I've developed a framework in Maple for playing with cyclic division algebras. I have methods for multiplication and passing to and from:

The standard basis over the base field in terms of x^i*y^j and:
The standard matrix basis for the central simple algebra when taking coefficients in the splitting field.

I have it done in the case of degree 7, but could generalise it to any prime degree if this is of use to anyone.

We just posted a submission to the Maple Application Center that I thought people might be interested in. Mathematics for Chemistry isn't a typical application - it's an e-book, written in Maple by J.F. Ogilvie. It covers both standard mathematics topics chemistry students are expected to know,  such as calculus and linear algebra, as well as chemistry-specific topics like chemical equilbrium, quantum chemistry, and nuclear-magnetic-resonance spectra.

There's lots of interesting content on the Application Center, and the range of topics is always fascinating, but it's not every day I see an entire e-book come across my desk(top)!

If you are interested, you can find it on the Application Center, here: Mathematics for Chemistry

eithne

While preparing for a recent webinar, I ran across something that didn't behave the same way in Maple 2017 as it did in previous releases. In particular, it was the failure of the over-dot notation for t-derivatives to display with the over-dot. Turns out that this is due to a change in behavior of typesetting that was detailed in the What's New page for Maple 2017, a page I had looked at many times in the last few months, but apparently didn't comprehend fully. The details are below.

Prior to Maple 2017, under the aegis of extended typesetting, the following two lines of code would alert Maple that the over-dot notation for t-derivatives should be used in the output display.

However, this changed in Maple 2017. Extended typesetting is now the default, but these two lines of code are no longer sufficient to induce Maple to display the over-dot in output. Indeed, we would now have

as output. The change is documented in the following paragraph

lifted from the help page 

Thus, it now takes the additional command

to induce Maple to display the over-dot notation in output.

I must confess that, even though I pored over the "What's New" pages for Maple 2017, I completely missed the import of this change to typesetting. I stumbled over the issue while preparing for an upcoming webinar, and frantically sent out help calls to the developers back in the building. Fortunately, I was quickly set straight on the matter, but was disappointed in my own reading of all the implications of the typesetting changes in Maple 2017. So perhaps this note will alert other users to the changes, and to the help page wherein one finds those essential bits of information needed to complete the tasks we set for ourselves.

And one more thing - I was cautioned that the "= true" was essential. Without it, the command would act as a query, echoing the present state of the setting, and not making the desired change to the setting.
 

A question was raised recently on Stewart Gough platforms.  I decided to tidy up some old code to show platform position and leg lengths for any given displacement.
 

Download Reverse_Kinematics_Stewart_Gough_Platform.mw

With this application the components of the acceleration can be calculated. The components of the acceleration in scalar and vector of the tangent and the normal. In addition to the curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanics, civilians and more.

In Spanish.

Kinematics_Curvilinear v18.mw

Kinematics_Curvilinear_updated_v2017.mw

Cinemática_en_Coordenadas_Polares_Cilindricas.mw

Kinematics_Curvilinear_updated_v2018.mw

Cinemática_de_una_partícula_nueva_sintaxis.mw

Lenin Araujo Castillo

Ambassador of Maple

Maple 2017 has launched!

Maple 2017 is the result of hard work by an enthusiastic team of developers and mathematicians.

As ever, we’re guided by you, our users. Many of the new features are of a result of your feedback, while others are passion projects that we feel you will find value in.

Here’s a few of my favourite enhancements. There’s far more that’s new - see What’s New in Maple 2017 to learn more.

MapleCloud Package Manager

Since it was first introduced in Maple 14, the MapleCloud has made thousands of Maple documents and interactive applications available through a web interface.

Maple 2017 completely refreshes the MapleCloud experience. Allied with a new, crisp, interface, you can now download and install user-created packages.

Simply open the MapleCloud interface from within Maple, and a mouse click later, you see a list of user-created packages, continuously updated via the Internet. Two clicks later, you’ve downloaded and installed a package.

This completely bypasses the traditional process of searching for and downloading a package, copying to the right folder, and then modifying libname in Maple. That was a laborious process, and, unless I was motivated, stopped me from installing packages.

The MapleCloud hosts a growing number of packages.

