Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

Hi

I use Maple 2016.

The following command calculates semicircle perimeter, but it returns infinity.

`assuming`([int(sqrt(1+(diff(sqrt(R^2-(x-R)^2), x))^2), x = 0 .. 2*R)], [R > 0])

I was trying to learn more about the commands in this package and found it to be someone non satisfying:


 

Download sockets_strangeness.mw

 

Maple gave Lie algebras of a system of PDE in which some of them do not leave the system invariant. Dont know whether the mistake is maple's or mine. File attached.



Maple_2016_bug_or...mw

 

restart:
with(PDEtools);
PDE :=  diff(y(x,t), t)-diff(y(x,t), x,x,t)-diff(y(x,t), x$2)+ diff(y(x,t), x)+y(x,t)*diff(y(x,t),x)=exp(-t)*(cos(x)-sin(x)+1/2*exp(-t)*sin(2*x));

# Initial/boundary conditions 
  BCs:=y(0,t) = 0, y(Pi,t)=0;
  ICs:=y(x,0) =sin(x) ;

pdsolve(PDE, {BCs,ICs});
exact_solution:=exp(-t)*sin(x);
Test1:=pdetest(exact_solution,[PDE, BCs,ICs]); 

The solution of the PDE is exp(-t)*sin(x).

I want to check whether it is right or not by Maple. 

I wrote the code. You can download the code.mw  

But, the code doesn' t work. What is the problem?

Thanks.

 

The worksheet below animates a hamster running back and forth on a linear floor within a wheel. Its motion is such that the wheel remains stationary.

What math would describe the hamster running back and forth such that the wheel oscillates with a constant frequency and the floor's vertical angle oscillates between plus and minus an angle greater than zero and less than 2 Pi?

Hamster_in_wheel.mw

I am trying to solve a simple two-equation linear system with solve, but I keep getting this weird result where the magnitude order of the numerator and denominator don't cancel out. Whenever I have a linear system with floating-point numbers, more unknowns than equations and try to solve it for a specific set of variables, this happens.

Any suggestions on how to get around this? Or do I need to solve it manually?

Can you help me

myproc := proc () local img1, img2, img3;

with(DocumentTools); with(DocumentTools:-Layout);

img1 := "c:\\1.jpg"; img2 := "c:\\2.jpg"; img3 := "c:\\3.jpg";

print("Title 1 row 1, picture 1"); print(img1); print("Title 2 row 2, picture 2");

print(img2); print("Title 3 row 3, picture 3"); print(img3);

print("The End");

end proc

``

myproc := proc () local img1, img2, img3; with(DocumentTools); with(DocumentTools:-Layout); img1 := "c:\\1.jpg"; img2 := "c:\\2.jpg"; img3 := "c:\\3.jpg"; print("Title 1 row 1, picture 1"); print(img1); print("Title 2 row 2, picture 2"); print(img2); print("Title 3 row 3, picture 3"); print(img3); print("The End") end proc:

``


 

Download insert_picture.mw

print monitor

 

Can someone please explain to me why this occurs:

 


 

with(StringTools):

Join(["H:\\USB 1 BACKUP\\ESD-USB\\", "Chemical Engineering"])

"H:\USB 1 BACKUP\ESD-USB\ Chemical Engineering"

(1)

convert("H:\\USB 1 BACKUP\\ESD-USB\\ Chemical Engineering", 'symbol')

`H:\USB 1 BACKUP\ESD-USB\ Chemical Engineering`

(2)

convert('`H:\USB 1 BACKUP\ESD-USB\ Chemical Engineering`', 'string')

"H:USB 1 BACKUPESD-USBChemical Engineering"

(3)

``


 

Download this_makes_me_grumpy.mw

Hello,

I am trying to solve a set of coupled ODEs in the following code (ODE_Prob.mw). But I am getting an error.

Please, what does this error mean and what is the solution.

