Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

https://social.msdn.microsoft.com/Forums/vstudio/en-US/cc2a85ad-30ec-44ed-8c75-636ff71eade2/how-to-convert-integer-or-decimal-number-into-any-base-number?forum=csharpgeneral

1. for example how to convert decimal or integer number into base 3 number, base 5 number etc.

2.how to do logical operation with custom logic table for example,

 

120 special operator 235 

01111000

11101011

 

special operator according to logical table is

1st op 2nd op output
0 0 1
0 1 0
1 0 1
1 1 0

 

  01111000

  11101011

=00010100 = 20

Hi,

I'm trying to solve the following non-linear ODE numerically:

by ececuting

but maple gives me this error-message:

"Error, (in dsolve/numeric/make_proc) Could not convert to an explicit first order system due to 'RootOf'"

I couldnt find any useful information in the manual. What does this error mean? Is there something wrong with my maple code or is there just no solution for this particulare differential equation?

 

Thanks in advance

Hi

I have this PDE and was wondering how I can get Maple to solve it

utt+2ut-uxx=18sin(3πx/l)

with conditions u(0,t)=u(l,t)=0 and u(x,0)=ut(x,0)=0

Thanks

James

 

 

 

Could anyone assist in rectifying this error ''Error, (in fsolve) {f[1], f[2], f[3], f[4], f[5], f[6], f[7], f[8], f[9], f[10], f[11], theta[11]} are in the equation, and are not solved for''. Here is the worksheet FDM_Revisit_1.mw

I am using the SumOverRepeatedIndices and get a Length of Output Exceeded error. Sometimes if I close the file and restart the program then I get a result and no error.  However, if I recalculate then I get the error.

 


restart; with(Physics); with(Tetrads)

[e_, eta_, gamma_, l_, lambda_, m_, mb_, n_]

(1)

`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))` := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(zeta, zetabar, u, v)), (du+Physics:-`*`(Ybar(zeta, zetabar, u, v), dzeta)+Physics:-`*`(Y(zeta, zetabar, u, v), dzetabar)-Physics:-`*`(Physics:-`*`(Y(zeta, zetabar, u, v), Ybar(zeta, zetabar, u, v)), dv))^2)

2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2

(2)

X = [zeta, zetabar, u, v]

X = [zeta, zetabar, u, v]

(3)

PDEtools:-declare(`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))`)

Ybar(zeta, zetabar, u, v)*`will now be displayed as`*Ybar

(4)

Setup(coordinates = (X = [zeta, zetabar, u, v]), metric = 2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2)

[coordinatesystems = {X}, metric = {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}]

(5)

g_[]

g_[mu, nu] = (Matrix(4, 4, {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 1) = 1+2*H(X)*Ybar(X)*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 1) = 2*H(X)*Ybar(X), (3, 2) = 2*H(X)*Y(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 1) = -2*H(X)*Ybar(X)^2*Y(X), (4, 2) = -2*H(X)*Y(X)^2*Ybar(X), (4, 3) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}))

(6)

NULL

``

eqn1 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[1, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

(7)

eqn2 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[2, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

(8)

eqn3 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[4, `~mu`])) = x

(1/2)*(-(diff(Y(Zeta, zetabar, u, v), zetabar))*(Y(X)*Ybar(X)+1)*2^(1/2)+(diff(Y(Zeta, zetabar, u, v), u))*2^(1/2)*(Y(X)-Ybar(X))-(diff(Y(Zeta, zetabar, u, v), v))*2^(1/2)*(Y(X)-Ybar(X)))/((-(Ybar(X)^2+1)*(Y(X)^2+1)/(Y(X)-Ybar(X))^2)^(1/2)*(Y(X)-Ybar(X))) = x

(9)

eqn1 := `[Length of output exceeds limit of 1000000]` = 0

`[Length of output exceeds limit of 1000000]` = 0

(10)

algsubs(`[Length of output exceeds limit of 1000000]` = 0, `[Length of output exceeds limit of 1000000]`)

0

(11)

``

simplify(`[Length of output exceeds limit of 1000000]`)

``


Download Derive_Eq_4.4.mw

In brief the problem can be stated as follows:

 

Given dependent variables Qi i=1,...,N and independent variables xi, yi, and zi i=1,...,N

which are related via the following system of N linear equations with parameters P1, P2 and P3 :

Qi = P1xi+P2yi+P3zi   i=1,...,N

How to find the optimal values of  P1, P2 and P3 which satisfy the above system of linear equations subject to the following constraints:

Pi>=0   i=1,2,3

and  P1>=P2P3

 Without the requirement of P1>=P2P3, the problem can be solved with the Non-negative Least Squares Method of Lawson and Hanson.  But with this additional constraint, I am stuck.  

 

Your suggestions are welcome.

 

 

 

 

I am trying to find the root of an equation that involves a procedure and a definite integral (solved numerically). Of course, I don't need the root to be found symbolically, but numerically would be fine. The problem is, I keep getting the error

"Error, (in fsolve) Can't handle expressions with typed procedures"

whenever I try to solve it. Anyone have any ideas? My worksheet is here: Table-1-duplication-mapleprimes.mw 

 

Hi,

I'm trying to fit some parameters to the data of multiple slightly different experiments.

I've written a function which returns the sums of the error for all experiments.

