I was asked if I would put together a list of top resources to help students who are using Maple for the first time.  An awful lot of students will be cracking Maple open in the next few weeks (the ones who are keeping up with their assignments, at least – for others, it sometimes takes little longer :-), so it seemed like a good idea.

So then I had to decide what to do. I know Top N lists are very popular (Ten Things that Will Shock You about Your Math Software!), and there are tons of Maple training resources available to fill such a list without any difficulties.  But personally, I don’t always like Top N lists. What are the chances that there are exactly N things you need to know, for nice values of N? And how often you are really interested in all N items? I just want to get straight to the points I care about.

I decided I’d try a matrix. So here you go: a mini “choose your own adventure” guide for getting to know Maple.  Pick the row that corresponds to what you want to do, and the column for how you want to do it.  All on a single, page, and ad-free!

And best of luck for the new school year.

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra -2017" . It was a very interesting event. This fourth presentation, about "The FunctionAdvisor: extending information on mathematical functions with computer algebra algorithms", describes the FunctionAdvisor project at Maple, a project I started working during 1998, where the key idea I am trying to explore is that we do not need to collect a gazillion of formulas but just core blocks of mathematical information surrounded by clouds of algorithms able to derive extended information from them. In this sense this is also unique piece of software: it can derive properties for rather general algebraic expressions, not just well known tabulated functions. The examples illustrate the idea.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.
 

Download FunctionAdvisor.mw

Download FunctionAdvisor.pdf

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra - 2017" . It was a very interesting event. This second presentation, about "Differential algebra with mathematical functions, symbolic powers and anticommutative variables", describes a project I started working in 1997 and that is at the root of Maple's dsolve and pdsolve performance with systems of equations. It is a unique approach. Not yet emulated in any other computer algebra system.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.
 

Download DifferentialAlgebra.mw

Download DifferentialAlgebra.pdf

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

We have just released an update to Maple. Maple 2017.2 includes updated translations for Japanese, Traditional Chinese, Simplified Chinese, Brazilian Portuguese, French, and Spanish. It also contains improvements to the MapleCloud, physics, limits, and PDEs. This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2017.2 download page.

 Eithne

It appears google doesn't know about the haversine formula.  Huh?  Well at least google can't draw the proper path for it.  I typed in google "distance from Pyongyang to NewYork city"  and got 10,916km.  Ok that's fine but then it drew a map

The map path definitely did not look right.  Pulled out my globe traced a rough path of the one google showed and I got 13 inches (where 1 inch=660miles) -> 8580 miles = 13808 km .. clearly looks like google goofed. 

So we need Maple to show us the proper path.
 

with(DataSets):
with(Builtin):
m := WorldMap();
AddPath(m, [-74.0059, 40.7128], [125.7625, 39.0392]):
Display(m):

Ok so you say that really doesn't look like the shortest path.  Well, lets visualize that on the globe projection

Display(m, projection = Globe, orientation = [-180, 0, 0])

Ah, now it is clear
Pyonyang_to_NewYork.mw

Yahoo Finance recently discontinued their (largely undocumented) historical stock quote API.

Previously, you simply send a HTTP:-Get request like this…

…and get historical OHLCV (open, high, low, close, trading volume) data in your worksheet (in this case for AAPL between 1 January 2016 and 1 January 2017).

This no longer works! Yahoo shut the door on this easy-to-use and widely disseminated API.

You can still download historical stock quotes from Yahoo Finance into Maple, but the process is now somewhat more involved. My complete code in this worksheet but I'll step through the process below.

If you visit the updated Yahoo Finance website and download historical data for a ticker, you see a URL like this in the status bar of your browser

Let's examine how ths URL is constructed.

• period1 and period2 are Unix time stamps for your start and end date
• interval is the data retrieval interval (this can be either 1d, 1w or 1m)
• crumb is an alphanumeric code that’s periodically regenerated every time you download new historical data from from the Yahoo Finance website using your browser. Moreover, crumb is paired with a cookie that’s stored by your browser.

