300) times. However as our friend, Iprime, he has also not recieved any votes.  So they both still end up with 2000 points except that one member has contributed quite extensively over the last 9 months but his points wouldn't reflect that (they both already have all the badges so a badge wouldn't do).  In fact it would look as if he had been dormant just the same as someone doing nothing.  Now comparing the two using the single point system.  2000 vs. 2300 pts.  you could see some activity had taken place even though he had no votes.  Otherwise one might make a foolhardy decision that both members had left the forum when in fact it was maybe just one (not that, that's what the points were for but .. I think you get my point)

Sorry for the lengthy thoughts I was hoping other users would also chime in their opinions.  I'd hate to be a minority on the decision making. 

Also one more suggestion.  The poll questions added a small dimension of amusement in the days of old.  It might be worth considering adding this to the our forum again?

@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.

@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.

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])

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])

And the same with the RiemannZeta function the Mathematica plot looks finer.  Unless they used many points and a very fast computer?  More grid points like 1000 would run me into a few hours

The first image is Maple

complexplot3d(Zeta(z), z = -40-2*I .. 10+48*I, orientation = [-90, 0], style = patchnogrid, grid = [100, 100])

And the same one by Mathematica (phase plot of the RiemannZeta function)

Granted it was copied from pdf and saved as jpg so it is worse than the original but still much better than Maple's  What grid do I need to achieve the same result in Maple?  Is complexplot3d the right way to go to produce these plots or is there another way? 

I'd like to see a finer image as shown here by mathematica (a phase plot showing essential singularity of
f(z)=exp(1/z)

Inserting the images used to work, hopefully the above works.

As for the error - I think it is native to Maple 12.  I briefly had access to a newer maple version and the grid is working however the resolution is not comparable (I'd like it to be :)  )  Also I can't go over grid 130 for Maple12, and for different functions of z a grid of [200,200] runs into the 45 minute range. 

As for the floating point error message - I hope this image uploads ...

Here is my attempt at exactly recreating the first image of the article in Maple.  Not sure how to create the other phaseplots in the article though.  And I noticed complexplot3d doesn't accept shading arguments, although it is accessible in the context menu of the plot??? 

with(plots):
f:=(z-1)/(z^2+z+1):
complexplot3d(f, z = -2-2*I .. 2+2*I, view = [-4 .. 4, -4 .. 4, 0 .. 4], style = patchnogrid, scaling = constrained, orientation = [-45, 70], grid = [150, 150], color = "DarkGray", light = [60, 5, 1, 1, 1]);

Also does anyone happen to remember a post or worksheet created with these graphics?  I seem to recall there was but I can't find it.