 

The function which has to be minimized does the following:

1) Set parameters for the model ODE based on the input parameters

2) calculate the difference (numeric solution of ODE <-> experimentel data)

3) repeat step 1+2 for all experiments

4) return the sum of all differences

 

The function works as aspected. But when I try to minimize it by calling:

I got an error:

"Error, (in dsolve/numeric/process_parameters) parameter values must evaluate to numeric, got A = A"

For some reason Maple isnt able to set the new parameters of the ODE.

Anyone got an idea how to fix this?

 

Thanks in advance.

 

 

 

I got a problem with solving a second order ODE. 

The ODE is :

-V(xi)+(1/2)*xi*(diff(V(xi), xi))+(1/4)*(diff(V(xi), xi, xi))=-(1/2)*k2*(diff(H(xi), xi))-k1*n*X/E+1+k2

where k1,k2,n,X,E  all are constant.

the condition is :

V(xi) tends to 2*xi^2 as xi tends to infinity.

I used 'dsolve' to solve the equation firstly, and got a solution with two constant C1 and C2, I want to use the condition to elimilate C2, so I used limit(sol,xi=infinity)=2*xi^2. But when I used the command 'limit', I can't get the answer.

Could any one help me? 

Many thanks!!!

Hi,

I'm a newer of maple .I want to prove x=z,y=z from equations of parametric z.But maple don't solve what I want,who can give me a help .thank you

 

howdy.

evalf(map(log10,[25,5,1,10,4,20]))=

[1.39794000867203, .698970004336017, 0., 1., .602059991327960, 1.30102999566398]

How do I reverse this process , ie get back [25,5,1,10,4,20] using map command. Obviously it's 10 to the power but map(10^,[1.39794000867203, .698970004336017, 0., 1., .602059991327960, 1.30102999566398]) won't work

 

I'd like to plot the following inequalities:

sqrt(x)<=1/sqrt(2)

1/sqrt(2)<sqrt(x)<=1/sqrt(2)

 

Hey!

I have this MATLAB script, but as I work in Maple, I'll need to translate it to Maple. 
I know how to define symbols and functions, but I don't know which Maple commands to use, of if it needs to be done in another way, so the problem is translating from " dZ = [dx; dy; ax; ay; dm];" and down.

Any help would truly be greatly appreciated! Thank you!  



This is the script:

function dZ = meteor_step(~, Z)

  P = 1.2; % initial atmospheric pressure
  H = 1.39E-4; % scale height of atm pressure
  E = 8.11131859E6; % evaporation energy
  D = 1; % drag constant
  G = 9.814; % acceleration due to gravity
  PM = 3.3E3; % density of the meteor
  
  S = 3.986E14; % standard gravitational parameter of Earth (G*M)
  R = 6.3674447E6; % radius of the Earth (meters)

  x = Z(1);  
  y = Z(2);
  dx = Z(3);
  dy = Z(4);
  m = Z(5);
  
  atm = P*exp(-y*H);

  v = sqrt(dx^2+dy^2);

  area = pi * ( (3*m)/(4*PM) )^(2/3);

  dist = sqrt(x^2+y^2);
  Gv = -9.8;

  accel = -(D*atm*area)/m*v;
  ax = accel * dx;
  ay = accel * dy + Gv;
  

  dm = -(atm*v^3*area)/(2*E);
  
  dZ = [dx; dy; ax; ay; dm];
  
end

 

 

 

 

[t, R] = ode45(@meteor_step, [0 250], [0, 100000, 100, -300, 25]);

x = R(:,1);
y = R(:,2);

dx = R(:,3);
dy = R(:,4);

v = (dx.^2+dy.^2).^(1/2);

m = R(:,5);

figure(1);
plot(t, y);
  title('Meteor Kinematics: Height vs Time');
  xlabel('Time elapsed (s)');
  ylabel('Height (m)');

figure(2);
plot(x, y);
  title('Meteor Kinematics: Horizontal vs Vertical Position');
  xlabel('Horizontal (m)');
  ylabel('Vertical (m)');

figure(3);
plot(t, v);
  title('Meteor Kinematics: Speed vs Time');
  xlabel('Time elapsed (s)');
  ylabel('Absolute speed (m/s)');

figure(4);
plot(t, m);
  title('Meteor Kinematics: Mass vs Time');
  xlabel('Time elapsed (s)');
  ylabel('Mass (kg)');

  
figure(5);
plot(t, dy);
  title('Vertical Velocity vs Time');
  xlabel('Time elapsed (s)');
  ylabel('Vertical velocity (m/s)');

temp = abs(y - 52900);
[~, index] = min(temp);
  
t(index)
dx(index)/1000
dy(index)/1000

I've got a worksheet in which I have invested many hours of CPU execution time and if the computer goes down, or Maple fails for some reason, I'll lose it all.

If this happens I would like to be able to continue the calculation from where I left off.

By saving the worksheet periodically, I can save all the commands, but not the results, so if I have to restart, I'll have to wait many hours before the worksheet catches up to where it left off.

In ancient versions of Maple, you used to be able to save an executed worksheet including results (I sort of remember that you wrote a file with the extension ".M")  but the new help pages say that is now different from what it used to be. Obviously I can "save" individual symbols to a file, but for a complicated worksheet  that gets complicated.

I've read about "maplet" files, but that doesn't seem to fill the bill either.

So, is there any simple way to save a worksheet so you can continue seamlessly from where you left off after a crash, with all the previous results intact?

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