Here is a code

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/EQ.mw .

Download EQ.mw

A fragment of code

for b in extra_bcs do try print(b = 10^(-2)); res[b] := dsolve(dsys4 union {b = 10^(-2)}, numeric, initmesh = 2024, output = listprocedure, approxsoln = [omega2 = 0.1e-2, s(x) = cosh(upsilon*x)-cos(upsilon*x)-(cosh(upsilon)+cos(upsilon))*(sinh(upsilon*x)-sin(upsilon*x))/(sinh(upsilon)+sin(upsilon)), g(x) = sin(((2*n+1)*(1/2))*Pi)], abserr = 0.1e-1) catch: print(lasterror) end try end do; indx := indices(res, nolist); nops([indx]); res[indx[i]]; seq(subs(res[indx[i]](1), omega2(1)), i = 1 .. nops([indx]))

hi.

how i can select or chose proper polynomials or another functions that attached boundary conditions at points zero and one , weakly or strongly satisfy??polynomial.mw

Download polynomial.mw

thanks...

hi.i calculate this integral numerically but after use this result in my differential equation which is involve f3(x), i enconter with error

i found that this problem is due to answer of this integtal.may i use another way to calculte it?as shown power in result are very large!!!

Download integral.mwintegral.mw

thanks..

I have written a code which generates a Gaussian like curve as a set of points and have written some basic commands to find several important quantities from the plot. The three of importance here are the peak position, peak height and Full Width at Half Maximum.

See the attached minimal working example maple worksheet.

It can find the peak position and the peak height no problem, but another quantity I want it to find is the Full Width at Half Maximum (FWHM). I use the aforementioned calculated values to find the left and right components of the FWHM but the fsolve command just hangs.

In the worksheet this is not evident but in the much longer full code which I run through the terminal and prints the values to a file, it begins the fsolve command and reaches a particular value and it just hangs. No amount of waiting time makes it continue the calculation.

However if I use an approximate integration scheme (such as Riemann sums) then the fsolve part executed perfectly. fslove seems to get stuck during the numerical integration step.

There is probably an easy answer to this problem which I am missing. Any help is appreciated.

fsolve_numerical_integration.mw

- Yeti

I have an equation eq := diff(y(x), x$3)+3*diff(y(x), x$2)+12*y(x);

dsolve(eq, y(x)); gave me a general solution.

I tried to get a particular solution using dsolve({eq, y(0) = a, y'(0)=0, y"(0) = 0}, y(x));

But I got Error, (in dsolve) not a system with respect to the unknowns [y(x)].

Thank you for any help.

Heather

I have the system:

Update:

{-1/2 < 2*f*(1/53)+7*g*(1/53), 3/106 < 7*f*(1/53)-2*g*(1/53), 2*f*(1/53)+7*g*(1/53) < -37/106, 7*f*(1/53)-2*g*(1/53) < 1/2}

which I wish to solve over integers but isolve() gives me "Warning, solutions may have been lost and no solutions". The solutions exist and are {[f =0, g = -3] || [f = 1, g = -4], [f = 1, g = -3] || [f = 2, g = -4]}, but I cannot obtain them with Maple. Could you tell me what is wrong and how I should treat this kind of problems in the future, please.

Mathematica 10.0

Reduce[{-1/2 < 2*f*(1/53) + 7*g*(1/53), 3/106 < 7*f*(1/53) - 2*g*(1/53), 2*f*(1/53) + 7*g*(1/53) < -37/106, 7*f*(1/53) - 2*g*(1/53) < 1/2}, {f, g}, Integers]

(f == 0 && g == -3) || (f == 1 && g == -4) || (f == 1 &&
   g == -3) || (f == 2 && g == -4)

Maple

isolve({-1/2 < 2*f*(1/53)+7*g*(1/53), 3/106 < 7*f*(1/53)-2*g*(1/53), 2*f*(1/53)+7*g*(1/53) < -37/106, 7*f*(1/53)-2*g*(1/53) < 1/2});
Warning, solutions may have been lost

Gentlemen

As seen on tv.

Having issues with animating the movement of two fielders, (25m apart on a straight line) when a baseball is struck towards them. they're on the y axis when they should be on the x.... and they should be green and brown dots, not lines.....

BaseballBallistics.mw

Hello!

I am calculating the temperature of a rod which has one end at the temperature T₁ and the other end at T₂ and it's evolution. We were already given the formula for the numeric calculation and after a short while I managed to obtain a small program that would calculate the temperature of each segment of the T(x,t) grid:

>restart: with(plots): nx:=20: tmax:=50: T1:=1: T2:=10: L:=1: k:=1: rho:=1: cp:=1: chi:=k/rho/cp: h:=L/(nx-1): t:=1e-3:
>for k from 0 to nx do T(k,0):=T1 od:
for w from 1 to tmax do
T(0,w):=T1: T(nx,w):=T2:
for q from 1 to nx-1 do
T(q,w):=T(q,w-1)+chi*t/h^2*(T(q+1,w-1)+T(q-1,w-1)-2*T(q,w-1));
od: od:

With L the Length of the rod, t and h the time and space increment [h=L/(nx-1), where nx is the number of intervals we divide the x-axis, although I'm not quite sure the '-1' should be there], chi a constant different for each rod and tmax total time we want to calculate. The formula from the 5th line was given to us, so in that part there is no mistake.

Up until here everything works perfectly fine.