Many regular visitors to MaplePrimes are already familiar with Sergey Moiseev’s DirectSearch package for optimization, equation solving and curve fitting.

My fellow product manager, @DSkoog has written a package for grouping data into similar clusters (called ClusterAnalysis on the Package Manager)

Here’s a sample from a package I hacked together for downloading maps images using the Google Maps API (it’s called Google Maps and Geocoding on the Package Manager).

You’ll also find user-developed packages for exploring AES-based encryption, orthogonal series expansions, building Maple shell scripts and more.

Simply by making the process of finding and installing packages trivially easy, we’ve opened up a new world of functionality to users.

Maple 2017 also offers a simple method for package authors to upload workbook-based packages to the MapleCloud.

We’re engaging with many package authors to add to the growing list of packages on the MapleCloud. We’d be interested in seeing your packages, too!

Advanced Math

We’re committed to continually improving the core symbolic math routines. Here area few examples of what to expect in Maple 2017.

Resulting from enhancements to the Risch algorithm, Maple 2017 now computes symbolic integrals that were previously intractable

Groeber:-Basis uses a new implementation of the FGLM algorithm. The example below runs about 200 times faster in Maple 2017.

gcdex now uses a sparse primitive polynomial remainder sequence together.  For sparse structured problems the new routine is orders of magnitude faster. The example below was previously intractable.

The asympt and limit commands can now handle asymptotic cases of the incomplete Γ function where both arguments tend to infinity and their quotient remains finite.

Among several improvements in mathematical functions, you can now calculate and manipulate the four multi-parameter Appell functions.

Appel functions are of increasing importance in quantum mechanics, molecular physics, and general relativity.

pdsolve has seen many enhancements. For example, you can tell Maple that a dependent variable is bounded. This has the potential of simplifying the form of a solution.

Plot Builder

Plotting is probably the most common application of Maple, and for many years, you’ve been able to create these plots without using commands, if you want to.  Now, the re-designed interactive Plot Builder makes this process easier and better.

When invoked by a context menu or command on an expression or function, a panel slides out from the right-hand side of the interface.

Generating and customizing plots takes a single mouse click. You alter plot types, change formatting options on the fly and more.

To help you better learn Maple syntax, you can also display the actual plot command.

Password Protected Content

You can distribute password-protected executable content. This feature uses the workbook file format introduced with Maple 2016.

You can lock down any worksheet in a Workbook. But from any other worksheet, you can send (author-specified) parameters into the locked worksheet, and extract (author-specified) results.

Plot Annotations

You can now get information to pop up when you hover over a point or a curve on a plot.

In this application, you see the location and magnitude of an earthquake when you hover over a point

Here’s a ternary diagram of the color of gold-silver-copper alloys. If you let your mouse hover over the points, you see the composition of the points

Plot annotations may seem like a small feature, but they add an extra layer of depth to your visualizations. I’ve started using them all the time!

Engineering Portal

In my experience, if you ask an engineer how they prefer to learn, the vast majority of them will say “show me an example”. The significantly updated Maple Portal for Engineers does just that, incorporating many more examples and sample applications.  In fact, it has a whole new Application Gallery containing dozens of applications that solve concrete problems from different branches of engineering while illustrating important Maple techniques.

Designed as a starting point for engineers using Maple, the Portal also includes information on math and programming, interface features for managing your projects, data analysis and visualization tools, working with physical and scientific data, and a variety of specialized topics.

Geographic Data

You can now generate and customize world maps. This for example, is a choropleth of European fertility rates (lighter colors indicate lower fertility rates)

You can plot great circles that show the shortest path between two locations, show varying levels of detail on the map, and even experiment with map projections.

A new geographic database contains over one million locations, cross-referenced with their longitude, latitude, political designation and population.

The database is tightly linked to the mapping tools. Here, we ask Maple to plot the location of country capitals with a population of greater than 8 million and a longitude lower than 30.

There’s much more to Maple 2017. It’s a deep, rich release that has something for everyone.

Visit What’s New in Maple 2017 to learn more.

This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. I hope you use something that is fully developed with embedded components.

