Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Why  

eval(diff(u(x,t),x),x=0)=A(t)

gives

But

eval(diff(u(x,t),x),x=L)=A(t)

gives

I was expecting the same syntax in both cases. It seems for numbers Maple uses the first syntax and for symbols it uses the second syntax.

Does one need to worry about this difference?

 

I would like to animate the motion of a bicycle racer on a classic velodrome track i.e. one with varied vertical and horizontal curvatures along its length.

Is there a source which explains the math expressions which model the shape of such a track?

Let us consider S := [x^2 = A1, x*y = A2, z^2 = A3] as a list. Is there any command to obtain  SS = [A1=x^2 , A2=x*y , A3=z^2] from S?

My goal is to find a positive linear combination of a vector vec over a set of vectors M1,...,M6. In this case the Mi are the columns of the matrix M.

My reasoning is: solve the linear system M.x=vec, which gives me a parametrized solution, then check if there is at least one positive solution.

M:=Matrix([[3, 0, 2, 2, 1, 1], [-1, -1, 0, -1, 0, -1], [0, 3, 0, 1, 1, 2], [3, 0, 1, 2, 0, 1], [-1, -1, -1, -1, -1, -1]]);

vec:= Vector[column](5, [3, 1, 0, 0, -2]);

x:=LinearSolve(M,vec, free = s);

Vector[column](6, [-1+2*s[2]+s[5]+s[6], s[2], 3-s[5], -3*s[2]-s[5]-2*s[6], s[5], s[6]])

 

But when I use the LinearMultivariateSystem function I get an error

LinearMultivariateSystem({x[1]>=0, x[2]>=0, x[3]>=0, x[4]>=0, x[5]>=0, x[6]>=0},[s[1],s[2],s[3], s[4], s[5],s[6]]);
Error, (in Utilities:-SimpleAnd) invalid input: a string/name list is expected for sort method `lexorder`

 

Can anyone tell me what is wrong in the code?

If I manually type in the expressions, and use variables such as x,y,z... then I get the solution, but I want to put the function into a loop.

I am very open to suggestions on how to decide if a vector is a positive linear combination of other vectors.

Maria

 

Hi

I have the values of of a function A(x,y,z) in 3d cartesian coordinates as [x[1],y[1],z[1],A(x[1],y[1],z[1])], [x[2],y[2],z[2],A(x[2],y[2],z[2])], [x[i],y[i],z[i],A(x[i],y[i],z[i])],etc...where i vary from 1 to 300 (or higher).

How to plot A(x[i],y[i],z[i]) in 3d.

Thanks

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

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.

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