MaplePrimes Commons General Technical Discussions

The primary forum for technical discussions.

 

Here is the progress made in the investigation of what I call the convergents constants:
https://oeis.org/wiki/Table_of_convergents_constants

I wonder if anyone would be interested in adding anything to it. I would like to see the convergents constants studied some in Maple to compare with my Mathematica results; my investigation is in dire need of some proof other than my...

A problem with convert,StandardFunctions

 

P := hypergeom([-k,1/2-k],[-2*k],1-z^2);

(1)

convert(P,StandardFunctions);
P1a:=subs(k=1,%);

 

(2)

P1:=subs(k=1,P);

(3)

plot({P1,P1a},z=-1..1,0..2);

 

convert(P,StandardFunctions) assuming k::posint;

(4)

 

 

Download hyp.mw

 

Hello all,

I've noticed that something has changed to the type of sqrt in Maple 15, which breaks backward compatibility...

In Maple 14, we have

> type(sqrt,procedure);          true
> type(sqrt,`module`); false
> eval(sqrt);          proc(x::algebraic, f::identical(symbolic))  ...  end proc

while in Maple 15, we have

> type(sqrt,procedure);          false
> type(sqrt,`module`); true

Although the source is very old (Maple 6) the topic is interesting.  Should one come across the webpage Analysis and Synthesis of digital sound samples with Maple 6 located here http://www.maplesoft.com/applications/view.aspx?SID=3940&view=html they may have a dissapointing maple browsing experience when 3 of the links they try to access are broken and not available.  

Inside a procedure, local variables are evaluated only one level. Of what good is this, one might ask?

Well, for one thing it allows you to do checks or manipulations of an unevaluated function call without having that function call be evaluated over again. I mean, for function calls to routines which don't happen to remember earlier results.

This is a revision of an Answer

There have been some recent posts about interpolating data.

Attached below is a worksheet that shows some possibilities, with the functionality centering on the CurveFitting:-ArrayInterpolation command.

This is quick summary of parts of a broader document which covers both 2-d and 3-d methods (for regular grids), where I've left out the higher-efficiency methods and instead roughed in some examples involving integration and differentiation.

I've elected not to follow the 3-d Example from the ArrayInterpolation command's help-page, although using a pre-formed grid is a very fast approach to obtain just an interpolated 3-d plot. I also prefer to use the plots:-surfdata command rather than the plots:-matrixplot command, since the former let's one get the axes' tickmarks correct for the x- and y-data ranges.

The scenario is that you have a grid of data points in two dimensions (x- and y, or P- and T-, or what have you).

For each point (ie, for each 2-d pair of values) you have an associated value (or height in z, say). Hence you actually have data points in 3-d space.

How you obtained the associated (z) values depends on your own particular data collection method, or your own program. How you got the data is irrelevant here. What matters is that you have the finite number of data values, and no other easy way to generate data values at more points (let alone data for arbitrary new points). Below, we'll just create the data (once, at the start) for this example using an entirely made-up formula.

The presumption is that you might wish to plot a smooth surface that connects the 3-d data.

But you might also wish to write some program which requires interpolated (z) values at some new (x,y) 2-d points.  And you do not yet know what these 2-d point pairs are. So a pre-formed Array of points  at which to interpolate may not suffice.

Instead of using a pre-formed Array of output points, we'll contruct a procedure named `B` which can be supplied with a new (x,y) 2-d output point and (if that point lies within the original range) return an interpolated (z) value.

This procedure `B` can also be plotted, using the usual `plot3d` comamnd. It won't plot quite as fast as would a pre-computed and pre-interpolated finer grid of (x,y) values, but it should plot nicely. And the surface can be made quite smooth, by merely increasing the number of plotted points using plot3d's usual numpoints option. (Maple does not currently do "adaptive" 3-d plotting, so there's also no advantage in that respect.) But `B` does solve the secondary task, of being able to compute for any subsequent (x,y) point.

We can even integrate and differentiate `B` numerically. Of course we should keep in mind that this is somewhat error prone, since on top of usual issues with numerical differentiation there is also fact that we make the choice of interpolation method! The entire interpolated surface will differ considerably according to whether a spline, cubic (or other) interpolating scheme is chosen!

We'll use P and T as the x- and y- grid points, below, since "a name is just a name" and our choice of variables is arbitarary.

plot_interp.mw

One useful feature of the `evalf` command is that it remembers previous results. But it also stores the current value of Digits as well as its input argument, to be associated with the remembered result.

There are two reasons for this. The fancier reason is so that, when Digits is reduced from that of an earlier successful computation, `evalf` can simply round off the earlier result to the desired number of decimal digits. The more basic reason is that `evalf` might...

I can no longer see answers to questions or added comments to posts.

I was able to view them last night. 

So there is a maximum number of conditions that one can set... good to know!

I tried your solution, and it does work. I'll just have to determine the values of my b1 and b2 parameters with a little programming.

 

Thank you very much!

This page from the Online Help suggests that GMP 4.2.1 is still being used in Maple 15.

But the latest "stable" release is GMP 4.3.2, see release notes here (various fixes and improvements in the 4.3.xx series mentioned).

Perhaps this could be updated in a service release Maple 15.xx.

What happened to all the Maple 5 applications at the maplesoft application center? 

Why just the other day I was looking at them.  Very dissappointed to see them "removed".  In particular a series of applications for mapping. 

The drop down option for Maple5 has dissappeared. 

Are they gone?  Can you put them back?

Since -1 = i^2 I thought that there could be some meaning behind "alternating" series that instead of beginning with (-1)^n begin with (a+b*i)^n, with real coefficients, for abs(a)<1 and abs(b)<1. I'm not sure but it seems that such series are absolutely convergent, because (a+b*i)^n -> 0+0I as n->infinity, hence the term utterly diminishing series instead of alternating series.

As an example,
Where sum((-1)^n*(n^(1/n)-1),n=1..infinity)= 0.187859642462067120248... ,


It still seems that the original post won't accept new replies, so I'm starting a new post.

The maplecloud may in some respects reduce the sharing of applications on mapleprimes and at the maplesoft application center.  A maplecloud user may instead of sharing his application via mapleprimes applications or the maplesoft website may just make his worksheet publicly available over the cloud simply because it's easier to do. 

It is true that mapleprimes is a different type of serviece that allows the interaction of ideas/questions as well as the sharing...

Mapleprimes takes unusually longer to load than used to.  And some people complain about being emailed 3 x's I'm not sure it's fixed but I've noticed my page actually loading 3 times before it actually comes up.  I'm on dial up so I can notice things people on high speed won't notice.

One other thing possibly very important to the web program designers of this site.  If I load the mapleprimes web page and say stay offline, it does this 3 times. ...

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