Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

Hello. Tell me please how to fix it and build a graph? Thank you in advance.

p := PolyhedralSets([-x >= 0, -y >= 0, -z >= 0, -(1/2)*x >= 0, (-x-y)*(1/2) >= 0, (-x-z)*(1/2) >= 0], {y = -20}, [x, y, z]);
plot(p);
Error, (in plot) cannot determine plotting variable
 

I am trying to solve the equation

exp(2*sin(t))-1=0, over the interval 0 <= t <=  16

I tried entering this into Maple:

solve({exp(2*sin(t))-1=0, 0 <= t,t <= 16}, AllSolutions, Explicit)

When I enter it, Maple just says "Evaluating"... and then returns nothing.

I tried "solve" without AllSolutions/Explicit, and even fsolve.

Then Maple only gives me the trivial result t = 0.

Is there a way to approximate the roots, like a root solver.

Ideally I would like to get the exact roots over the interval [0,16].

Wolfram has no problem solving this exactly.https://www.wolframalpha.com/input/?i=solve(%5Bexp(2*sin(t))-1%3D0,+0+%3C%3D+t,t+%3C%3D+16%5D,+AllSolutions,+Explicit)

I posted the worksheet

solveroots.mw

Hello. I have the system of inequalities -x / 2> 0, -x> 0, (-x-y) / 2> 0, (-x-z) / 2> 0, -y> 0, -z> 0. Tell me, please, how to build a graph on it?

How I can pdsolve this partial fractional  equation?

1.mw
 

restart; CK := .3; Z := 10; L := 1; alpha := .95

###The Riemann–Liouville fractional integral H^alpha  is written in a convolution-form as:

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

 

#where GAMMA(...) represents the Gamma function

 

 
PDE := diff(theta(xi, beta), beta, beta)+L*(diff(theta(xi, beta), xi, beta, beta))+diff(theta(xi, beta), beta, beta, beta)+(1/2)*(diff(theta(xi, beta), beta, beta, beta, beta)) = H^(alpha-1)*CK*(diff(theta(xi, beta), xi, xi))+H(CK*Z+1)^(alpha-1)*(diff(theta(xi, beta), xi, xi, beta))+H^(alpha-1)*Z*(diff(theta(xi, beta), xi, xi, beta, beta))

Init := {theta(xi, 0) = 0, (D[2](theta))(xi, 0) = 0}

{theta(xi, 0) = 0, (D[2](theta))(xi, 0) = 0}

(1)

Bdry := {theta(0, beta) = 1, theta(10, beta) = 0}

{theta(0, beta) = 1, theta(10, beta) = 0}

(2)

smod1 := pdsolve(PDE, Init, Bdry, numeric)

 

 

``


 

Download 1.mw

 

Hi, 

I'm currently studying the Rossler Attractor, which is the following system:

diff(x(t), t) = -y(t)-z(t)

 diff(y(t), t) = x(t)+a*y(t)

diff(z(t), t) = b+x(t)*z(t)-c*z(t).

I have found the points of equilibrium of the system.

But now I need to draw bifurcation diagrams: one for varying a, one for varying b, and one for varying c.

 

Can someone please help me with a procedure of how to do this?

Thanks in advance.

 

Hi!

Consider, fixed an integer m>1, the mapping given by the following procedure:

 

G := proc (t) local k, C; C := NULL; C := t; for k from 2 to d do C := C, 1/2-(1/2)*cos(Pi*m^(k-1)*t) end do; return [C] end proc

Then, it can be proved that given x in the cube [0,1]^{d} there is t in [0,1] such that the norm of x-G(t) is less, or equal, than sqrt(d-1)/m. Indeed, dividing the cube [0,1]^{d} into m^{d-1} subcubes of side-length 1/m x ... x 1/m x 1, the point x belongs to some of these subcubes, say J. As, by the properties of the cosines function, the curve G(t) lies in J whenever t in certain subinterval of [0,1], the result follows.

In other words, computing all the solutions of the equation

1/2*(1-cos(Pi*m^(d-1)*t)) = x[d], (j-1)/m <= t and t <= j/m

for some of these solutions the desired t is obtained, where j is such that x1 in [(j-1)/m,j/m] (x1 is the first coordinate of the point x). However, for large values of m and d, the above equation have many solutions, I have tried find all of them and the process is extremely slow....Other way to find such a t can be the following: find a t satisfying the following system of inequalities

EQ := abs(t-x[1]) <= 1/m; for k from 2 to d do EQ := EQ, abs(1/2*(1-cos(Pi*m^(k-1)*t))-x[k]) <= 1/m end do

 

and then, a solution of this system is a such t. I do not know how to find, efficiently, a t such that of x-G(t) is less, or equal, than sqrt(d-1)/m   :(

Some idea?

Many thanks for your comments in advance.

 

Hi,
I am new to using maple and was wondering if i could get some help with this problem...