Here’s how to extract and supply the cookie-crumb pair to Yahoo Finance so you can still use Maple to retrieve historical stock quotes

Send a dummy request to get a cookie-crumb pair

Grab the crumb from the response

Store the cookie from the response

Construct the URL

• Your desired start and end dates have to be defined as Unix time stamps. Converting a human readable date (like 1^st January 2017) to a Unix timestamp is simple, so I won't cover it here.
• The previously retrieved crumb has to be added to the URL.

Send the request to Yahoo Finance, including the cookie in the header

Your historical data is now returned

The historical data is now easily parsed into a matrix.

Please note that any use of Yahoo Finance has to be consistent with their terms of service.

We have just released the 3rd edition of the Mathematics Survival Kit – Maple Edition.

The Math Survival Kit helps students get unstuck when they are stuck. Sometimes students are prevented from solving a problem, not because they haven’t understood the new concept, but because they forget how to do one of the steps, like completely the square, or dealing with log properties.  That’s where this interactive e- book comes in. It gives students the opportunity to review exactly the concept or technique they are stuck on, work through an example, practice as much (or as little) as they want using randomly generated, automatically graded questions on that exact topic, and then continue with their homework.

This book covers over 150 topics known to cause students grief, from dividing fractions to integration by parts. This 3^rd edition contains 31 additional topics, deepening the coverage of mathematical topics at every level, from pre-high school to university.

See the Mathematics Survival Kit for more information about this updated e-book, including the complete list of topics.

eithne

This post is the answer to this question.

The procedure named  IntOverDomain  finds a double integral over an arbitrary domain bounded by a non-selfintersecting piecewise smooth curve. The code of the procedure uses the well-known Green's theorem.

Each section in the border should be specified by a list in the following formats :    
1. If a section is given parametrically, then  [[f(t), g(t)], t=t1..t2]    
2. If several consecutive sections of the border or the entire border is a broken line, then it is sufficient to set vertices of this broken line  [ [x1,y1], [x2,y2], .., [xn,yn] ] (for the entire border should be  [xn,yn]=[x1,y1] ).

Required parameters of the procedure:  f  is an expression in variables  x  and  y , L  is the list of all the sections. The sublists of the list  L  must follow in the positive direction (counterclockwise).

The code of the procedure:

restart;
IntOverDomain := proc(f, L) 
local n, i, j, m, yk, yb, xk, xb, Q, p, P, var;
n:=nops(L);
Q:=int(f,x);  
for i from 1 to n do 
if type(L[i], listlist(algebraic)) then
m:=nops(L[i]);
for j from 1 to m-1 do
yk:=L[i,j+1,2]-L[i,j,2]; yb:=L[i,j,2];
xk:=L[i,j+1,1]-L[i,j,1]; xb:=L[i,j,1];
p[j]:=int(eval(Q*yk,[y=yk*t+yb,x=xk*t+xb]),t=0..1);
od;
P[i]:=add(p[j],j=1..m-1) else
var := lhs(L[i, 2]);
P[i]:=int(eval(Q*diff(L[i,1,2],var),[x=L[i,1,1],y=L[i,1,2]]),L[i,2]) fi;
od; 
add(P[i], i = 1 .. n); 
end proc:

Examples of use.

1. In the first example, we integrate over a quadrilateral:

with(plottools): with(plots):
f:=x^2+y^2:
display(polygon([[0,0],[3,0],[0,3],[1,1]], color="LightBlue"));  # Visualization of the domain of integration
IntOverDomain(x^2+y^2, [[[0,0],[3,0],[0,3],[1,1],[0,0]]]);  # The value of integral

2. In the second example, some sections of the boundary of the domain are curved lines:

display(inequal({{y<=sqrt(x),y>=sin(Pi*x/3)/2,y<=3-x}, {y>=-2*x+3,y>=sqrt(x),y<=3-x}}, x=0..3,y=0..3, color="LightGreen", nolines), plot([[t,sqrt(t),t=0..1],[t,-2*t+3,t=0..1],[t,3-t,t=0..3],[t,sin(Pi*t/3)/2,t=0..3]], color=black, thickness=2));
f:=x^2+y^2: L:=[[[t,sin(Pi*t/3)/2],t=0..3],[[3,0],[0,3],[1,1]], [[t,sqrt(t)],t=1..0]]:
IntOverDomain(f, L);

3. If  f=1  then the procedure returns the area of the domain:

IntOverDomain(1, L);  # The area of the above domain
evalf(%);

IntOverDomain.mw

Edit.

