Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Since I am a very recent Maple user, I do not know why I obtained a wrong answer with the following two comands:

Exp:= Psi(rho(x,t),theta(x,t));
                  Psi(rho(x, t), theta(x, t))
Exp1:= diff(Exp,t);
     / d           \                                  
     |--- rho(x, t)| D[1](Psi)(rho(x, t), theta(x, t))
     \ dt          /                                  

          / d             \                                
    + |--- theta(x, t)| Psi(rho(x, t) + 1, theta(x, t))
          \ dt            /                                
 

Can someone, please, help me?

Thank you.

 

The purpose of this post is to review how well-designed Maple 2017 GUI is for a Microsoft surface pro 4 tablet touch screen with windows 10 pro (64-bit) and to determine the performance of Maple 2017 on my tablet which has a m3 CPU with a 0.9 GHZ base frequency and 4 GB RAM.

First, my experience is that 4 GB of RAM is far from enough. Under heavy load I have had problems before on other software with 4 GB of RAM. 68 % of my RAM and 41% of the CPU is already gone by simply running Maple and my web browser at the same time before I have even instructed Maple to do any calculations.

 

I think a tablet with at least 8 GB of RAM would be preferred. If you only want to use Maple as an expensive calculator then you would most likely not even need 4 GB of RAM. I find that the surface pro 4 to be overpriced for the hardware it provides. I think eve windows 10 tablet http://eve-tech.com/ with up to 16 GB of RAM and with a much cheaper price looks much more promising than the Microsoft surface pro 4. When I use the surface pro 4 with word 2016 and the reference manager zotero word plugin I sometime notice a trailing line when I sweep up or down in a document with a lot of references which I suspect is because of the low amount of RAM. When I played with Maple 2017 on my surface pro I noticed the same trailing line which again indicates to me that there is not enough RAM. However, I am not certain that low RAM is the cause of such problem.  

Secondly, I managed to increase the size of the Maple icons under the File, Edit etc. menu so now they have a perfect size for a touch screen tablet. Very cool!

 

However, as you can see words in the text menu File, Edit etc. are way too small for a touch screen tablet. There is a lot of room to the right so the words could easily be increased in size. I am also a missing a menu item called maplet where you can attach your own maplets for easy access. It appears that Maple 2017 GUI has not been designed with a touch screen tablet in mind. I wish the words in the text menu File, Edit etc. would have increased when I increased the size of the icons. The text and icons in the sidebar are also way too small for a touch screen tablet. The name of the open tabs is also to small and x that you tap on to close the worksheet is also to small. It is almost impossible to close a worksheet because the x is so small. 

I thinks there are ways in windows 10 to increase the text size in the menus but I have only been able to increase the text size and icon size for all software at the same time. Since, Maple is more or less the only software that I have where the menu text is too small this is not an optimal solution.   

The table of content for Maple help files also has too small text as seen in the below picture. However, the biggest problem is not the small words it is the row spacing of the table of content. Some of the words appear almost to be on top of each other. I think the row spacing need to be increased. The text within the help files itself displays beautifully and is in the perfect size.   

 

Another problem is that when you swipe up or down on the touch screen you dont go up or down in the maple document. You just highlight text as seen in the picture below. This needs to be fixed. Highlighting should be done by a long tap on the screen as in word 2017 on a touch screen devices.

 

 

The norm today might be to use Maple on a desktop computer or on a laptop but I am convinced that in the future touch screen tablet will become more and more powerful making them an excellent computers to run Maple on because they are so light and portable. I think Maplesoft must have this in mind when they design the GUI.

Now to test the performance of Maple 2017 on my tablet I decided to generate 1 000 000 random number and see how long it takes. Since I dont have a benchmark it becomes very hard to comment on how fast maple 2017 is on my tablet but I am hoping that someone can run the same code on their machine and comment on this post so we can get a benchmark.        

time(rand()$1000000)

Maple 2017 claims that running such code took about 50 seconds on my tablet however when I timed it with a stop watch it only took around 30 seconds hence I am a bit confused as to where the 20 seconds difference comes from?  

 

I am using Maple to model Gaussian Wave Packets and the do loop creates an array of plots. I want to animate these plots to show the movement of the wave packet and was wondering if there is a way to animate the array or perhaps another way to produce the animation. 

how to add two algebaric equations? I have two equation (1) and (2). i simply wrote (1) + (2) instead of adding the eqautions i got result is 3. i think there is some mistake of writng text for calling equation that was in bold. 

adding_two_equations.mw

I am trying to evaluate the following triple integral but it takes much time so i kill the job.