 

I'm having problems with 2b)

pell := proc (d, K)

local y; 

y := sqrt(d*x^2+1); 

d := 2; 

if y <= K then print*(x, y) end if 

end proc


this is what i have come up with, feel like it is completely wrong though.

Any help would be much appreciated.

I am having trouble getting Maple 2017.3 with latest Physics update to give solution to Burger's PDE for viscous fluid flow with the following initial condition. May be I am not doing something right. I tried different HINTS, but no luck.

Maple can solve the PDE without the initial conditions.

May be a Maple expert can find work around or show what I might be doing wrong.

restart;
pde := diff(u(x, t), t) + u(x, t)*diff(u(x, t), x) = mu*diff(u(x,t),x$2);
ic  := u(x,0) = PIECEWISE([0,x>=0],[1,x<0]);
sol := pdsolve({pde,ic}, u(x, t)) assuming mu>0;

Maple returns () as solution.

This PDE can be solved analytically. Here is Mathematica' solution

ClearAll[u,x,y,mu]
pde = D[u[x,t],{t}]+u[x,t]*D[u[x,t],{x}]==mu*D[u[x,t],{x,2}];
ic  = u[x,0]==Piecewise[{{1,x<0},{0,x>=1}}];
sol = DSolve[{pde,ic},u[x,t],{x,t},Assumptions->mu>0]

 

 

This is on Maple 2017.3 under windows

After obtaining solution from pdsolve(), I tried to see if Maple can convert it to hyperbolic trig functions by calling `convert(sol,trigh)`. 

 

I waited and waited and nothing happened. Then clicked on the `interrupt current operation` button at top of menu. 

But I found that mserver.exe has hanged in a loop. Taking 100% CPU and still running. So Had to terminate it from task manager.

Question is: It is ok if Maple can't do the conversion, but why does it hang? Maybe if I want for one hr it will finish, I do not know. But the important part, why does `interrupt current operation` does not work, in the sense that the mserver.exe is still running?

Is this common thing to happen? Should this be fixed? 

Here is example

 

restart;
interface(showassumed=0);
pde:=diff(u(x,y),x$2)+diff(u(x,y),y$2)=0;
f:=x-> piecewise(x>0 and x<1/2, 2*x, x>1/2 and x<1, 2-2*x);
bc:=u(0,y)=0,u(1,y)=0,u(x,0)=f(x),u(x,2)=f(x);
sol:=pdsolve([pde,bc],u(x,y)) assuming x>0,y>0;

The above works OK and generates a solution. Now the next call hangs mserver.exe

convert(sol,trigh);

In case your Maple version can't solve the above PDE. Here is the solution obtained, so you can try this below without having to solve the PDE

 

sol := u(x, y) = Sum(8*sin((1/2)*n*Pi)*sin(Pi*x*n)*(exp(Pi*n*(3*y-2))-
         exp(Pi*n*(3*y-4))+exp(Pi*y*n)-exp(Pi*n*(y-2)))*exp(-2*Pi*n*(y-2))/(Pi^2*n^2*(exp(4*n*Pi)-1)),
            n = 0 .. infinity);
convert(sol,trigh);

I also tried convert(rhs(sol),trigh); but it made no difference.

 

This is my code.  It's not appending as I need it to.  Any help would be humbly and gratefully appreciated!

 


 

restart; Sort4 := proc (Q, T, U, Rx1, Ry1, Rx2, Ry2, Rx3, Ry3, Rx4, Ry4) local i, k; description "Organizes vectors Q,T into new vectors Rx1...Ry4 correspponding to values of U."; for i from 5 to nops(U) do if U(i) = 1 then Append(Rx1, Q(i)); Append(Ry1, T(i)) elif U(i) = 2 then Append(Rx2, Q(i)); Append(Ry2, T(i)) elif U(i) = 3 then Append(Rx3, Q(i)); Append(Ry3, T(i)) elif U(i) = 4 then Append(Rx4, Q(i)); Append(Ry4, T(i)) end if end do; return Rx1, Rx2, Rx3, Rx4, Ry1, Ry2, Ry3, Ry4 end proc

Q, T, U := `<,>`(0, 2, 4, 6, 7, 17, 27, 57, 67, 97), `<,>`(0, 2, 1, 8, 19, 20, 21, 22, 23, 24), `<,>`(o, o, o, o, 1, 2, 3, 2, 4)

Vector[column](%id = 18446744078670632710), Vector[column](%id = 18446744078670632830), Vector[column](%id = 18446744078670632950)

(1)

Rx1 := Vector([Q(1)]); Ry1 := Vector([T(1)]); Rx2 := Vector([Q(2)]); Ry2 := Vector([T(2)]); Rx3 := Vector([Q(3)]); Ry3 := Vector([T(3)]); Rx4 := Vector([Q(4)]); Ry4 := Vector([T(4)])

_rtable[18446744078670623558]

 

