MaplePrimes Questions

Hello, 

I hope you are doing well. I have the followig equation which I want to solve w.r.t.o (x). Maple took more than 12 hours for evaulation and still no solution. What could be the reason? Could you please help. 

 

 

(.5*(-sqrt(1/(.5*(sqrt(2*x)-sqrt(2*(1-x)))^2)+1)+1/(.5*(sqrt(2*x)-sqrt(2*(1-x)))^2)+1))/(2/(.5*(sqrt(2*x)-sqrt(2*(1-x)))^2)+2)+(.5*(-sqrt(1/(.5*(sqrt(2*x)+sqrt(2*(1-x)))^2)+1)+1/(.5*(sqrt(2*x)+sqrt(2*(1-x)))^2)+1))/(2/(.5*(sqrt(2*x)+sqrt(2*(1-x)))^2)+2) = (1/2)*sqrt(2)*(2*(-2^1.5*sqrt(.5*sqrt(2*(1-x))^2)/(2*sqrt(2*sqrt(2*(1-x))^2*.5+1))+sqrt(.5*sqrt(2*(1-x))^2)/(2*sqrt(.5*sqrt(2*(1-x))^2+1))+.5)-sqrt(.5*(sqrt(2*x)+sqrt(2*(1-x)))^2)/(2*sqrt(2*(sqrt(2*x)+sqrt(2*(1-x)))^2*.5+1))-sqrt(.5*(sqrt(2*x)+sqrt(2*(1-x)))^2)/(2*sqrt(.5*(sqrt(2*x)+sqrt(2*(1-x)))^2+1))-.5+sqrt(.5*(2*sqrt(2*x)+sqrt(2*(1-x)))^2)/(2*sqrt(2*(2*sqrt(2*x)+sqrt(2*(1-x)))^2*.5+1))+sqrt(.5*(2*sqrt(2*x)+sqrt(2*(1-x)))^2)/(2*sqrt(.5*(2*sqrt(2*x)+sqrt(2*(1-x)))^2+1))+.5+(sqrt(.5*(sqrt(2*x)-sqrt(2*(1-x)))^2)/(2*sqrt(2*(sqrt(2*x)-sqrt(2*(1-x)))^2*.5+1))+sqrt(.5*(sqrt(2*x)-sqrt(2*(1-x)))^2)/(2*sqrt(.5*(sqrt(2*x)-sqrt(2*(1-x)))^2+1))+.5)-sqrt(.5*(2*sqrt(2*x)-sqrt(2*(1-x)))^2)/(2*sqrt(2*(2*sqrt(2*x)-sqrt(2*(1-x)))^2*.5+1))-sqrt(.5*(2*sqrt(2*x)-sqrt(2*(1-x)))^2)/(2*sqrt(.5*(2*sqrt(2*x)-sqrt(2*(1-x)))^2+1))-.5)*c

As a challenge problem.  At what x,y coordinate does circle B (radius r) make contact with circle A (radius R)?  Let's suppose the center of circle A is at (0,0).  The height circle B sits at, is d above the 0 x-axis. 

 

I'm trying to create an ellipsoid using spherical coordinates.

 
                   "x^2 + y^2/4 + z^2/9 = 1" how can I enter this?

This is what I have , but shape show up really crazy

plot3d([cos(theta)*sin(phi),sin(theta)*sin(phi),cos(phi)],theta=0..2*Pi,phi=0..Pi,scaling=constrained,axes=boxed);

Thanks

[An edited and reposted version of this Question, which has subsequently been deleted, specifically asked that the plot be done by making a small adjustment to Maple's spherical coordinates. The deleted version also named the ellipsoid E, a detail which is important for understanding correctly the OP's subsequent integration Question. --Carl Love acting as a Moderator]

I have a system of 3 equations in four variables (x, y, s, t) that I would like to solve (numerically).  I would like to obtain a plot in 2 dimensions (x,y) of the curve of solutions. I'm not so bothered about what the corresponding (s,t) values are.  The equations are huge, taking up many screens worth and of very high degree.  What is the best way in Maple to solve / draw the plot numerically?

restart;
The integral int(x, x);
Error, missing operator or `;`

 

So from this

https://www.maplesoft.com/support/help/maple/view.aspx?path=MaplePortal%2FTutorial2#bkmrk1

I tried to switch between both modes, but I get the error above. Why does it not work? Do I need to consider something else? I'm switching with F5. The text is red and math is 2d math black.