 

restart; R := 5; KK := proc (theta) options operator, arrow; evalf(int(int(int(1/(R*sin(theta)^2+(R*cos(theta)+Z)^2+(2*R*k.sin(theta))*cos(p))^2, p = 0 .. 2*Pi), Z = 0 .. 60), k = 1 .. 10, numeric)) end proc; evalf(KK((1/6)*Pi))

Warning,  computation interrupted

 

``


 

Download int_maple_prime2.mw

with(DEtools, buildsym, equinv, symtest):
ans := dsolve([eq2,eq3,eq4], Lie);
Error, (in dsolve) too many arguments; some or all of the following are wrong: [{a(t), b(t), c(t)}, Lie]
 
ans := dsolve([eq2+eq3+eq4 = exp(t)], Lie);
Error, (in PDEtools/sdsolve) too many arguments; some or all of the following are wrong: [{a(t), b(t), c(t)}, Lie]
 
ans := dsolve([eq2,eq3,eq4]);
sym2 := buildsym(ans);
Error, (in buildsym) invalid input: `ODEtools/buildsym` expects its 1st argument, sol, to be of type {algebraic, algebraic = algebraic}, but received [{c(t) = ...}, {b(t) = ...}, {a(t) = ...)}]
 
 
PDEtools[declare](a(t), b(t), c(t), prime = t):
symgen(eq2+eq3+eq4=0);
                       a(t) will now be displayed as a
                       b(t) will now be displayed as b
                       c(t) will now be displayed as c
   derivatives with respect to t of functions of one variable will now be
      displayed with 'symgen(....)'
 
 
update
if it can not do for 3 function a(t),b(t),c(t) system of differential equations
then
 
i change to use
eq2 := subs(b(t)=a(t),subs(c(t)=a(t),eq2));
eq3 := subs(b(t)=a(t),subs(c(t)=a(t),eq3));
eq4 := subs(b(t)=a(t),subs(c(t)=a(t),eq4));
 
with(DEtools, buildsym, equinv, symtest):
ans := dsolve(eq2 = 0, Lie);
buildsym(ans[1], a(t));
buildsym(ans[2], a(t));
buildsym(ans[3], a(t));
 
there are 3 answers, can i use one of it to recover the equation eq2 or  eq3 or eq4?
 
ans := dsolve(eq3=0, Lie);
buildsym(ans[1], a(t));
sym2 := buildsym(ans[2], a(t));
buildsym(ans[3], a(t));

sym := [_xi=rhs(sym2[2]),_eta=rhs(sym2[1])];
ODE := equinv(sym, a(t));
eq3 - ODE;
sym := [_xi=rhs(sym2[1]),_eta=rhs(sym2[2])];
ODE := equinv(sym, a(t));
eq3 - ODE;
but ODE is not equal to original eq3
ans := dsolve(eq4=0, Lie);
buildsym(ans[1], a(t));
buildsym(ans[2], a(t));
 
ans := dsolve(eq2+eq3+eq4=0, Lie);
sym := buildsym(ans[1], a(t));
ODE := equinv(sym, a(t));
eq2+eq3+eq4 - ODE;
sym := buildsym(ans[2], a(t));
ODE := equinv(sym, a(t));
eq2+eq3+eq4 - ODE;
sym := buildsym(ans[3], a(t));
ODE := equinv(sym, a(t));
simplify(eq2+eq3+eq4 - - ODE);
 
can not recover the original result

Maple newbie here.

I do not understand why algsubs do not replace the symbol in the denominator in the following example, but does replace it in the numerator. This is on Maple 2017 on windows 7

Here is the expression

sol := u(x, t) = Sum((2*cos((1/2)*Pi*_Z1)+
       2+4*(-1)^(1+_Z1))*sin(Pi*_Z1*x/L)*
       exp(-k*Pi^2*_Z1^2*t/L^2)/(Pi*_Z1), 
       _Z1 = 1 .. infinity);

I wanted to replace _Z1  with n

But algsubs will not replace _Z1 in the denominator as seen in this screen shot but subs does:

 

 

From help, my impression is that algsubs is superset of subs. Only case where algsubs will not do what subs does is, according to help:

The algsubs command goes recursively through the expression . Unlike the subs command it does not substitute inside indexed names, and function calls are applied to the result of a substitution

 

But There is no indexed names here? 

Can someone please explain why algsubs fails to do the substitution in the denominator in this example?

 

 

 

 

I am trying to evaluate the following function for which I am getting a result 0. I just need to make sure the approach as well as result is correct or not. Thanks in advance. 
 

restart; Digits := 20; r := 5; Z := 0; KK := proc (phi) options operator, arrow; evalf(int(sin(phi)*sin(-arctan((p*cos(phi)+Z)/sqrt(p^2*sin(phi)^2+r^2)))*hypergeom([5/2, 3/2], [5/2], sin(-arctan((p*cos(phi)+Z)/sqrt(p^2*sin(phi)^2+r^2)))^2)/(p^2*sin(phi)^2+r)^2, p = -1 .. 1, numeric)) end proc; evalf(KK((1/6)*Pi))

0.

