why is simplify is making errors - me or maple?

Ec := (1/2)*Kc*(2*Pi*h0/Pi(a0^2+h0^2)-2*Pi*h/Pi(a^2+h^2))^2;
2
1 / 2 Pi h0 2 Pi h \
- Kc |------------- - -----------|
2 | / 2 2\ / 2 2\|
\Pi\a0 + h0 / Pi\a + h //
simplify(%);
2
2 Kc (-h0 + h)

Simplify is erasing the varibles a0 and a. Is there a secret to using simplify?

In Maple 2015.1 we have

restart;

solve([sin(2*x)/cos(x+3*Pi/2)=1,  x>-4*Pi, x<-5*Pi/2], x, allsolutions, explicit);

solve([sin(2*x)/cos(x+3*Pi/2)=1, x>0, x<2*Pi], x, allsolutions, explicit);

In the first example, the error message is not clear (actually there exists a unique root  x=-11*Pi/3), in the second example, one root  (x=5*Pi/3) is lost.

I've got this huge chunk of code which leads to an optimiazation at the very last line (Bestangles:=minimize(maximize()-minimize))). This minization is taking a very long time (havent solved it yet) and I would very much like to reduce that time. As I've understood maple does optimization by differentiating and then finding all extremes and comparing. Would this mean that since I minimize and optimize within a minimization command, it differentiates a ton of times? And if this is the case, can I somehow do the differentiation beforehand, since it is the same function being differentiate all the time? Or is there some other way I can improve the code? 
Thanks alot!

Heres the full code:

I am very beginner about Maple. How to get the general solution from the follwoing equations by Maple. Please help me. Its Urgent. Please help me out.

I am learning to use maple for my notes preparation for the subject Finite Element Analysis. It is interesting to know that how often we blame maple or computer for the silly mistakes we made in our commands and expect the exact answers. I have used a small file and find it easy to analyse my mistakes fatser. If we make a small mistake in a big file, it not only gives us problem finding our mistakes, it leads to more mistakes in other parts as well. A command working in one document need not necessarily work the same way in other document.

I have made my first document and people will come with suggestions to make appropriate modifications in the various sections to improve my knowledge on maple as well as the subject.

Download FINITE_ELEMENT_ANALYSIS.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

why the the software can't plot the function like x^(4/3)*sin(1/x) or x^(1/3)

it could only plot where x>0,but the value is does exist where x<0.

Thanks in advance for your help.

Download wrong_answers.mwwrong_answers.mwwrong_answers.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

Greetings all,

I was wondering if any Maple users out there are using the lastest Microsoft tablet, the Surface Pro 4 with Maple?

I would be interested in any opinions and specifically if the pen is effective when used as an input device with Maple

Thanks

hello everyone

can any one tell me what is this anti reduction method. In the paper of serdal palmuk,the link is given bellow

http://www.hindawi.com/journals/mpe/2009/202307/

in this paper question #4 is first solved by anti reduction method for  exact solution.

but i dont understand this method,

if anybody know this then please also tell me how to solve this,

and in the next  (6 & 7 ) examples "in the pourus media equation" they first find its particular exact solution.i also dont understand this,so please tell me

actually i know how to solve ODE to find its exact solution but  i dont know how we find exact solutions of partial differtial equations,

so please help me to solve this problem

thanks

I wish to define a function with a finite number of inputs, but I do not know that number ahead of time (in other words the user will specify n and my function operates on vectors of size n). How can this be done?

How to find the integral
,

assuming k and n  integer?
It is known (McCrea W. H., Whipple F. J. W.Random paths in two and three dimensions, Proc. Roy. Soc. Edinburgh. 1940. V. 60. P. 281–298) that

G(n,n)=2/Pi*sum(1/(2*k-1),k=1..n).

The general case is reduced to the case k=n.
This is not a creature of pure reason: the one appears in electric circuits
(see M. Skopenkov, A. Paharev, A. Ustinov, Through resistor net, Mat. pros. Issue 18 (2014), 33-65, in Russian, http://www.mccme.ru/free-books/matpros/pdf/mp-18.pdf).
I found G(8,8) = 182144/(45045*Pi) in 657.797 s and G(9,9) = 3186538/(765765*Pi) in 4157.687 s on my comp by

restart; s := time():(1/2)*VectorCalculus:-int((1-cos(9*Pi*x)*cos(9*Pi*y))/(sin((1/2)*Pi*x)^2+sin((1/2)*Pi*y)^2), [x, y] = Rectangle(0 .. 1, 0 .. 1)); time()-s;
Mathematica 10.3.0 does G(9,9) in 250.391 s on my comp.

