MaplePrimes Questions

Hi,

It might be a silly question but here it goes. I have a sin function in terms of sin(omega*(T0-T)+Phi) and i need to expand it by keeping omega*T0+phi as a single term. One way is by subs omega*T0+phi as a constant 'c' and then after expanding we can back substitute. But is there any option in expand function itself?

 

Regards

Sunit

Hi,

I have encountered some strange issue with symbolic summation. Would be grateful for any help.

Here is the code (inserted as image):

Symbolic summation of powers of sines & cosines

 

Code in text:

restart;
F:=(n,a,b)->sum(r^(a+b)*cos(2*Pi/n*j+t)^a*sin(2*Pi/n*j+t)^b,j=0..n-1);

F(n,2,2);
F(4,2,2); 

The issue is that symbolic summation produces the formula (for general n) which contradicts the particular case (n=4).

Could somebody explain why this is happening? Is it a bug or am I missing something here?

I have tried all versions of Maple downto 14 - same situation.
Also Mathematica givers the same answer.

Thank you in advance,
Pavel Holoborodko.

--
Multiprecision Computing Toolbox
http://www.advanpix.com/

Couple of questions actually,

writebytes("c:/testfile.txt","hello") in Maple 2016 doesn't create a file to write the bytes to unless the file already exists.  In Maple 12 if the file didn't already exist Maple would create it.  Is this a programming change for writebytes?

After writing to the file, if you open the file with notepad (or any text editor) there is nothing in that file.  It is only once you write in maple ..

     filepos("c:/testfile.txt",0)

.. that you can then see something in the edited file with an external editor. 

This is probably connected but how do get Maple to relinquish command of the file I've used writebytes on?  The error message I get is "The process cannot access the file because it is being used by another process" I would guess once Maple releases command on that file all data written to it will be visible regardless of what filepos I'm at. 

 

How can I limit the number of processors that are used by a multi-threaded operation? The help pages ?multithreaded and ?kernelopts both suggest, vaguely, that this can be controlled with kernelopts(numcpus). The following worksheet shows, however, that this doesn't work: While Maple does remember what you set numcpus to, this setting has no effect on the number processors used by Threads. And, if this doesn't work, what purpose is there in being able to set the value of numcpus?

restart:

First, warm-up and stretch the memory. Otherwise, the timings are invalid.

L:= RandomTools:-Generate(list(integer, 2^18)):

CodeTools:-Usage(Threads:-Mul(x, x= L)):

memory used=1.21GiB, alloc change=0.98GiB, cpu time=18.66s, real time=3.75s, gc time=27.54m

Now this is the actual test.

L:= RandomTools:-Generate(list(integer, 2^18)):

gc();

for n to kernelopts(numcpus) do
     print(kernelopts(numcpus= n));
     CodeTools:-Usage(Threads:-Mul(x, x= L), iterations= 4)
end do:

8

memory used=1.21GiB, alloc change=322.34MiB, cpu time=4.04s, real time=933.75ms, gc time=566.41ms

1

memory used=1.21GiB, alloc change=-2.00MiB, cpu time=4.22s, real time=859.50ms, gc time=656.25ms

2

memory used=1.21GiB, alloc change=-1.17MiB, cpu time=4.03s, real time=841.75ms, gc time=566.41ms

3

memory used=1.21GiB, alloc change=256.00MiB, cpu time=4.47s, real time=911.25ms, gc time=738.28ms

4

memory used=1.21GiB, alloc change=0 bytes, cpu time=4.33s, real time=852.50ms, gc time=605.47ms

5

memory used=1.21GiB, alloc change=0 bytes, cpu time=4.34s, real time=853.50ms, gc time=628.91ms

6

memory used=1.21GiB, alloc change=0 bytes, cpu time=4.27s, real time=826.75ms, gc time=535.16ms

7

memory used=1.21GiB, alloc change=0 bytes, cpu time=4.19s, real time=841.50ms, gc time=308.59ms

 

Download numcpus.mw

You'll get equivalent results if you replace Mul by Add and increase the size of L to about 2^24.

