I have run into a problem with a file I am preparing for a class. The file is in Document mode with one large section and a number of subsections. Input is 2-d input.

The first subsection behaves normally, input is there, output is there and so on.

The second section does not display the input. The input is still there, somewhere, as the sheet recalculates properly and I can also see there is input when looking at the file with an editor. But no show in Maple.

The third subsection does not show input either.

The fourth subsection is normal again and shows input.

Each of these sections is several screens long. The file actually is an older one where I am adding subsections. The first one (that works normal) is a new one. The original file (before I edited it to add a subsection) works fine still.

So I assume I inadvertently did something that causes this, even though the old subsections are not being edited. I do load Physics[Vectors] but cannot believe that does it. The original file also loads it.

The file was created in Maple 15 and that is where I edited this one. I opened it in Maple 2015 on a different computer, but the behaviour is identical.

Again, the input is there somewhere; the sheet recalculates corrrectly, but I cannot edit the input in the sections that do not show it (I guess that is not a surprise, but it excludes things like a white font color on a white background as there is nothing to select).

Does anyone have a hint how to unhide the input? I tried many things (menu, contextual menu, prefs,...) but no help. It is actually kind-of annoying.

FWIW, this is on Mac OS X, 10.10.5 Yosemite for Maple 2015.1. And 10.5.8 for Maple 15.

Thanks,

M.D.

I have a polynomial expression that I would like to cast into a specific form. The expression is

and I know that it can be simplified into a form involving squares of (A[Qi]-Pi). It is trivial to do this on paper; how can I convince Maple to do this.

The solution I came up with was to use mtaylor and expand about the forms I know to be there:

mtaylor((3),[A[Q1]=P1,A[0]=P2*rho/(rho+Q1),A[Q3]=P3],6);

which is what I want (close to, anyway). Now, I consider this to be a bit of a dirty trick that works here as the expression is simple and no higher-order terms are present so in fact the solution is exact. But, are there methods along simplify and friends that can do this? I have not been successfull with those...

This is a part of a much longer worksheet and part of a lecture, so I need Maple to be able to do this. The mtaylor trick works, but I would not want to miss an obvious approach that may work where mtaylor would get confused.

Thanks,

M.D.

test.mw

I'd like to pay attention to an article J, B. van den Berg and J.-P. Lessard, Notices of the AMS, October 2015, p. 1057-1063.  We know numerous  applications of CASes to algebra. The authors present such  applications to dynamics. It would be interesting and useful to obtain  opinions of Maple experts on this topic.

Here is its introduction:

"Nonlinear dynamics shape the world around us, from the harmonious movements of celestial bod-
ies,  via  the  swirling  motions  in  fluid  flows,  to the  complicated  biochemistry  in  the  living  cell.
Mathematically  these  beautiful  phenomena  are modeled by nonlinear dynamical systems, mainly
in  the  form  of  ordinary  differential  equations (ODEs), partial differential equations (PDEs) and
delay differential equations (DDEs). The presence of nonlinearities severely complicates the mathe-
matical analysis of these dynamical systems, and the difficulties are even greater for PDEs and DDEs,
which are naturally defined on infinite-dimensional function spaces. With the availability of powerful
computers and sophisticated software, numerical simulations have quickly become the primary tool
to study the models. However, while the pace of progress increases, one may ask: just how reliable
are our computations? Even for finite-dimensional ODEs, this question naturally arises if the system
under  study  is  chaotic,  as  small  differences  in initial conditions (such as those due to rounding
errors  in  numerical  computations)  yield  wildly diverging outcomes. These issues have motivated
the development of the field of rigorous numerics in dynamics"

hi guys,

i have a first order differential equation and i want to plot it with odeplot in polar coordinates .

thanks in advance1.mw

As the year draws to a close, we start looking forward to a new year and a new release of Maple. With every new release comes many new features and updates to explore.

We are looking for several new beta testers with a good working knowledge of Maple; We need your input, your ideas, and your experience with our products to help us improve the software and get it ready for general release.

There are many benefits to becoming a beta tester:

• You’ll get to use the new software before anyone else does.
• You’ll help us make our software better in ways that work for you.
• Your suggestions could determine the future direction of the software.
• You’ll get feedback right from the development team.

If you are interested in becoming a beta tester for the next version of Maple, please email: beta (at) maplesoft.com for more information.

