Ukaine-2012. External independent evaluation. A trial version in Maple, by Maple.
HTML, Java-Interactive:
http://webmath.exponenta.ru/zno_11/ranok/z.html
Maple:2012_ranok_ru_bez.mw

I was trying to put together a series of plots that each included multiple dataseries.  I wanted to color them to help distinguish the various curves.  When I went into Maple's help page for the "colornames" that Maple recognizes, I was surprised to find that there were no color swatches to help you pick what color you wanted to use.  So I copied the color names from the help into a worksheet and told it to plot some color swatches for me. Here is the result:

MapleColors.mw 

Note that the fixed width web page is cutting off two columns of colors.  Click the image to see the whole set of colors.

Check this:

111.mw

Don't forget set Plot0 component manipulator to "Click and Drag" to test "on click" event. Localizing of problem takes for me ~4 days. It's terrible!

---------for stupid tags

global

The directional derivative of a scalar function , computed in the direction u in Cartesian coordinates, is defined by

Suppose that you wish to animate the whole view of a plot. By whole view, I mean that it includes the axes and is not just a rotation of a plotted object such as a surface.

One simple way to do this is to call plots:-animate (or plots:-display on a list of plots supplied in a list, with its `insequence=true` option). The option `orientation` would contain the parameter that governs the animation (or generates the sequence).

But that entails recreating the same plot each time. The plot data might not even change. The key thing that changes is the ORIENTATION() descriptor within each 3d plot object in the reulting data structure. So this is inefficient in two key ways, in the worst case scenario.

1) It may even compute the plot's numeric results, as many times as there are frames in the resulting animation.

2) It stores as many instances of the grid of computed numeric data as there are frames.

We'd like to do better, if possible, reducing down to a single computation of the data, and a single instance of storage of a grid of data.

To keep this understandable, I'll consider the simple case of plotting a single 3d surface. More complicated cases can be handled with revisions to the techniques.

Avoiding problem 1) can be done in more than one way. Instead of plotting an expression, a procedure could be plotted, where that procedure has `option remember` so that it automatically stores computed results an immediately returns precomputed stored result when the arguments (x and y values) have been used already.

Another way to avoid problem 1) is to generate the unrotated plot once, and then to use plottools:-rotate to generate the other grids without necessitating recomputation of the surface. But this rotates only objects in the plot, and does alter the view of the axes.

But both 1) and 2) can be solved together by simply re-using the grid of computed data from an initial plot3d call, and then constructing each frame's plot data structure component "manually". The only thing that has to change, in each, is the ORIENTATION(...) subobject.

At 300 frames, the difference in the following example (Intel i7, Windows 7 Pro 64bit, Maple 15.01) is a 10-fold speedup and a seven-fold reduction is memory allocation, for the creation of the animation structure. I'm not inlining all the plots into this post, as they all look the same.

restart:
P:=1+x+1*x^2-1*y+1*y^2+1*x*y:

st,ba:=time(),kernelopts(bytesalloc):

plots:-animate(plot3d,[P,x=-5..5,y=-5..5,orientation=[A,45,45],
                       axes=normal,labels=[x,y,z]],
               A=0..360,frames=300);

time()-st,kernelopts(bytesalloc)-ba;

                                1.217, 25685408

restart:
P:=1+x+1*x^2-1*y+1*y^2+1*x*y:

st,ba:=time(),kernelopts(bytesalloc):

g:=plot3d(P,x=-5..5,y=-5..5,orientation=[-47,666,-47],
          axes=normal,labels=[x,y,z]):

plots:-display([seq(PLOT3D(GRID(op([1,1..2],g),op([1,3],g)),
                           remove(type,[op(g)],
                                  specfunc(anything,{GRID,ORIENTATION}))[],
                           ORIENTATION(A,45,45)),
                    A=0..360,360.0/300)],
               insequence=true);

time()-st,kernelopts(bytesalloc)-ba;

                                0.125, 3538296

By creating the entire animation data structure manually, we can get a further factor of 3 improvement in speed and a further factor of 3 reduction in memory allocation.

restart:
P:=1+x+1*x^2-1*y+1*y^2+1*x*y:

st,ba:=time(),kernelopts(bytesalloc):

g:=plot3d(P,x=-5..5,y=-5..5,orientation=[-47,666,-47],
          axes=normal,labels=[x,y,z]):

PLOT3D(ANIMATE(seq([GRID(op([1,1..2],g),op([1,3],g)),
                           remove(type,[op(g)],
                                  specfunc(anything,{GRID,ORIENTATION}))[],
                           ORIENTATION(A,45,45)],
                    A=0..360,360.0/300)));

time()-st,kernelopts(bytesalloc)-ba;

                                0.046, 1179432                            

Unfortunately, control over the orientation is missing from Plot Components, otherwise such an "animation" could be programmed into a Button. That might be a nice functionality improvement, although it wouldn't be very nice unless accompanied by a way to export all a Plot Component's views to GIF (or mpeg!).

The above example produces animations each of 300 frames. Here's a 60-frame version:

The cost of some mathematical sites (estimated bizinformation.org):
 8.000.000 $ - wolfram.com
   372.456 $ - webmath.exponenta.ru (Russian Maple in education)
   292.301 $ - maplesoft.com

    82.342 $ - exponenta.ru
    61.278 $ - webmath.ru
    54.895 $ - math.ege
    43.302 $ - univ.kiev.ua (Kiev National University)

Problems concerning integration have been discussed on  maple primes  before with piecewise continuous antiderivatives explaining  difficulties. Here an example is given using Maple 15 where a continuous antiderivative is returned but definite integration fails to give the correct answer.

Integration_anomal.mw

In case if you like notepad++  under windows, and still didn't do smth like that then this is for you .userDefineLang.zip

Unpack to notepad++ folder. In case if you already had had other
own language then just copy "Maple language" section.

I have below outlined the different probabilities for different poker hands given
5 cards from a 52 cards deck. The frequencies are from wikipedia
http://en.wikipedia.org/wiki/Poker_probability

These frequencies are quite interesting....I wonder if they found them by "brute fource"

I have contributed another application to the Application Center: "Street-fighting Math".
This interactive Maple document contains a simple street-fighting game and performs a
mathematical analysis of it, involving probability and game theory. 

Download Jan72012.mw

A recent Tips and Techniques article in the Maple Reporter contained the following five "gems" from my Red Book of Maple Magic. These 'gems' are tricks and techniques for Maple that I've discovered in my years here at Maplesoft. The previous 15 gems have appeared in three other issues of the Reporter, as...

index.mw

Higher Mathematics for external students of  biological faculty.
Solver-practicum.
1st semester.
300 problems (15 labs in 20 variants).
mw.zip

Before use - Shake!
(Click on the button and activate the program and Maplet).

One of the challenges in Linear Algebra is in developing problems, projects, and exercises that are both larger dimensional and student-accessible. Indeed, round-off error, computational complexity, difficulty factoring characteristic polynomials of degree 3 or higher, and similar aspects often mean that any problems or applications of rank 3 or higher are approached solely via technology. 

However, that same technology can be used to create...