 

 

Also the [CTRL]+[=] doesn't work in this german version, since I would need to press

[CTRL]+[SHIFT]+[=] which doesn't work.

Hello

I am looking for the table containing the value m,vv and mm. and these values I can easily copy and paste in excel sheet. 

Plz suggest commands 

 

Thanks Dummy_5.mw

Given the following functions, graph them and identify relative and absolute extrema (if any).

f(x)=3x^3-2x^2+5x-7     [-3,6]

Hello

for Example

A is vector A[r[= x+y , this is the equation generating multiple values. some are real and some are imaginery like,20,133, 2+3i,3+3i. I am interested the value which ilies within certain limits like 10-30. Here in this example 20 fits. So A[r] vector should store 20 only. How to do it.

 

Please help me on that. 

Thanks 

I'm doing a statistic analysis on a lot of data which i have imported from Excel into a matrix. I've got about 2880 data points and i'm trying to use regression and its giving me an error which i do not know how to deal with.

How would i execute the following calculate? I know i could use the statistics package but i want to do with with the formula. I'm trying to find the standard deviation. Look at the attached picture so see. I've also attached a copy of the calculations in maple format.

Download Test.mw

Also another little side thing, but not necessary. Is it possible to have a matrix with empty spaces in it and return it?

Is there any Maple code that allows to view a complex function using the "domain coloring" technique?

This technique is described for example in Wikypedia: https://en.wikipedia.org/wiki/Domain_coloring

How I can determine a function that satisfy these boundary and initial conditions.

Thank you

S2

Maple Worksheet - Error

Failed to load the worksheet //convert/S2
 

Download S2

 

How I can do ?

Thank you.

 

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and q = {`u__m,n`(t), `v__m,n`(t), `w__m,n`(t)}^T.

\where the elements of the vector,q_i are the time-dependent generalized coordinates.

L_Maple
 

U = (1/2)*(int(int(int(E*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x))+v(x, y, t)*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y))))*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x)))/(-nu^2+1)+E*(`∂`(nu(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y))+v(x, y, t)*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*(`∂`(w(x, y, t))/`∂`(x))^2+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w__0(x, y, t))/`∂`(x))-z*(diff(w(x, y, t), x, x))))*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*(`∂`(w(x, y, t))/`∂`(y))^2+`∂`(w(x, y, t))/`∂`(y)*(`∂`(w__0(x, y, t))/`∂`(y))-z*(diff(w(x, y, t), y, y)))/(-nu^2+1)+E*(`∂`(u(x, y, t))/`∂`(y)+`∂`(v(x, y, t))/`∂`(x)+`∂`(w(x, y, t))/`∂`(x)*(`∂`(w(x, y, t))/`∂`(y))+`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y))+`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y))-2*z*(diff(w(x, y, t), x, y)))^2/(2*(1+nu))+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), y, y)-(diff(w(x, y, t), x, x)))^2/(2*(1+nu))+E*l^2*(diff(v(x, y, t), y, y)-(diff(u(x, y, t), x, x)))^2/(8*(1+nu))+E*l^2*(diff(v(x, y, t), x, y)-(diff(u(x, y, t), y, y)))^2/(8*(1+nu)), z = -(1/2)*h .. (1/2)*h), y = 0 .. b), x = 0 .. a))

U = (1/2)*(int(int((1/12)*(-E*(-v(x, y, t)*(diff(diff(w(x, y, t), y), y))-(diff(diff(w(x, y, t), x), x)))*(diff(diff(w(x, y, t), x), x))/(-nu^2+1)-E*(-v(x, y, t)*(diff(diff(w(x, y, t), x), x))-(diff(diff(w(x, y, t), y), y)))*(diff(diff(w(x, y, t), y), y))/(-nu^2+1)+4*E*(diff(diff(w(x, y, t), x), y))^2/(2+2*nu))*h^3+E*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2+v(x, y, t)*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2))*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2)*h/(-nu^2+1)+E*(`∂`(nu(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2+v(x, y, t)*(`∂`(u(x, y, t))/`∂`(x)+(1/2)*`∂`(w(x, y, t))^2/`∂`(x)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(x)^2))*(`∂`(v(x, y, t))/`∂`(y)+(1/2)*`∂`(w(x, y, t))^2/`∂`(y)^2+`∂`(w(x, y, t))*`∂`(w__0(x, y, t))/`∂`(y)^2)*h/(-nu^2+1)+E*(`∂`(u(x, y, t))/`∂`(y)+`∂`(v(x, y, t))/`∂`(x)+`∂`(w(x, y, t))^2/(`∂`(x)*`∂`(y))+2*`∂`(w__0(x, y, t))*`∂`(w(x, y, t))/(`∂`(x)*`∂`(y)))^2*h/(2+2*nu)+2*E*l^2*(diff(diff(w(x, y, t), x), y))^2*h/(1+nu)+E*l^2*(diff(diff(w(x, y, t), y), y)-(diff(diff(w(x, y, t), x), x)))^2*h/(2+2*nu)+E*l^2*(diff(diff(v(x, y, t), y), y)-(diff(diff(u(x, y, t), x), x)))^2*h/(8+8*nu)+E*l^2*(diff(diff(v(x, y, t), x), y)-(diff(diff(u(x, y, t), y), y)))^2*h/(8+8*nu), y = 0 .. b), x = 0 .. a))