(1)

``


 

Download int(maple_prime).mw

I did change of variables as below:

 


 

``

restart

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

 

``

UP := Int(1/2*(K__ux0*u0(x, y, t)^2+K__vx0*v0(x, y, t)^2+K__wx0*w0(x, y, t)^2+`K__φx0`*phi(x, y, t)^2+`K__ψx0`*psi(x, y, t)^2), y = 0 .. b)+Int(1/2*(K__uxa*u0(x, y, t)^2+K__vxa*v0(x, y, t)^2+K__wxa*w0(x, y, t)^2+`K__φxa`*phi(x, y, t)^2+`K__ψxa`*psi(x, y, t)^2), y = 0 .. b)+Int(1/2*(K__uy0*u0(x, y, t)^2+K__vyb*v0(x, y, t)^2+K__wyb*w0(x, y, t)^2+`K__φyb`*phi(x, y, t)^2+`K__ψy0`*psi(x, y, t)^2), x = 0 .. a)+Int(1/2*(K__uyb*u0(x, y, t)^2+K__vyb*v0(x, y, t)^2+K__wyb*w0(x, y, t)^2+`K__φyb`*phi(x, y, t)^2+`K__ψyb`*psi(x, y, t)^2), x = 0 .. a):

varchange := {t = a*tau*sqrt(rho/A__ref), x = (1/2)*a*(Zeta+1), y = (1/2)*b*(eta+1), phi(x, y, t) = h*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau), psi(x, y, t) = h*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau), u0(x, y, t) = h*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau), v0(x, y, t) = h*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau), w0(x, y, t) = h*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)}:

``

Ut := PDEtools:-dchange(varchange, UP, [`#mover(mi("u"),mo("&uminus0;"))`, `#mover(mi("v"),mo("&uminus0;"))`, `#mover(mi("w"),mo("&uminus0;"))`, `#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`, `#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`, Zeta, eta, tau], params = [a, b, rho, A__ref]):

Ut

Int((1/2)*((1/2)*K__ux0*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vx0*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wx0*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φx0`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψx0`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*b, eta = -1 .. 1)+Int((1/2)*((1/2)*K__uxa*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vxa*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wxa*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φxa`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψxa`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*b, eta = -1 .. 1)+Int((1/2)*((1/2)*K__uy0*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vyb*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wyb*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φyb`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψy0`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*a, Zeta = -1 .. 1)+Int((1/2)*((1/2)*K__uyb*h^2*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__vyb*h^2*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*K__wyb*h^2*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__φyb`*h^2*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2+(1/2)*`K__ψyb`*h^2*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, eta, tau)^2)*a, Zeta = -1 .. 1)

(1)

simplify(Ut)

(1/4)*(b*(Int(K__ux0*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__vx0*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__wx0*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__φx0`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__ψx0`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2, _a = -1 .. 1))+b*(Int(K__uxa*`#mover(mi("u"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__vxa*`#mover(mi("v"),mo("&uminus0;"))`(Zeta, _a, tau)^2+K__wxa*`#mover(mi("w"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__φxa`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2+`K__ψxa`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(Zeta, _a, tau)^2, _a = -1 .. 1))+a*(Int(K__uy0*`#mover(mi("u"),mo("&uminus0;"))`(_a, eta, tau)^2+K__vyb*`#mover(mi("v"),mo("&uminus0;"))`(_a, eta, tau)^2+K__wyb*`#mover(mi("w"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__φyb`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__ψy0`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2, _a = -1 .. 1)+Int(K__uyb*`#mover(mi("u"),mo("&uminus0;"))`(_a, eta, tau)^2+K__vyb*`#mover(mi("v"),mo("&uminus0;"))`(_a, eta, tau)^2+K__wyb*`#mover(mi("w"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__φyb`*`#mover(mi("φ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2+`K__ψyb`*`#mover(mi("ψ",fontstyle = "normal"),mo("&uminus0;"))`(_a, eta, tau)^2, _a = -1 .. 1)))*h^2

(2)

``

``


 

Download simplifyss.mw

 

But I amezed when I use simplify command deteriorate my eq.

 

Why?

UPDATE

Thanks for checking. I verify I get the error and made screen shots below

When I add the convert() command, the error goes away. Here is screen shot

 

I am using Maple 2017, student version, on windows 7, 64 bit, home edition.

 

Original post

This is using Maple 2017 on windows.

