Never before has the educational landscape been changing as fast as it is today, driven by a new generation of students who are growing up with instant access to on-demand information. This generation relies on ubiquitous network access and takes for granted technology that permeates every aspect of their lives. Phones and tablets are everyday companions and are used to connect with their peers, take classroom notes and research school projects. Beyond being mere consumers...

Here is a plot in table format of the standard Times, Helvetica, and SYMBOL fonts. This plot provides a reference table that can be used to find the character codes to plot any one-byte character that can be plotted, which is especially useful for the SYMBOL characters and character codes 128-255 in the standard fonts. These characters are available for plotting in both the Standard and Classic GUIs.

All characters are aligned to be immediately above and immediately...

Well, it’s been more than 17 years since First Leaves: A Tutorial Introduction to Maple V was first published as a hardcover book, and since that time, Maple, the Maple documentation, and the world have undergone huge changes.   We are now in a state where all our documentation is available electronically, including both in-product and online; where the vast majority of our customers receive our products electronically and never even see the printed...

Maple T.A. 9 is here!

The new release includes a large selection of useful new features and enhancements, including:

- Content. Maple T.A. 9 includes an easy mechanism to share questions with the community and access questions created by others, through the Maple T.A. Cloud. The Maple T.A. Cloud already contains thousands of questions that you can use and modify.

- Adaptive Testing. Expanding on the adaptive question...

The latest version of the Iterator package is now available at the Maplesoft Application Center.  It provides a new export, MultiPartition, extensions to existing exports, and options to most exports for transforming the output to a more desirable form. The help pages have been improved, with some hopefully interesting examples.  Here is one, showing how it can be used to write a procedure for solving a generalized ...

Maple 16 introduces the ?ModuleIterator method, which can be assigned in a module so that it can be used  in a for-loop, or in the seq, add, and mul procedures.

ModuleIterator should return two procedures.  The first (referred to as hasNext) is a predicate that returns true if the iterator is not finished.  The second (referred to as ...

We have just released Maple 16.02 and MapleSim 6.01.

Maple 16.02 includes updated platform support, enhancements to the Physics package (including fixes to problems first reported on MaplePrimes - thank-you),  connectivity to the latest version of MATLAB and Visual Studio , as well as some efficiency and interface improvements. See the Maple 16.02 update page for more details.

MapleSim...

I would like to be able to read Maple manuals and the AEM book that I have bought on the ipad. I can understand that I will not be able to run the commands. But it woud be nice to read through the different sections while reclining on my bed. Hope that you will make it possible.

On several occasions, while working with lists or Matrices, I have been drawn to using a combination of seq and if, as in the following:

seq(`if`(a,b,c), i = 1 .. 10 )

This appears to be a powerful approach. Unfortunately, I have not found much documentation on it.

I have been able to pattern-guess to a limited extent for my limited needs.

Would you know of a good place to go for information?

My understanding is: "a" is the conditional...

I have found very little help about the Generate command of the RandomTools package.

I also have minor gripes about the syntax. And what better way to deal with these than to voice them?

This is how I was able to generate random lists and random Matrices.

A list of 10 random integers between 1 and 100:

L := RandomTools:-Generate(list(integer(range=1..100),10));

      L := [47, 8, 46, 44, 9, 77, 59, 16, 1, 70]

In it's recent edition of Mathematics Today (in print and online), the UK-based Institute of Mathematics and it's Applications, compared 4 symbolic solvers: Maple 15, Mathcad 15, the student edition of Matlab v5 and the Casio CFX-9970G calculator, concluding that "Maple would be the natural choice for research mathematicians, theortetical physicists, those working in any area where mathematics is demanding or for mathematics undergraduates for whom costs are lower"

I wanted to point the MaplePrimes community in the direction of the new MapleSim training videos. These videos cover a variety of common tasks within MapleSim, and demonstrate the concept in just a few minutes each. I'd highly recommend you take a look at them to learn more about using MapleSim.