Now I want to be able to draw this and here is where all the problems appear. I want to draw this in a 2D graph with position in the x-axis and time in the y-axis. I have tried "densityplot(T(x,y),x=0..nx,y=0..tmax)" which would seem to be the logical whay to continue this. As I understand it, this plot would draw an nx times tmax grid and colour the whole plpot black-white acording to the maximum and the minimum value (as shown in the maple help page of this plot).

However, when I do this a black square appears (or red if I add colorstyle=HUE). I have tried a lot of things and none seemed to work.

I would also like to be able to draw the isotherms on the plot but that is secondary.

I am pretty new to Maple. I have studied the most basic things but don't really understand the whole complexity of this program. Thanks a lot in advance and forgive my faulty english,

Enrique

>assume(x>0, n>0):int(x^n*ln(x)^n,x);

I_Mariusz

I am currently working in Maple, following an example on the Maplesoft site very closely. I am trying to make use of the 'Colorize' function in the Escape-Time Fractals package.

I have a Newton's basin with the standard colouring but am trying to make my image more sophisticated. I have tried following the example given for the Mandelbrot set (At the bottom of the page - http://www.maplesoft.com/support/help/Maple/view.aspx?path=Fractals/EscapeTime/Mandelbrot) as there isn't one on the Newton Fracal page but keep receiving the Kernel lost message. I do not think the issue is my firewall.

My code is as follows,

with(Fractals:-EscapeTime);

with(ImageTools);

Everything works up until I go to evaluate P. I have tried giving both Arrays datatype=float[8] and have tried getting rid of the datatype section completely as to use the default. Neither of these have helped.

Any insight as to why this may be happening would be appreciated.

Hello,

Paraphrasing:

https://en.m.wikipedia.org/wiki/Langford_pairing

given a sequence of 2n numbers 1,1,2,2,3,3,...n,n in which the two 1's are 1 slot apart, the two 2's are 2 slots apart, the two 3's are 3 slots apart, -> generally the two n's are n slots apart.

for n=3, a possible sequence is [2,3,1,2,1,3]. 

There is sequences for n=4,7,8...

i havent a clue how to write a maple procedure to generate a sequence for given n, but I'm hoping an expert here can.

I'm trying to write a procedure that computes Pollard's P-1 Method for a given integer n, and then outputs the prime factorisation of n.

Here is what I have so far:

Pollard := proc (n)
local i, r, g;
r[1] := `mod`(2^factorial(2), n);
for i from 2 while gcd(`mod`(r[i-1]-1, n), n) = 1 do
r[i] := `mod`(2^factorial(i+1), n) end do;
g[i] := gcd(`mod`(r[i-1]-1, n), n);
if g[i] < n then return g[i]
else return n
end if
end proc;

But my procedure doesn't seem to work for a lot of large values for n.
And also I can't figure out how to make it actually output the factorisation.

Any help would be appreciated.

Maybe this is trivial but could somebody tell me how to get bounds of interval returned by shake? For instance,

shake(sqrt(2)) gives INTERVAL(1.41421356167 .. 1.41421356308), and I would like to store the upper and lower bounds as rational numbers in two variables. 

how draw a line x+y = 1 on a sphere x^2+y^2+z^2 = 1 in maple

Hello, I have a somewhat math and Maple question I'm hoping some can help with.

I have this curve,

curve:=alpha^2*beta^10-alpha^2*beta^9+4*alpha*beta^7-2*alpha*beta^6-2*alpha*beta^5-alpha*beta^4+alpha*beta^3-2*beta+1;

and if I solve this system (numerically);

sol:= solve([curve=0,diff(curve,beta)=0],[alpha,beta]);

I get 6 special points (8 actually but two are critical). So I'll refer to them by subscript "i".

If I then do a coordinate transformation by;

alpha=exp(u)

beta=exp(v)

and convert the 6 coordinates and curve, I'll get everything in terms of (u,v) coordinates.

curve2:=subs([alpha=exp(u),beta=exp(v)],curve);

soluv:=map(ln,sol);  (this is just pseudo - I don't know how to do it this way)

So now the 6 points are referred to by (u_i,v_i).

Next, I want to expand this curve locally around these six points, using the following (where "z" is the local coordinate);

u -> u_i + z^2

v -> v_i + sum(a_j*z^j,j=1..n)

where n is reasonable, though around 15.

curve3(i):=subs(u=z^2 + cat(Ubp,i),curve2);

curve4(i,n):=subs(v=cat(Vbp,i)+sum(a[i,j]*z^j,j=1..n),curve3(i));

Here, I'm not sure of the pros/cons of cat() vs a[i,j]....

Anyway, I'll then have an equation in terms of only the local coordinate "z". If I then solve each coefficient of "z", at each order, I should then be able to determine the power series v(z). I reason that since the curve is initially equal to zero, that every non-zero power of z will have a coefficient/equation (in terms of unknowns a[i,j]) that should be equal to zero.

This is analagous to solving differential equations with power series...

However, I'm a little lost in implementing this,

I am currently trying, for instance,

l1:= series(curve4(1,10),z,0,9);

e1:= seq(coeff(l1,z,i),i=1..4):

s1:=seq(a[1,j],j=1..4):

sol:=solve(e1,s1);

I believe I am doing something wrong though bcause every odd power is zero.

Thank you a lot for any suggestions and/or help,

sbh

PS>

Ubp and Vbp are those 6 points - I just kept them as symbols initially because I was still getting odd-powered coefficients as zero, regardless of their actual values. Hence a little bit of the "math" side of the problem...