Dear all,

I am trying to solve a differential equation like the one below:

f := y(x)+5*(diff(y(x), x))+2*x^3*(eval(diff(y(x), x), x = 0))+3*y(0)

however, because of having y(0) in the quation, I get the error below:

Error, (in dsolve) found the indeterminate function y with different arguments {y(0), y(x)}

does anyone know how I could solve this?

Suppose that I have the equation x=1. I want to manipluate it. For example, I want to multiply by 2. Then, Take the power of two. Next, take a cubic root. How can I do this in Maple?

Qu_in_maple.mw

How to compute the  n component of U[i] even to reach the exact solution?

Download Qu_in_maple.mwQu_in_maple.mw

How to find the  n component of U[i] even to reach the Exact solution cos(x)

I am trying to solve 4 nonlinear equations for four variables using fsolve  and the output that i am getting is basically the same equations repeated after some time.  I even tried reducing one of the equations using assumptions from my side but it results in same behaviour..  Quite new to maple, would like some advice as to this behaviour. Thanks

 Here's the file

fsolve_1.mw

PS- using do loop is part of the solving so i cannot remove that

I am not seeing any reference in help to TRDPolynomial_ring in PolynomialRing function in RegularChains. Though if I debug it, I can get in it. Is it that it is part of kernel ?

Hi all

I need to convert int matrix into matrix over finite field.

E.g: Convert inform integer number

      A := <140, 155, 162, 64;

               218, 12, 245, 50;

                36, 251, 34, 253;

                171, 251, 184, 37>;

 into B = <x^7+x^3+x^2,x^7+x^4+x^3+x+1,x^7+x^5+x, x^6;

             x^7+x^6+x^4+x^3+x, x^3+x^2, x^7+x^6+x^5+x^4+x^2+1, x^5+x^4+x;

            x^5+x^2, x^7+x^6+x^5+x^4+x^3+x+1, x^5+x, x^7+x^6+x^5+x^4+x^3+x^2+1;

            x^7+x^5+x^3+x+1, x^7+x^6+x^5+x^4+x^3+x+1, x^7+x^5+x^4+x^3, x^5+x^2+1>;

(Matrix B over finite field GF(2^8)/f(x) =x^8 + x^6 +x^5 +x^3 +1) 

Thanks alot.

Dear all,

I like to plot a function, let's say x^2 in a boxed axis mode; i.e. 

plot(x^2,axis=boxed)

Howeve, I want the plot to have tickmarks on all four axises, and not only the normal x and y axis.

Can anyone help me with this please? 

plotpoints.mw

I want to plot points when i_t =1,2,3,..,11,12 instead of a continous line displayed in the worksheet I uploaded. How to modify the function? Thank you for helping:)

How to  compute the recurrence relation and I find the problem when the summation of U because appear noise term self-canceling and I can not find the nth component of U?Mixed_volterra_-Fredholm_(278)_Ex(8.17).mw

Download Mixed_volterra_-Fredholm_(278)_Ex(8.17).mwMixed_volterra_-Fredholm_(278)_Ex(8.17).mw

thank you for helping:)

The well known William Lowell Putnam Mathematical Competition (76th edition)  took place this month.
Here is a Maple approach for two of the problems.

1. For each real number x, 0 <= x < 1, let f(x) be the sum of  1/2^n  where n runs through all positive integers for which floor(n*x) is even.
Find the infimum of  f.
(Putnam 2015, A4 problem)

f:=proc(x,N:=100)
local n, s:=0;
for n to N do
  if type(floor(n*x),even) then s:=s+2^(-n) fi;
  #if floor(n*x) mod 2 = 0  then s:=s+2^(-n) fi;
od;
evalf(s);
#s
end;

plot(f, 0..0.9999);

min([seq(f(t), t=0.. 0.998,0.0001)]);

        0.5714285714

identify(%);

So, the infimum is 4/7.
Of course, this is not a rigorous solution, even if the result is correct. But it is a valuable hint.
I am not sure if in the near future, a CAS will be able to provide acceptable solutions for such problems.

2. If the function f  is three times differentiable and  has at least five distinct real zeros,
then f + 6f' + 12f'' + 8f''' has at least two distinct real zeros.
(Putnam 2015, B1 problem)

restart;
F := f + 6*D(f) + 12*(D@@2)(f) + 8*(D@@3)(f);

dsolve(F(x)=u(x),f(x));

We are sugested to consider

g:=f(x)*exp(x/2):
g3:=diff(g, x$3);

simplify(g3*8*exp(-x/2));

So, F(x) = k(x) * g3 = k(x) * g'''
g  has 5 distinct zeros implies g''' and hence F have 5-3=2 distinct zeros, q.e.d.