They're located here: http://www.maplesoft.com/support/training/videos.aspx

-Graham

It is the first time  I post a Maple bug in MaplePrimes because I use to submit an SCR.
There is a serious reason to do so. Let us look at the output of
> with(plots):
> implicitplot(sqrt(x^2+y^2)-sqrt((x-4)^2+(y-3)^2) = 5, x = -20 .. 20, y = -20 .. 20,
numpoints = 10^6, thickness = 5, scaling = constrained);
(both in Maple 13 and in Maple 16)

Let's see how we can display patterns, or even images, on 3D plot surfaces. Here's a simple example.

The underlying mechanism is the COLOR() component of a POLYGONS(), GRID(), or MESH() piece of a PLOT3D() data structure. (See here, here, and here for some older posts which relate to that.)

The data stored in the MESH() of a 3D plot structure can be a list-of-lists or, more efficient, an Array. The dimensions of that Array are m-by-n-by-3 where m and n are usually the size of the grid of points in the x-y plane (or of points in the two independent parameter spaces). In modern Maple quite a few kinds of 3D plots will produce a GRID() or a MESH() which represent the m-by-n independent data points that can be controlled with the usual grid=[m,n] option.

The plot,color help-page describes how colors may specified (for each x-y point pair to be plotted) using a procedure f(x,y). And that's fine for explicit plots, though there are some subtleties there. What is not documented on that help-page is the possibility of efficiently using an m-by-n-by-3 or an m*n-by-3 datatype=float[8], order=C_order Array of RGB values or am m*n float[8] Vector of hue values to specify the color data. And that's what I've been learning about, by experiment.

A (three-layer, RGB or HSV) color image used by the ImageTools package is also an m-by-n-by-3 Array. And all these Arrays under discussion have m*n*3 entries, and with either some or no manipulation they can be interchanged. I wrote earlier about converting ImageTools image structures to and from 2D density-plots. But there is also an easy way to get a 3D density-plot from an ImageTools image with a single command. That command is ImageTools:-Preview, and it even has a useful options to rescale. The rescaling is often necessary so that the dimensions of the COLOR() Array in the result match the dimensions of the grid in the MESH() Array.

For the first example, producing the banded torus above, we can get the color data directly from a densityplot, without reshaping/manipulating the color Array or using any ImageTools routines. The color data is stored in a m*n Vector of hue values.

But first a quick note: Some plots/plottools commands produce a MESH() with the data in a list-of-lists-of-lists, or a POLYGONS() call on a sequence of listlists (eg. `torus` in Maple 14). For convenience conversion of the data to a 3-dimensional Array may be done. It's handy to use `op` to see the contents of the PLOT3D() structure, but a possible catastrophe if a huge listlist gets printed in the Standard GUI.

restart:
with(ImageTools):with(plots):with(plottools):
N:=128:

d:=densityplot((x,y)->frem((x-2*y),1/2),0..1,0..1,
                      colorstyle=HUE,style=patchnogrid,grid=[N,N]):
#display(d);

c:=indets(d,specfunc(anything,COLOR))[1];

                         /     [ 1 .. 16384 Vector[column] ]\
                         |     [ Data Type: float[8]       ]|
               c := COLOR|HUE, [ Storage: rectangular      ]|
                         \     [ Order: C_order            ]/

T:=display(torus([0,0,0],1,2,grid=[N,N]),
           style=surface,scaling=constrained,axes=none,
           glossiness=0.7,lightmodel=LIGHT3):
#op(T); # Only view the operands in full with Maple 16!

# The following commands both produce the banded torus.

#op(0,T)(MESH(op([1,1..-1],T),c),op([2..-1],T)); # alternate way, M16 only

subsop([1,1]=[op([1,1],T),c][],T);

Most of the examples in this post use the command `op` or `indets` extract or replace the various parts of of the strcutures. Perhaps in future there could be an easy mechanism to pass the COLOR() Array directly to the plotting commands, using their `color` optional parameter.