_rtable[18446744078670624518]

 

_rtable[18446744078670625238]

 

_rtable[18446744078670625958]

 

_rtable[18446744078670626678]

 

_rtable[18446744078670619222]

 

_rtable[18446744078670619942]

 

Vector[column](%id = 18446744078670620662)

(2)

Sort4(Q, T, U, Rx1, Ry1, Rx2, Ry2, Rx3, Ry3, Rx4, Ry4)

Vector[column](%id = 18446744078670623558), Vector[column](%id = 18446744078670625238), Vector[column](%id = 18446744078670626678), Vector[column](%id = 18446744078670619942), Vector[column](%id = 18446744078670624518), Vector[column](%id = 18446744078670625958), Vector[column](%id = 18446744078670619222), Vector[column](%id = 18446744078670620662)

(3)

``


 

Download Sort4_320.mw

f(x)=sqrt(sin(x)); x over the intervall [0,T]

can anyone help me to find this integral ?

 

I might be doing something wrong since I expected Maple to be able to solve this. Could some Maple manage to make Maple solve the following beam PDE problem taken from a textbook?

 

This is what I tried.

restart;
pde:=diff(u(x,t),t$2)+diff(u(x,t),x$4)=0;
bc:=u(0,t)=-12*t^2,u(1,t)=1-12*t^2,D[1,1](u)(0,t)=0,D[1,1](u)(1,t)=12;
ic:=u(x,0)=x^4,D[2](u)(x,0)=0;
sol:=pdsolve({pde,ic,bc},u(x,t));

But Maple returns no solution.

I am using Maple 2017.3 on windows.

 

I have two tensors, E_ and F_ below, that I believe should be equal. But they are not, and I cannot understand why. The problem does not appear in, say, Schwarschild spacetime, but it appears in Boyer-Lindquist spacetime, metric [5,29,1]; perhaps it appears only if the vierbein is nondiagonal?

The code: Loading the packages and the metric:

restart:
with(Physics):
with(Tetrads):
g_[[5,29,1]];   # The Boyer-Lindquist metric

Set up galilean and nongalilean Levi-Civita's, respectively, following the recipe given elsewhere:

Define(varepsilon[a,b,c,d] = Array((1..4)$4,rhs(LeviCivita[nonzero])),quiet):
Setup(levicivita = nongalilean):
# Checking that the Levi-Civita's are indeed different
varepsilon[1,2,3,4];   # The galilean case
LeviCivita[1,2,3,4];   # The nongalilean case

Define the two tensors E_ and F_, using mixed type Levi-Civita's for the latter:

Define(
   E_[~a,mu] = varepsilon[~a,~b,~c,~d]*LeviCivita[mu,nu,rho,sigma]*e_[b,~nu]*e_[c,~rho]*e_[d,~sigma],
   F_[~a,mu] = varepsilon[~a,b,c,d]*LeviCivita[mu,~nu,~rho,~sigma]*e_[~b,nu]*e_[~c,rho]*e_[~d,sigma]
,quiet):
E_[definition];
F_[definition];

Compare the two expressions, which should be equal, I believe.

expr := simplify(TensorArray(E_[~a,mu] - F_[~a,mu])) assuming a::real,theta > 0,theta < Pi;
eval(expr,{a = 1,m = 1,r = 2,theta = Pi/4});   # Just to make the difference completely obvious

[I have trouble copy-pasting the output from these two lines, so you will have to execute the worksheet provided below to see it.]

However, they are not equal. Why not?

Download worksheet: MixedTypeLeviCivitas.mw.


 

Suppose I am given the following summation:

 

sum(a*i, i = 1 .. n)

``

Can Maple write the first few terms of the summation? For example, if I want to see first three terms of the summation, I'd like Maple to output the following:

 

a + 2 a + 3 a

 

My use case is that if I am given a complicated summation, it can be useful to look at the first few terms to see if there are any patterns.

 

The things I've tried are:

 

sum(a*i, i = 1 .. 3)

6*a

(1)

'sum(a*i, i = 1 .. 3)'

sum(a*i, i = 1 .. 3)

(2)

eval(sum(a*i, i = 1 .. 3))

6*a

(3)

expand(sum(a*i, i = 1 .. 3))

6*a````

(4)

``


 

Download expandsum.mw

In the realm of tetrads where both world indices and Lorentz indices are present, contractions, say, using simultaneously the Minkowskian (galilean) Levi-Civita symbol,

and the curvilinear Levi-Civita (pseudo-)tensor,

can be considered. Although each of the two types of Levi-Civitas can easily be obtained separately by specifying Setup(levicivita = galilean) or Setup(levicivita = nongalilean), I cannot figure out how to have them both available at the same time. Any suggestions?

PS: I am, of course, aware of the fact that the two Levi-Civitas are related by some appropiate square-root of the determinant of the metric, but I have no desire to fiddle around with explicit such determinants if they can be avoided.

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