In Spanish

Vector_Force.mw

Vector_Force_updated.mw

Lenin Araujo Castillo

Ambassador Of Maple

Let us consider 

sol := pdsolve({diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) = (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t}, {u(0, t) = 0, u(x, 0) = 0, v(0, t) = 0, v(x, 0) = 0}, time = t, numeric, timestep = 0.1e-1, spacestep = 0.1e-1, range = 0 .. 1); 
sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 .. 1);

A nice plot similar to the one produced by Mma (see the  attached pdf file pdesystem.pdf) is expected. 
The exact solutions u(x,t)=x*t,v(x,t)=x*t^2 are known

pdetest({u(x, t) = x*t, v(x, t) = x*t^2}, {diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) =
(1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t});
                              {0}

But the wrong result

               module() ... end module         
Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.26000000000000006):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

is obtained. Also 

sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 ..0.1);

The plot 

sol:-plot3d(v(x, t), x = 0 .. .5, t = 0 .. .1);

is not better.

Here is a problem from SEEMOUS 2017 (South Eastern European Mathematical Olympiad for University Students)
which Maple can solve (with a little help).

For k a fixed nonnegative integer, compute:

Sum( binomial(i,k) * ( exp(1) - Sum(1/j!, j=0..i) ), i=k..infinity );

(It is the last one, theoretically the most difficult.)

Application that allows us to measure the reliability of a group of data through a row and columns called cronbach alpha at the same time to measure the correlation of items through the pearson correlation of even and odd items. It can run on maple 18 to maple 2017. This will be useful when we are developing a thesis in the statistical part.

In Spanish

StatisticsSocialCronbachPearson.zip

Lenin Araujo Castillo

Ambassador of Maple

Here's a little procedure to fish out data from the Simbad database.  Some star names may not work if the page Simbad brings up is not completely filled, but it should work for most queries.

Download star_database_-_simbad.mw

I found this http://www.atlasoftheuniverse.com/50lys.html and wondered how to do it in Maple. With a bit of data file editing I came up with this.  All stars within 50 light years that are visible to the naked eye.

The modified data file and the maple worksheet below

stars3.txt

Download Stars50LY.mw

Sudoku is a well known Latin square type game, see https://en.wikipedia.org/wiki/Sudoku

Here is a Sudoku game and its (unique) solution:

A,Sol:=  # A = Sudoku matrix, 0 for each empty cell
Matrix(9, [
[0,0,3,0,9,0,1,0,0],
[0,5,0,3,0,0,7,0,0],
[1,0,2,0,0,5,0,6,4],
[0,1,0,0,2,0,9,0,0],
[2,0,0,6,0,3,0,0,1],
[0,0,7,0,8,0,0,3,0],
[7,6,0,9,0,0,8,0,5],
[0,0,8,0,0,7,0,9,0],
[0,0,4,0,6,0,2,0,0]]),
Matrix(9, [
[4,7,3,2,9,6,1,5,8],
[8,5,6,3,4,1,7,2,9],
[1,9,2,8,7,5,3,6,4],
[3,1,5,7,2,4,9,8,6],
[2,8,9,6,5,3,4,7,1],
[6,4,7,1,8,9,5,3,2],
[7,6,1,9,3,2,8,4,5],
[5,2,8,4,1,7,6,9,3],
[9,3,4,5,6,8,2,1,7]]);

The procedure which follows is a very compact Sudoku solver. It uses Groebner bases. I hope that you will like it.
The input is the Sudoku matrix and the solution matrix is returned.
Note that the Sudoku matrix must be valid and must have a unique solution.
(Otherwise, theoretically, the error "Invalid Sudoku matrix" should appear.)
Note also that the procedure may be very slow for some games or Maple may crash. This happened to me once with a very "hard" matrix.

I was impressed that Maple's implementation for Groebner bases works now so well for this problem!

