Questions - MaplePrimes

How to get the real and imaginary parts of complex...

Asked by: Alger 524

February 20 2020

0 3

Hi all,

How to get the real and imaginary parts of this complex expression.

Thank you in advance

real_imag_parts.mw

A problem for function or expression evaluation in...

Asked by: Alireza1982 0

February 20 2020

0 1

Hello every one
I have a question!
My code starts with assuming the time variable (t) to be specified in a an interval for each time that the for loop executes as follows:

discontinuity := [0.403e-8, 0.45e-8, 0.478e-8, 0.55e-8];
for j from 1 to 3 do
assume(discontinuity[j]<=t,t<discontinuity[j+1]);

After that the code runs and calculate every thing. For the second time, I mean for J=2, it does not work properly.
T[1] is the result of its first running (for j=1):
T[1]:=3.000023586*10^(-6)*exp(-4977.085344*t~)-1.325122648*10^(-6)*exp(-4.015800624*10^9*t~)
When it wants to evaluate this expression at specific time such as discontinuity[2] it cannot evaluate it. I tried to use unapply command to consider it as a function of t but it did not work. Here is the results:
AA:=simplify(eval(T[1], t = discontinuity[1]));
This is its result: AA:=3.000023586*10^(-6)*exp(-4977.085344*t~)-1.325122648*10^(-6)*exp(-4.015800624*10^9*t~)
Without unapply command: AA:=T[1]
Please answer my question.
Thank you so much

Maybe a bug in MAPLE 2015's Explore ?...

Asked by: mmcdara 7896

February 20 2020

1 6

Hi,

Here is the minimal situation that reveals which that could be a (little) bug in the MAPLE 2015 version of Explore.

In the attached file y is a list of numbers and val(r) a procedure that just print the value the rth element of y.
Changing the value of r is done with Explore (of course of no interest at all).
If I define the parameter r as a list ( r=[1..numelems(y)] ), only the value of y[1] is displayed: changing the value of r generates an error.
This doesn(t happen if r is defined as a slider ( r=1..numelems(r) ).

I discovered than the initial instance of Explore defines r as an integer while all the others (due to a change of r) define r as a string.
In the last command of the attached file you will see hjow I have circumvent this problem.

Is it a bug in Explore or does it exist some way to force the values of r to the implicit type they have in r=[$1..numelems(y)] ?

TIA

Download explore.mw

how to write this ODE in Maple?...

Asked by: nm 11373

February 20 2020

0 6

I'd like to solve this ODE

But not sure how to write it in Maple. In Mathematica, this is what I do

ClearAll[F, x, y, t];
ode = D[F[x[t], y[t]], x[t]]*D[x[t], t] + D[F[x[t], y[t]], y[t]]*D[y[t], t] == 0;
DSolve[ode, F[x[t], y[t]], {x[t], y[t]}]

and it gives

In Maple, I tried

ode:=diff(F(x(t),y(t)),x(t))*diff(x(t),t)+diff(F(x(t),y(t)),y(t))*diff(y(t),t)=0

Error, invalid input: diff received x(t), which is not valid for its 2nd argument

ode:=D[1](F)(x(t),y(t))*diff(x(t),t)+D[2](F)(x(t),y(t))*diff(y(t),t)=0;
dsolve(ode,F(x(t),y(t)))

Error, (in dsolve) expected the indeterminate function as, say, F(x) where x is of type "name" - and also cannot be a procedure name. Received: [F(x(t), y(t))]

What is the correct way to write this in Maple?

How do I sort a formula in the following form...

Asked by: ing123 5

February 20 2020

1 0

Hello,

I want to sort the formulae to Psi and Beta, but I don't know how it works. I have tried it with sort, simplify, isolate, but that isn't what I'm searching.