Do you have Maple content that you want to protect from editing and viewing, while still allowing others to execute the code within and obtain results? In Maple, worksheets can be password protected so the users of your Maple application can benefit from the specialized routines you've created while the details remain hidden.

The password protection feature can be useful for a variety of situations, such as:

• • Providing a Maple-based solution while protecting the intellectual property embodied in your algorithms
• • Ensuring the users of your application can not accidentally make changes that break your code

To learn more about this feature in Maple, you can download the free Tips & Techniques from the Application Center.

We have just released an update to Maple, Maple 2017.1.  It includes improvements to the display on high resolution monitors for the debugger, MapleCloud, and help system table of contents. It also contains a variety of small improvements to the math engine, including in limit, series, Physics, typesetting, and PackageTools. This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2017.1 download page.

eithne

Download PhysicsMaple2017.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

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.
 

Let us consider the help to RectangleWindow SignalProcessing-RectangleWindow.pdf SignalProcessing-RectangleWindow.mw.
Let us execute the example, taking N:=4 (in order to display the outputs).

with(SignalProcessing):
N := 4;
a := GenerateUniform(N, -1, 1);
         Matrix(1, 4, [[.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156]])         
RectangleWindow(a);
         Vector[row](4, [.396167882718146, -.826878267806025, -0.908376742154361e-2, .324899681378156])      
c := Array(1 .. N, 'datatype' = 'float'[8], 'order' = 'C_order'):
RectangleWindow(Array(1 .. N, 'fill' = 1, 'datatype' = 'float'[8], 'order' = 'C_order'), 'container' = c);
              Vector[row](4, [1., 1., 1., 1.])
u := `~`[log](FFT(c)):
plots:-display(Array([plots:-listplot(Re(u)), plots:-listplot(Im(u))]));

We see an uncommented code which (intentionally or unintentionally) produces two empty plots.
The questions arise:

• What is the aim of the RectangleWindow command which does nothing 
  but the conversion of a Matrix(1,N,...) /Array(1..N,...) to a Vector[row](N,...)? 
• Could such help be called friendly to Maple users?

There are many questions to Maplesoft and there are no answers from them: strategic silence.
RectangleWindow.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.

Let us consider the linear integer programming problem:

A := Matrix([[1, 7, 1, 3], [1, 6, 4, 6], [17, 1, 5, 1], [1, 6, 10, 4]]):
 n := 4; z := add(add(A[i, j]*x[i, j], j = 1 .. n), i = 1 .. n):
restr := {seq(add(x[i, j], i = 1 .. n) = 1, j = 1 .. n), seq(add(x[i, j], j = 1 .. n) = 1, i = 1 .. n)}:
 sol := Optimization[LPSolve](z, restr, assume = binary);

Error, (in Optimization:-LPSolve) no feasible integer point found; 
use feasibilitytolerance option to adjust tolerance

sol1 := Optimization[LPSolve](z, restr, assume = binary, feasibilitytolerance = 100, integertolerance = 1);

Error, (in Optimization:-LPSolve) no feasible integer point found;
 use feasibilitytolerance option to adjust tolerance

That was OK in Maple 16, outputting

.

The bug in one of the principal Maple commands lasts since Maple 2015, where the above code causes "Kernel connection has been lost". The SCRs about it were submitted three times (see http://www.mapleprimes.com/questions/204750-Bug-In-LPSolve-In-Maple-20151).