In the next example we'll use an image file that is bundled with Maple as example data, and we'll use it to cover a sphere. We won't downsize the image, so that it looks sharp and clear (but note that this may make your Standard GUI session act a bit sluggish). Because we're not scaling down the image we must specify a grid=[m,n] size in the plotting command that matches the dimensions of the image. We'll use ImageTools:-Preview as a convenient mechanism to produce both the color Array as well as a 3D densityplot so that we can view the original image. Note that the data portion of the sphere plot structure is an m-by-n-by-3 Array in a MESH() which matches the dimensions of the m-by-n-by-3 Array in the COLOR() portion of the result from ImageTools:-Preview.

restart:
with(ImageTools):with(plots):with(plottools):
im:=Read(cat(kernelopts(mapledir),"/data/images/tree.jpg")):

p:=Preview(im):

op(1,p);

                 /                    [ 235 x 354 2-D  Array ]  
                 |                    [ Data Type: float[8]  ]  
             GRID|0 .. 266, 0 .. 400, [ Storage: rectangular ], 
                 \                    [ Order: C_order       ]  

                    /     [ 235 x 354 x 3 3-D  Array ]\\
                    |     [ Data Type: float[8]      ]||
               COLOR|RGB, [ Storage: rectangular     ]||
                    \     [ Order: C_order           ]//

q:=plot3d(1, x=0..2*Pi, y=0..Pi, coords=spherical, style=surface,
          grid=[235,354]):

display(PLOT3D(MESH(op([1,1],q), op([1,4..-1],p)), op(2..-1,q)),
           orientation=[-120,30,160]);

Apart from the online description of this new Maple 16 feature here, there is also the help-page for subexpressionmenu.

I don't know of a complete listing of its current functionality, but the key thing is that it acts in context. By that I mean that the choice of displayed actions depends on the kind of subexpression that one has selected with the mouse cursor.

Apart from arithmetic operations, rearrangements and some normalizations of equations, and plot previews, one of the more interesting pieces of functionality is the various trigonometric substitutions. Some of the formulaic trig substitutions provide functionality that has otherwise been previously (I think) needed in Maple.

In Maple 16 it is now much easier to do some trigonometric identity solving, step by step.

Here is an example executed in a worksheet. (This was produced by merely selecting subexpressions of the output at each step, and waiting briefly for the new Smart Popup menus to appear automatically. I did not right-click and use the traditional context-sensitive menus. I did not have to type in any of the red input lines below: the GUI inserts them as a convenience, for reproduction. This is not a screen-grab movie, however, and doesn't visbily show my mouse cursor selections. See the 2D Math version further below for an alternate look and feel.)

The very first step above could also be done as a pair of simpler sin(x+y) reductions involving sin(2*a+a) and sin(a+a), depending on what one allows onself to use. There's room for improvement to this whole approach, but it looks like progress.

Download trigident1.mw

In a Document, rather than using 1D Maple notation in a Worksheet as above, the actions get documented in the more usual way, similar to context-menus, with annotated arrows between lines.

Download trigident2.mw

I am not quite sure what is the best way to try and get some of the trig handling in a more programmatic way, ie. by using the "names" of the various transformational formulas. But some experts here may discover such by examination of the code. Ie,

eval(SubexpressionMenu);

showstat(SubexpressionMenu::TrigHandler);

The above can leads to noticing the following (undocumented) difference, for example,

> trigsubs(sin(2*a));
              
                                 1       2 tan(a)
[-sin(-2 a), 2 sin(a) cos(a), --------, -----------,
                              csc(2 a)            2
                                        1 + tan(a)

    -1/2 I (exp(2 I a) - exp(-2 I a)), 2 sin(a) cos(a), 2 sin(a) cos(a)]

> trigsubs(sin(2*a),annotate=true);

["odd function" = -sin(-2 a), "double angle" = 2 sin(a) cos(a),

                               1                       2 tan(a)
    "reciprocal function" = --------, "Weierstrass" = -----------,
                            csc(2 a)                            2
                                                      1 + tan(a)

    "Euler" = -1/2 I (exp(2 I a) - exp(-2 I a)),

    "angle reduction" = 2 sin(a) cos(a),

    "full angle reduction" = 2 sin(a) cos(a)]

And that could lead one to try constructions such as,

> map(rhs,indets(trigsubs(sin(a),annotate=true),
>                identical("double angle")=anything));

                             {2 sin(a/2) cos(a/2)}

Since the `annotate=true` option for `trigsubs` is not documented in Maple 16 there is more potential here for useful functionality.