It should looks like the simplier formula in the picture.

ab := (diff(Psii(t), t, t))*J-l[f]*(F[s, f, l]+F[s, f, r])+l[r]*(F[s, r, l]+F[s, r, r])-(1/2)*b[r]*(-F[s, r, l]*delta[l]+F[s, r, r]*delta[r]) = 0;
/ d / d \\
|--- |--- Psii(t)|| J - l[f] (F[s, f, l] + F[s, f, r])
\ dt \ dt //

+ l[r] (F[s, r, l] + F[s, r, r])

1
- - b[r] (-F[s, r, l] delta[l] + F[s, r, r] delta[r]) = 0
2
bc := (diff(betaa(t), t, t))*m*v*betaa(t)+F[s, r, l]*delta[l]+F[s, r, r]*delta[r]-(diff(Psii(t), t)) = 0;
/ d / d \\
|--- |--- betaa(t)|| m v betaa(t) + F[s, r, l] delta[l]
\ dt \ dt //

/ d \
+ F[s, r, r] delta[r] - |--- Psii(t)| = 0
\ dt /
cd := (diff(betaa(t), t))*m*v+F[s, r, l]+F[s, r, r]+F[s, f, l]+F[s, f, r]-(diff(Psii(t), t)) = 0;
/ d \
|--- betaa(t)| m v + F[s, r, l] + F[s, r, r] + F[s, f, l]
\ dt /

/ d \
+ F[s, f, r] - |--- Psii(t)| = 0
\ dt /
F[s, f, l] := c[fl]*alpha[fl];
c[fl] alpha[fl]
F[s, f, r] := c[fr]*alpha[fr];
c[fr] alpha[fr]
F[s, r, l] := c[rl]*alpha[rl];
c[rl] alpha[rl]
F[s, r, r] := c[rr]*alpha[rr];
c[rr] alpha[rr]
alpha[fl] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(-v+(1/2)*b[f]*(diff(Psii(t), t)));
/ d \
-v betaa - l[f] |--- Psii(t)|
\ dt /
-----------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /
alpha[fr] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(v-(1/2)*b[f]*(diff(Psii(t), t)));
/ d \
-v betaa - l[f] |--- Psii(t)|
\ dt /
-----------------------------
1 / d \
v - - b[f] |--- Psii(t)|
2 \ dt /
alpha[rl] := delta[l]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v+(1/2)*b[r]*(diff(Psii(t), t)));
/ d \
-v betaa + l[r] |--- Psii(t)|
\ dt /
delta[l] + -----------------------------
1 / d \
-v + - b[r] |--- Psii(t)|
2 \ dt /
alpha[rr] := delta[r]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v-(1/2)*b[r]*(diff(Psii(t), t)));
/ d \
-v betaa + l[r] |--- Psii(t)|
\ dt /
delta[r] + -----------------------------
1 / d \
-v - - b[r] |--- Psii(t)|
2 \ dt /

ab;
/
|
/ d / d \\ |
|--- |--- Psii(t)|| J - l[f] |
\ dt \ dt // |
|
\

/ / d \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\ \ dt //
-------------------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /

/ / d \\\ / /
c[fr] |-v betaa - l[f] |--- Psii(t)||| | |
\ \ dt //| | |
+ -------------------------------------| + l[r] |c[rl] |delta[
1 / d \ | | |
v - - b[f] |--- Psii(t)| | | |
2 \ dt / / \ \

/ d \\
-v betaa + l[r] |--- Psii(t)||
\ dt /|
l] + -----------------------------|
1 / d \ |
-v + - b[r] |--- Psii(t)| |
2 \ dt / /

/ / d \\\ /
| -v betaa + l[r] |--- Psii(t)||| |
| \ dt /|| 1 |
+ c[rr] |delta[r] + -----------------------------|| - - b[r] |
| 1 / d \ || 2 |
| -v - - b[r] |--- Psii(t)| || |
\ 2 \ dt / // \
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
-c[rl] |delta[l] + -----------------------------| delta[l]
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\ \
| -v betaa + l[r] |--- Psii(t)|| |
| \ dt /| |
+ c[rr] |delta[r] + -----------------------------| delta[r]| =
| 1 / d \ | |
| -v - - b[r] |--- Psii(t)| | |
\ 2 \ dt / / /

0
bc;
/ d / d \\
|--- |--- betaa(t)|| m v betaa(t)
\ dt \ dt //

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rl] |delta[l] + -----------------------------| delta[l]
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rr] |delta[r] + -----------------------------| delta[r]
| 1 / d \ |
| -v - - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ d \
- |--- Psii(t)| = 0
\ dt /
cd;
/ d \
|--- betaa(t)| m v
\ dt /