(1)

T = rho*h*(int(int((`∂`(u(x, y, t))/`∂`(t))^2+(`∂`(v(x, y, t))/`∂`(t))^2+(`∂`(w(x, y, t))/`∂`(t))^2, y = 0 .. b), x = 0 .. a))

T = rho*h*(int(int(`∂`(u(x, y, t))^2/`∂`(t)^2+`∂`(v(x, y, t))^2/`∂`(t)^2+`∂`(w(x, y, t))^2/`∂`(t)^2, y = 0 .. b), x = 0 .. a))

(2)

F = (1/2)*c*(int(int((`∂`(u(x, y, t))/`∂`(t))^2+(`∂`(v(x, y, t))/`∂`(t))^2+(`∂`(w(x, y, t))/`∂`(t))^2, y = 0 .. b), x = 0 .. a))

F = (1/2)*c*(int(int(`∂`(u(x, y, t))^2/`∂`(t)^2+`∂`(v(x, y, t))^2/`∂`(t)^2+`∂`(w(x, y, t))^2/`∂`(t)^2, y = 0 .. b), x = 0 .. a))

(3)

W = int(int(w(x, y, t)*f__1(x, y, t)*cos(omega*t), y = 0 .. b), x = 0 .. a)

W = int(int(w(x, y, z)*f__1(x, y, z)*cos(omega*t), y = 0 .. b), x = 0 .. a)

(4)

u(x, y, t) = sum(sum(`u__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

u(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(5)

v(x, y, t) = sum(sum(`v__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

v(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(6)

w(x, y, t) = sum(sum(`w__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

w(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(7)

diff(`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), t)-`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(F(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`) = `∂`(W(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), j = 1, () .. (), N

(D(`∂`))(T(x, y, t))*(diff(T(x, y, t), t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)-`∂`(T(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+2*`∂`(U(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`)+`∂`(F(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`) = `∂`(W(x, y, t))/`∂`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("."),none(),none())`), j = 1, () .. (), N

(8)

NULL


 

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How come maple doesn't support symbolic matrix calculus?

For example, I'd like to differentiate or simplify expressions with relation to general vectors and matrices. Besides simpifying the expressions, in runtime (e.g. optimizing a function in matlab) my vector and matrix size change according to the data, so deriving specific expressions element-wise would only be valid for a specific case.

A simple example (A is a matrix, x is a vector):

f(x) = ||Ax||^2

df/dx = 2A'Ax

Recently, I stumbled into this

http://www.matrixcalculus.org/

where you can try my example above: norm2(A*x)^2

I was wondering how come that mature symbolic softwares on the market (maple and mathematica) can't do it?

An hour or two ago, I answered a question in which it was a question of plotting a complex-valued function of 2 real variables. But the question itself and also my answer to it disappeared somewhere. Therefore, I send my answer here below.

There are two options for plotting:
1. Graphs of real and imaginary parts (as 2 surfaces in 3D).
2. Graph of the absolute value of this function (one surface in 3d) .

restart;
f:=(1+cosh(2*x))*exp(-4*I*t):
plot3d([Re,Im](f), x=0..1, t=0..1, color=[red,blue]);
plot3d(sqrt(add([Re,Im](f)^~2)), x=0..1, t=0..1, color=green);

 

I define the spherical Bessel function with j([n, z]) := sqrt(2)*sqrt(Pi/z)*BesselJ(n + 1/2, z)/2.  Then I attempt to plot with

Digits := 20;
plot(j([1, z]), z = 0 .. 25);

I get an empty plot and an error message: 

Warning, expecting only range variable z in expression j([1, z]) to be plotted but found name j

which makes no sense to me.

(I am using Maple 2019.)

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