Thanks in advance. 
 

restart; PDEtools[declare](f(eta), prime = eta, theta(eta), prime = eta); Digits := 16; inf := 9

f(eta)*`will now be displayed as`*f

 

`derivatives with respect to`*eta*`of functions of one variable will now be displayed with '`

 

theta(eta)*`will now be displayed as`*theta

(1)

equ1 := (2*n+1)*f(eta)*(diff(theta(eta), eta))/(2*(n+1)) = (diff(theta(eta), eta, eta))/Pr^(2/(n+1))

(2*n+1)*f(eta)*(diff(theta(eta), eta))/(2*n+2) = (diff(diff(theta(eta), eta), eta))/Pr^(2/(n+1))

(2)

equ2 := (1/2)*(diff(f(eta), eta))^2-(2*n+1)*f(eta)*(diff(f(eta), eta, eta))/(2*n+2) = -n*(diff(f(eta), eta, eta))^(n-1)*(diff(f(eta), eta, eta, eta))+theta(eta)

(1/2)*(diff(f(eta), eta))^2-(2*n+1)*f(eta)*(diff(diff(f(eta), eta), eta))/(2*n+2) = -n*(diff(diff(f(eta), eta), eta))^(n-1)*(diff(diff(diff(f(eta), eta), eta), eta))+theta(eta)

(3)

indets(equ1);

{Pr, eta, n, Pr^(2/(n+1)), diff(diff(theta(eta), eta), eta), diff(theta(eta), eta), f(eta), theta(eta)}

 

{eta, n, (diff(diff(f(eta), eta), eta))^(n-1), diff(diff(diff(f(eta), eta), eta), eta), diff(diff(f(eta), eta), eta), diff(f(eta), eta), f(eta), theta(eta)}

(4)

Bcs := f(0) = 0, (D(f))(0) = 0, (D(f))(inf) = 1, theta(0) = 1, theta(inf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(f))(9) = 1, theta(0) = 1, theta(9) = 0

 

1.301763965

 

1.4

(5)

equ1;

.7916666666666667*f(eta)*(diff(theta(eta), eta)) = .8027059130737796*(diff(diff(theta(eta), eta), eta))

 

(1/2)*(diff(f(eta), eta))^2-.7916666666666667*f(eta)*(diff(diff(f(eta), eta), eta)) = -1.4*(diff(diff(f(eta), eta), eta))^.4*(diff(diff(diff(f(eta), eta), eta), eta))+theta(eta)

(6)

SolP1 := dsolve({Bcs, equ1, equ2}, numeric); SolP1(0); SolP1(inf)

Error, (in dsolve/numeric/BVPSolve) unable to store '-.4744942626692375+1.460343180701223*I' when datatype=sfloat

 

SolP1(0)

 

SolP1(9)

(7)

p1 := plots:-odeplot(SolP1, [eta, f(eta)], 0 .. inf); p2 := plots:-odeplot(SolP1, [eta, theta(eta)], 0 .. inf); p3 := plots:-odeplot(SolP1, [eta, diff(f(eta), eta)], 0 .. inf); plots:-display(Array([p1, p2, p3]))

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots:-display) element 1 of the rtable is not a valid plot structure

 

``


 

Download ODE_Prob.mw

 

The uploaded worksheet describes a mechanics scenario which I would like to animate.

While I understand the expression for the kinetic energy of the torus, the term containing cos(theta) within the expression for the KE of the pearl baffles me.

From which physics aspect of the scenario does this term derive?

Pearl_in_torus.mw


 

eq := solve({2*m-5 < 0, -3*m <= 5}, {m})

{-5/3 <= m, m < 5/2}

(1)

" implies result list m  in  `&Zopf;`, so m can m=0, m=1, m=2 and count=3"``

count := 0:

countt = 4

(2)

``

``

``

eq := solve({m-3 < 0, -m <= 6}, {m})

{-6 <= m, m < 3}

(3)

" implies result list m  in  `&Zopf;`, so m can m=-6, m=-5, m=-4, m=-3, m=-2, m=-1, m=0, m=1, m=2 and count=3"

count := 0:

countt = 9

(4)

``


i want to list variable m in integer number from solve?