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rl] |delta[l] + -----------------------------|
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rr] |delta[r] + -----------------------------|
| 1 / d \ |
| -v - - b[r] |--- Psii(t)| |
\ 2 \ dt / /

/ / d \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\ \ dt //
+ -------------------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /

/ / d \\
c[fr] |-v betaa - l[f] |--- Psii(t)||
\ \ dt // / d \
+ ------------------------------------- - |--- Psii(t)| = 0
1 / d \ \ dt /
v - - b[f] |--- Psii(t)|
2 \ dt /

Differential Transformation Method...

Asked by: PreethiPandian 15

February 20 2020

1 4

I'm trying to solve the couple of ode

and

with boundary conditions

using differential transformation method.Isolved the equations and found the parameter values,further i coudn't plot the graph.

Can any one help me out to solve this

Infinite summation problem...

Asked by: RLessard 90

February 19 2020

1 4

Hi !
I have several infinite sommations to evaluate. Maple 2018 on Windows 10 often gives me the solution in terms of hypergeometric functions. I know that the solution can be expressed in terms of sines and cosines.

I am not familiar with sumtools or Sumtools packages.

The convert (expr, StandardFunctions) or simplify (expr, hypergeom) commands do not work.

Here is an example of a sommation to evaluate.

My old version of Maple V release V (1997 version) gives me the desired result with the same commands.

Is there a command that forces Maple to give me the solution in terms of sines and cosines ?

I don't have Mathematica. I hate Mathematica with its difficult syntax but I have access to a computer with Mathematica.
There is a "FunctionExpand" command which converts hypergeometrics into standard functions.
For the previous summation it works very well.

Thanks !
Réjean

square power in maple...

Asked by: rameen hamood 30

February 19 2020

0 2

Use Maple to calculate 245 to the power of 272 (ie 245^272).

Enter the last three digits of this number in the box below.

Applying inverse Laplace and Fourier transforms...

Asked by: Jjjones98 45

February 19 2020

0 13

I have written a bit of code which solves a linear system for some quantities which have been Laplace and then Fourier transformed.

e1 := -2*D*i*k*pi + A*s = 0

e2 := 2*A*i*k*pi + 2*C*i*k*pi + B*s = a

e3 := s*C + 4/5*P*w3*(2*pi*i*k*D - 2*1/3*pi*i*k*D)/w2 = -2*(C + 2*K*(2*pi*i*k*B - 2*1/3*pi*i*k*B))/(w2*K)

e4 := s*D + 2*5/4*P*t4*pi*i*k*C/(t2*K) = -5/(2*P)*D/(t2*K)

sys := {s*C + 4/5*P*w3*(2*pi*i*k*D - 2*1/3*pi*i*k*D)/w2 = -2*(C + 2*K*(2*pi*i*k*B - 2*1/3*pi*i*k*B))/(w2*K), s*D + 2*5/4*P*t4*pi*i*k*C/(t2*K) = -5/(2*P)*D/(t2*K), -2*D*i*k*pi + A*s = 0, 2*A*i*k*pi + 2*C*i*k*pi + B*s = a}

solve(sys, [A, B, C, D])

Linear_System.mw

I get at the end some fractions where everything in the fractions is a constant with some physical meaning except for k which is the only frequency as I am working in one dimension so just need one-dimensional Fourier and Laplace transforms. s is the corresponding variable from the Laplace transform.

I was wondering if Maple had some functionality which would enable me to inverse Laplace and then inverse Fourier transform these quantities A, B, C and D from the linear system such that I obtain an algebraic expression at the end and not a numerical result.

Error, unable to parse...

Asked by: JTamas 20

February 19 2020

1 1

Hi all,

I have the attached code, it returns a "unable to parse" error after the line with the "FOC__1D1" assignment. I can't find out why.

Thank you for your help in advance,

JTamas

1_2_test.mw

How do I plot objects opaquely "in layer order"?...

