restart; with(plots); _EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; para := -2*p*x+y^2 = 0; para1 := -2*p1*x+y^2 = 0; t := y-m*x-p/(2*m) = 0; t1 := y+x/m+(1/2)*p1*m = 0; sol := op(solve([t, t1], [x, y])); eliminate({rhs(sol[1]), rhs(sol[2])}, m); for example : m := 2; p := 1; p1 := -2; PARA := implicitplot(para, x = -3 .. 3, y = -3 .. 3, color = blue); PARA1 := implicitplot(para1, x = -3 .. 3, y = -3 .. 3, color = green); Tang := implicitplot(t, x = -3 .. 3, y = -3 .. 3, color = brown); Tang1 := implicitplot(t1, x = -3 .. 3, y = -3 .. 3, color = aquamarine); NULL; #m is not constant display([PARA, PARA1, Tang, Tang1], view = [-3 .. 3, -3 .. 3], scaling = constrained);#on what curve is the vertex of the angle of 2 tangents ? Thank you.

i have a function which contains Ln and arctan fanctions in which the output function is complex.
how can i implicitplot this complex function? tnx for the help
 

>  >  >  (1) >  (2) >  P:=subs(y(w)=Y,eval(lhs(Ans[1, 1]), [_C1 = 0, m = 1])) (3) >  implicitplot(P,w=-10..0,Y=0..10) >  evalf((eval(P,[w=1,Y=1]))) (4) >    >

 

Download P2.mw

The sphere with radius 0.5 whose center has y coordinate = 0.5 and z coordinate = 0.5 is tangent internally to the ellipsoid centered on the origin with principal semi axes of 5, 3 and 2.

How can the x coordinate of the sphere's center be determined?

   I need to integrate x with a<=x<=b and k , l are constants.

I input foolowing code , it did not work. Maybe you have some good ideas to solve this! thanks!

I am trying to solve the pde:= (d/dt)^2v+(d/dx)^2v+v=0 with initial boundary conditions v=xexp(x^2)

I use pdsolve to get v but I wish to tell pdsolve to use a different numerical method because my output of v is coming out like a step function.

The time taken for thread is comparitively higher in following case. how to decrease time in threads

 

thread_time.mw

Dear reader,

Have to create digital questions in Mobius on quaternions. Aim is to teach students of robot engineering about rotations besides the matrix rotations. Made some code, it works but very simplistic. I could not load a quarternion-toolbox.

Any suggestions?

# quaternion product
# define two vecotrs p and q:
$p0=range(3,3,1);
$px=range(1,1,1);
$py=range(-2,-2,1);
$pz=range(1,1,1);
$q0=range(2,2,1);
$qx=range(-1,-1,1);
$qy=range(2,2,1);
$qz=range(3,3,1);
$p=maple("Vector([$px,$py,$pz])");
$q=maple("Vector([$qx,$qy,$qz])");
$displayp=maple("printf(MathML:-ExportPresentation($p))");
$displayq=maple("printf(MathML:-ExportPresentation($q))");
# p.q=p0.q0-(p.q)+p0.q+q0.p+p*q
# scalar part
$dot=maple("LinearAlgebra[DotProduct]($p,$q,conjugate=false)");
$scalar_part=$p0*$q0-$dot;
# vector part
$cross=maple("LinearAlgebra[CrossProduct]($p,$q)");
$p0q=maple("LinearAlgebra[MatrixMatrixMultiply]($p0,$q)");
$q0p=maple("LinearAlgebra[MatrixMatrixMultiply]($q0,$p)");
$pq=maple("LinearAlgebra[VectorAdd]($p0q,$q0p)");
$vector_part=maple("LinearAlgebra[VectorAdd]($pq,$cross)");
$displayvector_part=maple("printf(MathML:-ExportPresentation($vector_part))");
# unit vectors
$i=maple("Vector([1,0,0])");
$j=maple("Vector([0,1,0])");
$k=maple("Vector([0,0,1])");
# generate answers
$x=maple("LinearAlgebra[DotProduct]($vector_part,$i)");
$y=maple("LinearAlgebra[DotProduct]($vector_part,$j)");
$z=maple("LinearAlgebra[DotProduct]($vector_part,$k)");
 

Best regards,

Nico Booij

I have recently received a doc from my friend in privete group in maple cloud, the table showed both eye(view) icon and download icon).When I downloaded and run, the document does not run (maple 2019). 