I have run into a "funny" feature of 2-D input: It seems to convert something like k/2 into this k*`^`(2,-1). While this would often not be an issue (it is correct after all), it becomes a problem when used in an argument list to a procedure. It becomes even more of a problem when, by chance, I have overloaded `^` to act on specific types that I have defined.

Let me try to explain briefly. I have a package called "Lattice" that does whatever it does (not of relevance here). I am writing a little manual for this package, for which I use 2-D input so I can write it in Maple and have the examples right in it and "live".

Here is what happens:

with(Lattice) # load the package

QFh:=Quad(0,kf/2) # Define an element for Lattice

Error, invalid input: Lattice:-`^` expects its 1st argument, element, to be of type Element, but received 2

Copy-pasting kf/2 into a 1-d worksheet, I get

QFh := Quad(0, kf*Lattice[`^`](2, -1));

So it uses Lattice[`^`] which actually appears to bypass the overload I have in the Lattice package. `^` is defined like this in Lattice:

`^`:=proc(element::Element,n::algebraic) option overload; # Element is a defined type in Lattice
...
end proc;

How can I possibly rewrite `^` to fall-back to Maple's ^ operator when called as Lattice[`^`] ?? I know there is a function overload() but have no experience with it. Would it even help?

Or am I missing something completely here? I do not use 2-D input for my usual work, but in this case I want and need to use it. The reason for its bizarre rewrite of "/2" is beyond me. Note that I can replace /2 by *0.5; but that causes problems later on for algebraic work as 1/2 is not 0.5 in Maple. I tried *1/2 but that has the same problem.

Has anyone a clean solution for this? I assume this effect is not limited to my own package but would affect others as well.

M.D.

PS: I ran into this using Maple 15 but I doubt it is specific to this particular version.

Hello,

My code records the values I need, however, I need to implement a modulo of 2*Pi on my result for theta. But this leads to a graph with no plots and I'm not sure how to fix it. Any help is greatly aprreciated! Thank you in advance!

Kind regards,

Gam

bia Man

i've got a list of 6 ODEs with 6 initial conditions:

MH,MS,M,a,G,e,afb are just constants

Eqns2 := diff(xH(t), t) = vxH(t),
            diff(vxH(t), t) = -G*M*xH(t)/(xH(t)^2+yH(t)^2)^(3/2),
            diff(yH(t), t) = vyH(t),
            diff(vyH(t), t) = -G*M*yH(t)/(xH(t)^2+yH(t)^2)^(3/2),

            diff(theta(t), t) = omega(t),

            diff(omega(t), t) = -G*MS*afb^2*(xH(t)*sin(theta(t))-yH(t)*cos(theta(t))*            (xH(t)*cos(theta(t))+yH(t)*sin(theta(t)))/(xH(t)^2+yH(t)^2)^(5/2):

ICs2 := xH(0) = a*(1+e), vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e))), yH(0) = 0, 0 < theta(0), theta(0) <= Pi,        omega(0) = 10*Pi/T_H:

soln2 := dsolve({Eqns2, ICs2}, {omega(t), theta(t), vxH(t), vyH(t), xH(t), yH(t)}, numeric)

But it doesn't solve it , but instead displays this error message:

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

Can someone find a syntax error or a typo that would explain this?

When assigning a color to a given wave length I initially used ColorTools WavelengthToColor. Acer commented that this wasn't the most accurate. I looked into this a little further and it seems there could be a better result. The attached document compares some different ways of assigning colors to wave lengths. 

Warning- The CIEDE2000 computation for deltaE is very slow. I think this is because of the hue angle calculations which use piecewise a lot. The CIE94 delta E method produces nearly the same result and takes minutes instead of hours.

Questions;

 I think I could speed up my calculation if I could find the position of the minimum element of an Array similar to FindMinimalElement of a list. 

I created my own atan2 function (similar to Excel). If there were a built in Maple equivalent perhaps it would be faster? I didn't see any such function.

6bit_Wavelength_Color_CIEDE2000.mw