Can you help me?

@acer

@Carl Love

Download help_list_integer_equation.mw

Hello, i'm doing an interface for LU decomposition. I need to do a multiple windows interface using maplets, and i want to click one button on the inicial interface to open another window with other interface. I also need to create the second interface having N TextFields (N value will be inserted on the first window). Somebody knows how to do it?

Hello,

I'm new to Maple, but somewhat competent in computer mathematics. Below is some code that I wrote. I start off with f, my original function, and try to simplify it. I tried defining some assumptions as best I could. When I calculate the integral, it gives me an odd range of validity.

I'm wondering if I can further add to my assumptions to make the integral result more concise, i.e. without the piecewise range of validity. All my variables in f and g are already real and positive, so there is no reason one of the expressions should be less than zero. 

Thank you in advance for any insight.

 flat-geometry_recalc_Aug20_singleS.mw
 

f := (Pi*x+2*c+2*m)/(mu__c*S)+2*epsilon/(mu__a*S)+(Pi*x+2*c)/(mu__s*S)

(Pi*x+2*c+2*m)/(mu__c*S)+2*epsilon/(mu__a*S)+(Pi*x+2*c)/(mu__s*S)

(1)

g := simplify(f, symbolic)

(((Pi*x+2*c+2*m)*mu__s+2*((1/2)*Pi*x+c)*mu__c)*mu__a+2*epsilon*mu__c*mu__s)/(mu__c*S*mu__a*mu__s)

(2)

`assuming`([g], [S__s::positive]); 1; S__c::positive, S__a::positive, epsilon::positive, mu__s::positive, mu__c::positive, mu__a::positive, c::positive, m::positive

S__c::positive, S__a::positive, epsilon::positive, mu__s::positive, mu__c::positive, mu__a::positive, c::positive, m::positive

(3)

int(1/g, x = 0 .. w, AllSolutions)

`assuming`([int(1/g, x = 0 .. w)], [0 < w])

piecewise(And((c*mu__a*mu__c+c*mu__a*mu__s+epsilon*mu__c*mu__s+m*mu__a*mu__s)/(mu__a*(mu__c+mu__s)) < 0, -2*(c*mu__a*mu__c+c*mu__a*mu__s+epsilon*mu__c*mu__s+m*mu__a*mu__s)/(Pi*mu__a*(mu__c+mu__s)) < w), undefined, mu__s*S*mu__c*(-ln(2)-ln(c*mu__a*mu__c+c*mu__a*mu__s+epsilon*mu__c*mu__s+m*mu__a*mu__s)+ln(Pi*mu__a*mu__c*w+Pi*mu__a*mu__s*w+2*c*mu__a*mu__c+2*c*mu__a*mu__s+2*epsilon*mu__c*mu__s+2*m*mu__a*mu__s))/(Pi*(mu__c+mu__s)))``

(4)

 

NULL


 

Download flat-geometry_recalc_Aug20_singleS.mw

 

Hello!

I recently began learning how to 3D print with maple using the "Export & .stl " command together.

I was wondering if anyone knew how to increase the surface thickness for parametric plots and implicit plots. My hope would be to increase the "extrusion level" so to say.

I came across:

https://www.mapleprimes.com/questions/134103-Plotting-3d-Surfaces-With-A-Thickness

But I am not sure how to extend this idea to a parametric surface or an implict surface.

 

One more quick tidbit is that I will be trying to print several surfaces arising in differential geometry and algebraic geometry. Severel of these surfaces are open and or have singularities that I would like to "smooth out."

 

I would love to hear any ideas and thanks!

1 2 3 4 5 6 7 Last Page 1 of 51