MaplePrimes Questions

I am trying write a code for this question at here 

https://math.stackexchange.com/questions/170319/how-many-triangles-with-integral-side-lengths-are-possible-provided-their-perim/170325#170325

but I got the wrong answer. This is my code.
 

restart; 
L := []; 
for a to 18 do
 for b to 18 do 
for c to 18 do 
if a < b+c and b < a+c and c < b+a and a > abs(b-c) and b > abs(a-c) and c > abs(a-b) and a+b+c = 36 then
 L := [op(L), [a, b, c]] end if end do end do end do;
 nops(L); 
L

I got 136 triangles. This is a wrong answer. How can I repair my code?

how I can pdsolve these equations?

moadelat.mw


 

NULL

restart

f1 := -3*(diff(theta(r, z), z))+(diff(r*(diff(theta(r, z), r)), r))/r+diff(theta(r, z), z, z)+2*((diff(theta(r, z), r))*(diff(sigma(r, z), r))+(diff(sigma(r, z), z))*(diff(theta(r, z), z)))+4*((diff(theta(r, z), r))^2+(diff(theta(r, z), z))^2) = 0; f2 := -3*(diff(sigma(r, z), z))+2*((diff(r*(diff(sigma(r, z), r)), r))/r+diff(sigma(r, z), z, z))+(diff(r*(diff(theta(r, z), r)), r))/r+diff(theta(r, z), z, z) = 0

-3*(diff(theta(r, z), z))+(diff(theta(r, z), r)+r*(diff(diff(theta(r, z), r), r)))/r+diff(diff(theta(r, z), z), z)+2*(diff(theta(r, z), r))*(diff(sigma(r, z), r))+2*(diff(sigma(r, z), z))*(diff(theta(r, z), z))+4*(diff(theta(r, z), r))^2+4*(diff(theta(r, z), z))^2 = 0

 

-3*(diff(sigma(r, z), z))+2*(diff(sigma(r, z), r)+r*(diff(diff(sigma(r, z), r), r)))/r+2*(diff(diff(sigma(r, z), z), z))+(diff(theta(r, z), r)+r*(diff(diff(theta(r, z), r), r)))/r+diff(diff(theta(r, z), z), z) = 0

(1)

f3 := sigma(r, 0) = 1, theta(r, 0) = 1, (D[2](theta))(r, 1) = 0, (D[2](sigma))(r, 1) = 0, (D[1](theta))(0, z) = 0, (D[1](sigma))(0, z) = 0, sigma(1, z) = 1, theta(1, z) = 1

sigma(r, 0) = 1, theta(r, 0) = 1, (D[2](theta))(r, 1) = 0, (D[2](sigma))(r, 1) = 0, (D[1](theta))(0, z) = 0, (D[1](sigma))(0, z) = 0, sigma(1, z) = 1, theta(1, z) = 1

(2)

``


 

Download moadelat.mw

I have multiple accounts. I would like to delete them. Please tell me how to delete it. Thank you.


How can I plot functions Vc=(0.5+t)^n

with t=z/h, 

Hai any one help me to plot the curves and remove the errors  i am attaching the codes and  sample graph. thanks in advanced.
 

 

test.mw

 

 

Hi all,

I'm struggling with solving a delayed differential equation with time-dependent delay.

 

I have already use dde solver with matlab and find it cannot reaches my numerical accuracy. 

 

Does maple can solve this problem? I explore a little bit and don't find there is a document to guide how to tackle with this problem.

 

Constant delay cannot solve my problem.

 

Thank you very much,

 

Peter

Is there a solve(identity ...) command for systems? I have 4 identities in the variable t.
They are Q1, Q2, Q3, Q4. I try solve(identity(Q1,Q2,Q3,Q4),t), A, B, C, D), and other forms of it, but
nothing works.
Thank you!

maplatha
 

I solved an ODE numerically. Code: question_(2).mw

delta*(M(t)*diff~(X, t$2)+C(t)*diff~(X, t))+K(t)*X=f(t)

How to calculate X(t) for different values t and to create a table like following. 

 

 

 

I tried to solve an equation with a A0^2*v0 + .....................= 0 with 0 as a subscripted Index. The value of A0 was 0.35.

Maple returned the result with 0.350 as a variable with subscripted 0 and no numerical result.  When changing the variable to A0 without subscripted index 0 Maple returned the numerical result correct.

Hi there!

 

I am trying to calculate Eigenvectors of Matrices, Maple does not seem to understand that, however. I have used the structure of the example in the "help" section

A := `<|>`(`<,>`(-1, -3, -6), `<,>`(3, 5, 6), `<,>`(-3, -3, -4));
v, e := Eigenvectors(A) 

and even the example itself, it doesn't work. Maple always responds with   

"Error, (in Matrix) triangular[] storage expects name parameters"

What can I do?