A few years ago on this site: http://www.mapleprimes.com/questions/131939-Calculating-Groebner-Basis-For-Sudoku
it was an attempt to solve the problem with this method but it failed (due to wrong number of polynomials).

sudoku:=proc(A::'Matrix'(9,integer))
local x_A,x,Q,R,r, i,j,u,v,G;
Q:=proc(X,Y) normal((mul(X-i,i=1..9)-mul(Y-i,i=1..9))/(X-Y)) end;
x_A:=seq(seq( `if`(A[i,j]>0,x[i,j]-A[i,j],NULL),i=1..9),j=1..9);
R:={seq({seq(x[i,j],j=1..9)},i=1..9), seq({seq(x[i,j],i=1..9)},j=1..9),
    seq(seq({seq(seq(x[3*u+i,3*v+j],i=1..3),j=1..3)},u=0..2),v=0..2)};
G:=Groebner:-Basis({seq(seq(seq(Q(u,v),u=r minus {v}),v=r),r=R),x_A},'_vv');
if nops(G)<>81 then error "Invalid Sudoku matrix" fi;
eval(Matrix(9,symbol=x), `union`(map(u->solve({u}), G)[]));
end:

sudoku(A) < A; # Solving the previous game

# Let's solve another one:
A:=Matrix(9,9,[[0,0,0,4,0,0,0,8,0],[0,5,2,7,0,0,4,0,0],[3,0,0,0,0,0,0,0,0],[5,1,0,8,0,0,0,0,0],[0,0,0,5,0,0,6,7,0],[0,9,0,0,7,0,0,0,3],[2,4,0,0,0,5,0,0,0],[9,0,0,0,0,0,0,3,8],[0,0,0,0,0,0,9,4,0]]):
sudoku(A) < A;

Matrix   # A Sudoku matrix which crashes Maple!
(9,[[8,0,0,0,0,0,0,0,0],[0,0,3,6,0,0,0,0,0],[0,7,0,0,9,0,2,0,0],[0,5,0,0,0,7,0,0,0],[0,0,0,0,4,5,7,0,0],[0,0,0,1,0,0,0,3,0],[0,0,1,0,0,0,0,6,8],[0,0,8,5,0,0,0,1,0],[0,9,0,0,0,0,4,0,0]]):

The distance from the point to the surface easily calculated using the NLPSolve of Optimization package. If the point is not special, we will find for it a point on the surface, the distance between these two points is the shortest between the selected point and the surface.
Two examples:  the implicit surface and the parametric surface.
To test, we restore the normals from the  calculated  points (red) by using analytical equations.
DISTANCE_TO_SURFACE.mw

In the creation of this animation the technique from here  was used.

The code of this animation:

with(plots): with(plottools):
SmallHeart:=plot([1/20*sin(t)^3, 1/20*(13*cos(t)/16-5*cos(2*t)/16-2*cos(3*t)/16-cos(4*t)/16), t = 0 .. 2*Pi], color = "Red", thickness=3, filled):
F:=t->[sin(t)^3, 13*cos(t)/16-5*cos(2*t)/16-2*cos(3*t)/16-cos(4*t)/16]:
Gf:=display(translate(SmallHeart, 0,0.37)):
Gl:=display(translate(SmallHeart, 0,-1)):
G:=t->display(translate(SmallHeart, F(t)[])):
A:=display(seq(display(op([Gf,seq(G(-Pi/20*t), t=3..k),seq(G(Pi/20*t), t=3..k)]))$4,k=2..17),display(op([Gf,seq(G(-Pi/20*t), t=3..17),seq(G(Pi/20*t), t=3..17),Gl]))$30, insequence=true, size=[600,600]):
B:=animate(textplot,[[-0.6,0.25, "Happy"[1..round(n)]],color="Orange", font=[times,bolditalic,40], align=right],n=0..5,frames=18, paraminfo=false):
C:=animate(textplot,[[-0.2,0, "Valentine's"[1..round(n)]],color=green, font=[times,bolditalic,40], align=right],n=1..11,frames=35, paraminfo=false):
E:=animate(textplot,[[-0.3,-0.25, "Day!"[1..round(n)]],color="Blue", font=[times,bolditalic,40], align=right],n=1..4,frames=41, paraminfo=false):
T:=display([B, display(op([1,-1,1],B),C), display(op([1,-1,1],B),op([1,-1,1],C),E)], insequence=true):
K:=display(A, T, axes=none):
K;

The last frame of this animation:

display(op([1,-1],K), size=[600,600], axes=none);  # The last frame

ValentinelDay.mw
 

Edit. The code was edited - the number of frames has been increased.