When I sign in maple cloud and see the doc (only view button is ahow), the same document works fine. What could be the error?

I attach  a document extract showing the errors (unable to delimt   .../  identifiers).

Can any one help us please?

Thanks. Ramki.
 

Error, unable to delimit strings/identifiers   Dear Prof. The following code seems not copying properly (my communication error be allowed please)   Error, unable to delimit strings/identifiers   Error, unable to delimit strings/identifiers

 

Download forScotgould_Error_arrow.mw

Hi,

 

I have two functions that I took the inetgral of their product (1.3 and 1). Then i multiplied the resulting naswer with the variable and integrates again however the inetgral did not evaluate (3,4, and 5). 

I was able to calculate both inegrals using tables of integrals, MATLAB & Mathematica were able to evaluate.

any insights on why this may happening?

Integrals_Sheet2.mw

Hi,

 

I am trying to use Maple to evaluate the recursion series as below, but I am getting an error when I try to call c: Error, (in depends) too many levels of recursion

Recursion.mw

 

 

>  (1) >  (2) >  (3) >  Error, (in depends) too many levels of recursion     >  (4) >  Error, (in depends) too many levels of recursion   >  Error, (in depends) too many levels of recursion   >  (5) >  Error, (in _factorial) too many levels of recursion   >  (6) >  Error, (in unknown) too many levels of recursion

 

Download Recursion.mw

I have this equation 

 

x3l := -(1/2)*g*(f[3]*m[3]+f[2]*(m[2]+m[3])+f[1]*(m[1]+m[2]+m[3]))*tau^2/(m[1]+m[2]+m[3])+x30

 

f_i are Heaviside function of x3l, so I get  recrusive error

how can i avoid it ? 

A fouth order system is described by the differential equation

          (d^4 y)/(dt)^4 + a_3  (d^3 y)/(dt)^3 + a_2  (d^2 y)/(dt)^2 + a_1  dy/dt+ a_0 y(t)=u(t)      

Where y(t) is the output and u(t) is any input

• Determine the matrix A.
• Using the condition det[A – λI ]

Determine the eigen values λ.

• Compute the state transition matrix using maple.

I'm plotting some simple plots such as

plot(frac(x^2/3)*3,x=-5..5, discont=true);

 

Some discontinuities are connected. Using numpoints, resolution, and Digits doesn't help. Sometimes it will produce a plot with no connections but then other times it does. I need a general solution that is simple. Is there any way to refine the quality of discont?

 

discont=[usefdiscont=[bins=35]],

 

I have tried that and it seems to work but I haven't put it through the ringer. Is that all I have?

 

I'm using MAPLE 2019 and I'm sometimes surprised by its behaviour.  For example, I appear to have an example where it evaluates the integral of each of two terms but not their sum...  What's going on?  Please see the attached.

(1) (2) (3) (4) (5) (6)

 

Download Maplesumint.mw

I wrote a code.mw for a numerical method for a PDE. (You can find the numerical method, exact solution and error between them in the code.)

The method depends on parameters k, M, which are any positive integers, and also depends on teta, beta>-1 which are real numbers.

According to the used method,

when k and M increase, we expect that the error (exact-numeric) generally decreases. 

In the code, I selected k=2, M=2, teta=1 and beta=1. And so k=2, M=2, CPU time is low. Error is not bad.

But for k=4, M=3 and also for bigger values of them, CPU time is high. I can' t get the solution.

Question 1: 

I don't know, but it may be possible to simplify the code in order to calculate for k=4, M=4?

Question 2:

I want to find optimal values of teta and beta for minimizing the error between numerical and exact solution, when k=2, M=2, or k=3, M=1 etc.

How can we write a Maple code for finding optimal values of teta and beta?

You can download the code.mw