With the following input, Maple pdsolve gives an error

pde:=diff(u(x,t),t)=k*diff(u(x,t),x$2);
bc:=D[1](u)(0,t)=0,D[1](u)(L,t)=0:
assume(L>0):
ic:=u(x,0)=piecewise(0<x and x<=L/2,0,L/2<x and x<L,1):
sol:=pdsolve([pde,bc,ic],u(x,t)):

However, if I add one line to convert the piecewise function above to piecewise, then pdsolve no longer gives an error. So the following input works

restart;
pde:=diff(u(x,t),t)=k*diff(u(x,t),x$2);
bc:=D[1](u)(0,t)=0,D[1](u)(L,t)=0:
assume(L>0):
ic:=u(x,0)=piecewise(0<x and x<=L/2,0,L/2<x and x<L,1):
ic:=convert(ic,piecewise,x):
sol:=pdsolve([pde,bc,ic],u(x,t)):

 

Notice the extra line. Why does one have to convert piecewise to piecewise to make pdsolve accept the input?

sorry did not write down the error message and I am writing this from school library PC. But if you try the first case, you'll see the error.

 

Hi! I have the system of differential equations

restart; with(plots); with(DEtools);

a := 1;

deq1 := u(s)*(diff(varphi(s), s, s))+2*(diff(u(s), s))*(diff(varphi(s), s))+sin(varphi(s)) = 0;

deq2 := diff(u(s), s, s)-u(s)*(diff(varphi(s), s))^2-cos(varphi(s))+a*(u(s)-1) = 0;

sol := dsolve({deq1, deq2, u(0) = 1, varphi(0) = (1/4)*Pi, (D(u))(0) = 0, (D(varphi))(0) = 0}, {u(s), varphi(s)}, numeric)

 

which is perfectly solved, but I need to convert it to Cartesian coordinates and draw a plot, so what I tried is

x := u(s)*sin(varphi(s));

y := -u(s)*cos(varphi(s));

plot([x, y, s = 0 .. 20])

 

But I'm getting an error "Warning, expecting only range variable s in expressions [u(s)*sin(varphi(s)), -u(s)*cos(varphi(s))] to be plotted but found names [u, varphi]"

I don't know why is this happens if I have a solution. For example, I can get solution for 2 seconds:

sol(2)

[s = 2., u(s) = 2.33095721668252, diff(u(s), s) = 1.02513293353371, varphi(s) = .213677391510693, diff(varphi(s), s) = -.242430995691885]

 

I posted my question at here https://math.stackexchange.com/questions/2314488/how-can-i-find-maximum-and-minimum-modulus-of-a-complex-number.
With Mathematica, I got min is 22/5. This result is different from my solution by hand.

Repeat my problem. Let be the number z so that $|z+1| + 4|z-1| = 25$. Find the greastest and the least of the modulus of $z$. How can I find greastest and the least of modulus of z with Maple.

How can we find ricci tensor of a metric attaced in given file that involve two unknown functions phi(r) and nu(r).metric.mw

i have an optimization problem, i want to maximize an expression using assumption, what should i do?


 

restart:with(Optimization):

M1:=Matrix((1,4),[sqrt(p),0,0,sqrt(1-p)]);

M1 := Matrix(1, 4, {(1, 1) = p^(1/2), (1, 2) = 0, (1, 3) = 0, (1, 4) = (1-p)^(1/2)})

(1)

M2:=Matrix((1,4),[cos(theta[1])*cos(theta[2]),exp(I*phi[1])*sin(theta[1])*cos(theta[2]),exp(I*phi[2])*sin(theta[2])*cos(theta[1]),exp(I*(phi[1]+phi[2]))*sin(theta[1])*sin(theta[2])])^+;

M2 := Matrix(4, 1, {(1, 1) = cos(theta[1])*cos(theta[2]), (2, 1) = exp(I*phi[1])*sin(theta[1])*cos(theta[2]), (3, 1) = exp(I*phi[2])*sin(theta[2])*cos(theta[1]), (4, 1) = exp(I*(phi[1]+phi[2]))*sin(theta[1])*sin(theta[2])})

(2)

#Real:=rhs(op(op(2,Re(M1.M2))));

PP:=Re(M1.M2)(1,1);

Re(p^(1/2)*cos(theta[1])*cos(theta[2])+(1-p)^(1/2)*exp(I*(phi[1]+phi[2]))*sin(theta[1])*sin(theta[2]))

(3)

maximize(PP) assuming 0<p ,p<1;

Error, (in assuming) when calling 'maximize'. Received: 'invalid input: `minimize/continuous` expects its 2nd argument, yFP, to be of type {name, list(name)}, but received `theta[1]` = -infinity'

 

 


 

Download optimize.mw

I have final project to make a media for learning mathematic using maple. But I'm so confused to make a net of cuboid, anybody can help me? please :D

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