Asked by: bnpndxtrwp 35

February 19 2020

3 2

I'm am pretty new to maple, coming from a mathcad background, so sorry in advance if this is a dumb question. My original need was to plot text objects with sold backgrounds on top of other plotted objects. I saw in other posts that Maple doesn't natively support this. So instead I'm trying to create a composite plot of objects by plotting text objects over polygons or rectangles. However I can't seem to make a given plotted object "cover" another plotted object.

Below is a simple example. The easy analogy is just that I want to plot these objects in “layer order”, with L1 being the top layer. So I would like the polygon to opaquely obscure the “underlying” contour plot, and then in turn, the text object to behave as a “top-most layer” with the polygon acting as a background for the text.

L1 := textplot([2, 2, "Polygon"], color = white);

L2 := polygon([[0, 0], [3, 4], [3, 1]], color = red);

L3 := contourplot(x^2 + y^2, x = 1 .. 2, y = 1 .. 2);

display(L3, L2, L1);

2 coupled PDEs...can't get solution: not convergin...

Asked by: Melvin Brown 124

February 19 2020

0 0

Can anyone help get solution to a coupled pair of PDEs

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
Newton iteration is not converging..

I attach file: SemiclassicalTestfile.mw

Melvin

Area outside cardiode and inside circle...

Asked by: imparter 175

February 19 2020

0 2

Dear maple user ,

I want to draw the area outside r=2+2*cos(theta) and inside r=3 ,where theta=0..2*pi.

I am attacing the sample figure.

thanks in advance

solving a system of ODE...

Asked by: Abdulkasim 0

February 19 2020

0 1

Why does "table" appear right under my equation? Like

Eq1 := .9*(diff(f(eta), eta, eta, eta))+.1*We*(diff(f(eta), eta, eta))*(diff(f(eta), eta, eta, eta))-(diff(f(eta), eta))^2+f(eta)*(diff(f(eta), eta, eta))^2+0.6e-1-.5*(diff(f(eta), eta))+.1*(table([w = 1.1]))(eta)*(1+beta1*(table([w = 1.1]))(eta))+.1*phi(eta)*N*(1+.1[c]*phi(eta)) = 0

How do I solve a system of higher order ODE in Map...

Asked by: Abdulkasim 0

February 19 2020

0 1

Hi,

I am trying to solve a system of 3 ODE of order 4.

Is there any template to do it?

When I try it, I get a message:

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 10, got 8
What is wrong with it?

> restart;
> with*plots; blt := 5;
> lambda := .1; delta := .1;
0.1
0.1
> gamma2 := .1;
0.1
> lambda2 := .1; lambda[T] := .7; lambda[C] = .1;
> Pr := 2;
> Nb := 0.1e-1;
> Nt := 0.1e-1;
> Sc := 0.1e-1;
> M := .5; E = -.1;
> N := 0.1e-1; n = .1;
> sigma[1] := .1;
> alpha[0] := 0; omega := 0;
0
0
> Eq1 := diff(f(eta), eta, eta, eta)+gamma2*((diff(f(eta), eta, eta))*(diff(f(eta), eta, eta))-f(eta)*(diff(f(eta), eta, eta, eta, eta)))-(1+lambda2)*((diff(f(eta), eta))*(diff(f(eta), eta))-f(eta)*(diff(f(eta), eta, eta)))-(1+lambda2)*M*sin(omega)^2*(diff(f(eta), eta))+(1+lambda2)(lambda*(1+lambda[T]*theta(eta))*theta(eta)+lambda*N*(1+lambda[C]*phi(eta))*phi(eta))*cos(alpha[0]) = 0;
2
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + 0.1 |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d / d / d / d \\\\ / d \
- 0.1 f(eta) |----- |----- |----- |----- f(eta)|||| - 1.1 |----- f(eta)|
\ deta \ deta \ deta \ deta //// \ deta /

/ d / d \\
+ 1.1 f(eta) |----- |----- f(eta)|| + 1.1 = 0
\ deta \ deta //
> Eq2 := diff(theta(eta), eta, eta)+Pr*f(eta)*(diff(theta(eta), eta))+Pr*Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Pr*Nt*((diff(theta(eta), eta))*(diff(theta(eta), eta))) = 0;
/ d / d \\ / d \
|----- |----- theta(eta)|| + 2 f(eta) |----- theta(eta)|
\ deta \ deta // \ deta /