Hi There,

Im currently on using a trial version of maple for engineering students. I am looking to see how you can view a step by step method of solving equations. I can't seem to find a way of doing so and I keep just getting the final answer. Can you assist?

 

Also I can't find the quadratic equation option.

 

thanks,

 

stuart

I'm trying to solve vast system of differential equations (Hamiltonian equations of motions). 

I have this kind of error and don't know what to do with it:

Error, (in dsolve) found the independent variables {t} also present in the names of the functions of the system {(cos(varphi(t)))((3333333333/10000000000)/sin(theta(t))^2+(1/23)*cot(theta(t))^2/R(t)^2), (sin(psi(t)))((3333333333/10000000000)/sin(theta(t))^2+(1/23)*cot(theta(t))^2/R(t)^2)}

Here's the file:ClassicalTrajectoriesAr-CO2.mw

 

 

Hi everyone,

I've not been able to figure this one out. Say I have an expression dependant on two random variables, like this:

C:=A+B

where A and B are randomvariables, each following a specific distribution.

If I ask for a Sample of C

Sample(C,1)

Maple will sample A, sample B and compute C. But say that A and B are correlated (with a cc of 0.8). How do I define this?

Thanks in advance

 

Hello all,

I try to solve this system using maple 18 by "fsolve", but I don't get the solution, I don't Know what is the problem or What this mean.

Do you have any idea?

 

Best Regards L.Sn=10_R=23.5.mw

Maple debugger uses very small font, different from main worksheet. It seems to use its own font size. Changing font size on the main worksheet has no effect.

For example, if you type

restart;
f:=proc()
return 3;
end proc;

stopat(f);

f();

 

Now the debugger comes up. On my system, windows 7, and Maple 2016, the font is very small. I'd like to make it larger.

How can one do this? I looked at format->style but see nothing related to debugger.

when writing by error the following

restart;
f:=proc()
dsolve(diff(y(x),x)+y(x)=0,y(x));
end proc();

Maple did not complain and returned  f := y(x) = _C1*exp(-x)

Then I noticed I needed to change "end proc();" to "end proc;" 

The question is, why did Maple not generate a syntax error? If "end proc();" is valid Maple code, then what does it mean? or Did Maple ignore it? what is the parsing steps used to make Maple generate the above output? 

let aa = map (+1.2) [1,2]
let bb = map (+1.4) [2,3]
foldr (aa . bb) [3.0,4.0]

Hello people in mapleprimes,

I want to distribute limit or Limit to each terms of summation.

Limit(f(a+h)-f(a),h=0);

But, the output is not distributed one, but the same as the input, though

I want it to become Limit(f(a+h),h=0)+Limit(f(a),h=0), or

Limit(f(a+h),h=0)+f(a).

Isn't there any way for it, other than a trivial one that is

subs(Limit(f(a+h)-f(a),h=0)=Limit(f(a+h),h=0)+Limit(f(a),h=0),Limit(f(a+h)-f(a),h=0));

?

I hope someone will teach me.

Thanks in advance.

taro

 

I am trying to duplicate the answer to a problem of the nutation of a spinning top. The problem is number 6.1.3 in the book Computer Algebra Recipes for Classical Mechanics by Richard Ens and George McGuire.

TopSC := `<,>`(5*sin(z)*exp(-(Pi-z)/(1.5)), 0, z) for z = 0..Pi

Spacecurve TopSC, when rotated about the z axis, generates the surface of revolution of the top.

The solution requires knowing the moments of inertia (MI) of the top about the z axis and the x or y axis.

Does the following integral correctly calculate the MI about the z axis?

int(2*Pi*TopSC[1]*(TopSC[1]^2), [z = 0 .. z, z = 0 .. Pi])

What sequence of Maple 2016 commands will calculate the top's MI about the x or y axis?

The following command works fine until you use it in the combination conjugate and diff.

example in Physics:

declare(phi(X));

diff(conjugate(phi(X)),x1);

phi(X) should now appear as phi with index x1 and a bar only, but

it comes as phi(X) x1 , the declare command is not effective. Non conjugate works fine.

Any idea - thanks in advance

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