           

I am trying to do taylor series expansion around the critical point, but I keep getting an error, because I think Maple is taking my critical point as function {x(t) = 5, y(t) = 10}. I would like to get just the output of x(t)=  from the list of critical points. Ex. Does anyone know the maple code to get "5" and "10" from the list of critical points without typing in 5 and 10.

Hi guys;

can one please show me how to plot graphs in on layout. i want like soundalgekar2004-deka.pdf using this code

variable.mw
 

restart

with*plots; -1; ode1 := diff(f(eta), eta, eta, eta)-(diff(theta(eta), eta))*(diff(f(eta), eta, eta))/(theta(eta)-R)-(theta(eta)-R)*f(eta)*(diff(f(eta), eta, eta))/(2*R) = 0

diff(diff(diff(f(eta), eta), eta), eta)-(diff(theta(eta), eta))*(diff(diff(f(eta), eta), eta))/(theta(eta)-R)-(1/2)*(theta(eta)-R)*f(eta)*(diff(diff(f(eta), eta), eta))/R = 0

(1)

ode2 := diff(theta(eta), eta, eta)-N*pr*(diff(f(eta), eta))*theta(eta)+(1/2)*pr*f(eta)*(diff(theta(eta), eta)) = 0

diff(diff(theta(eta), eta), eta)-N*pr*(diff(f(eta), eta))*theta(eta)+(1/2)*pr*f(eta)*(diff(theta(eta), eta)) = 0

(2)

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(38) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(38) = 0

(3)

fixedparameter := [pr = 0.2e-1, N = 1];

[pr = 0.2e-1, N = 1]

(4)

ode3 := eval(ode1, fixedparameter);

diff(diff(diff(f(eta), eta), eta), eta)-(diff(theta(eta), eta))*(diff(diff(f(eta), eta), eta))/(theta(eta)-R)-(1/2)*(theta(eta)-R)*f(eta)*(diff(diff(f(eta), eta), eta))/R = 0

(5)

bcs2 := theta(38) = 0, theta(0) = 1;

theta(38) = 0, theta(0) = 1

(6)

ode4 := eval(ode2, fixedparameter);

diff(diff(theta(eta), eta), eta)-0.2e-1*(diff(f(eta), eta))*theta(eta)+0.1000000000e-1*f(eta)*(diff(theta(eta), eta)) = 0

(7)

L := [2, 10, 15];

[2, 10, 15]

(8)

``

for k to 3 do sol_All := dsolve(eval({bcs1, bcs2, ode3, ode4}, R = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); Y_sol || k := rhs(sol_All[5]); YP_sol || k := -rhs(sol_All[6]); ftheta || k := rhs(sol_All[3]); pftheta || k := -rhs(sol_All[4]) end do:

for k to 3 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do;

2, [HFloat(1.0000000000000002), HFloat(0.07429586344532203)]

 

10, [HFloat(1.0000000000000007), HFloat(0.06509471738660902)]

 

15, [HFloat(0.9999999999999997), HFloat(0.06453272061469233)]

(9)

NULL

NULL

  plot( [ seq((Y_sol||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((ftheta||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((pftheta||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, fprime(eta)],
         axes = boxed
      );

 

 

 

 

NULL

``


 

Download variable.mw

 

3.mw Here is my maple code that shows the animation for different values in b. The equation this is referring to is given in the code. I have done (b) and (c), and the animation is in the code, but I am not sure where for what value of b for the behavior changes, any tips on what to look for would be really helpful.

However, I am primarily concerned with (d) as I am not sure how to demonstrate periodic behaviour with dsolve. Thanks for the help!   

Hi, 
So I am trying to use Maple to find the integer points in a region(s) bounded buy a set of inequalities. But for a specific set of inequalities, in four variables,
inequalities:= [-a1-a2+a3+a4 <= 2, a1+a2 <= 3, -2*a1 <= -1, -2*a2 <= -1, -2*a3 <= -1, -2*a4 <= -1, -a1+a2+a3-a4 <= 4, -a1+a2-a3+a4 <= 4, a1-a2+a3-a4 <= 4, a1-a2-a3+a4 <= 4]; in four variables, vars :=[a1,a2,a3,a4];

I am getting the following error
Error, (in solver) invalid input: LinearMultivariateSystemInternal expects its 1st argument, eqns, to be of type ({list, set})({`<`, `<=`, `=`}), but received {a1-a2 = 0, -11/2+a1 <> 0}

Also, upon checking the inequalities by hand, I am sure that the region mentioned in the error doesnt come up. as based on the inequalities, it is not possible to have -11/2+a1 > 0. But though I could be wrong about my manual inequality analysis, the error is still suprising and worrying. 
Another point to note is that if I do a variable change, as
t1 := a1-a2;
t2 := a1+a2;
r1 := a3-a4;
r2 := a3+a4;
Then with new variables the inequalities are solved without any errors.

I am working with Maple2018 for this problem. 

Any help or insight into the root of this problem would be a lot of help. 


 

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