2
/ d \ / d \ / d \
+ 0.02 |----- theta(eta)| |----- phi(eta)| + 0.02 |----- theta(eta)| = 0
\ deta / \ deta / \ deta /
> Eq3 := diff(phi(eta), eta, eta)+Sc*f(eta)*(diff(phi(eta), eta))+Nt*(diff(theta(eta), eta, eta))/Nb-Sc*sigma[1]*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta))) = 0;
/ d / d \\ / d \
|----- |----- phi(eta)|| + 0.01 f(eta) |----- phi(eta)|
\ deta \ deta // \ deta /

/ d / d \\
+ 1.000000000 |----- |----- theta(eta)||
\ deta \ deta //

n / E \
- 0.001 (1 + 0.1 theta(eta)) exp|- ------------------| = 0
\ 1 + 0.1 theta(eta)/
> bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(blt) = 0, (D(D(f)))(blt) = 0, theta(0) = 1, theta(blt) = 0, Nb*(D(phi))(0)+Nt*(D(theta))(0) = 0, phi(blt) = 0;
f(0) = 0, D(f)(0) = 1, D(f)(5) = 0, @@(D, 2)(f)(5) = 0, theta(0) = 1,

theta(5) = 0, 0.01 D(phi)(0) + 0.01 D(theta)(0) = 0, phi(5) = 0
> NULL;
> L := [.1, .5, 1.0, 5.0, 10.0];
[0.1, 0.5, 1.0, 5.0, 10.0]
>
> for k to 5 do R := dsolve(eval({Eq1, Eq2, Eq3, bcs1}, M = L[k]), [f(eta), theta(eta), phi(eta)], numeric, method = bvp[midrich], maxmesh = 4096, abserr = 0.1e-1, output = listprocedure); X1 || k := rhs(R[3]); X2 || k := rhs(R[4]); X3 || k := rhs(R[5]); Y1 || k := rhs(R[6]); Y2 || k := -rhs(R[7]); Z1 || k := rhs(R[8]); Z2 || k := -rhs(R[9]) end do;
Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 10, got 8
> R;
R

> print([(X1 || (1 .. 5))(0)]);
[X11(0), X12(0), X13(0), X14(0), X15(0)]
> print([(X2 || (1 .. 5))(0)]);
[X21(0), X22(0), X23(0), X24(0), X25(0)]
>
> print([(Y1 || (1 .. 5))(0)]);
[Y11(0), Y12(0), Y13(0), Y14(0), Y15(0)]
> print([(Y2 || (1 .. 5))(0)]);
[Y21(0), Y22(0), Y23(0), Y24(0), Y25(0)]
> print([(Z1 || (1 .. 5))(0)]);
[Z11(0), Z12(0), Z13(0), Z14(0), Z15(0)]
> print([(Z2 || (1 .. 5))(0)]);
[Z21(0), Z22(0), Z23(0), Z24(0), Z25(0)]
> NULL;
> NULL;
> plot([X1 || (1 .. 5)], 0 .. blt, labels = [eta, (D(f))(eta)], thickness = 1, color = black);
Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

> plot([Y1 || (1 .. 5)], 0 .. blt, labels = [eta, theta(eta)], thickness = 1, color = black);
Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

>
> plot([Z1 || (1 .. 5)], 0 .. blt, labels = [eta, phi(eta)], thickness = 1, color = black);
Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

>

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MaplePrimes Questions

How to get the real and imaginary parts of complex...

A problem for function or expression evaluation in...

Maybe a bug in MAPLE 2015's Explore ?...

how to write this ODE in Maple?...

How do I sort a formula in the following form...

Differential Transformation Method...

Infinite summation problem...

square power in maple...

Applying inverse Laplace and Fourier transforms...

Error, unable to parse...

How do I plot objects opaquely "in layer order"?...

2 coupled PDEs...can't get solution: not convergin...

Area outside cardiode and inside circle...

solving a system of ODE...

How do I solve a system of higher order ODE in Map...

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