MaplePrimes Questions

I am trying to draw the streamline for my coupled system but do not get the outcome. Could anyone please help in this regard?

Detail: My system contains x and y;  Regrading x=0, if I do not assign it to zero, do not get the results. Otherwise, there is no need to put x=0 because I am interested in plotting stream plots between y and x (y on the vertical axis and x on the horizontal axis). Besides this, I solved this system analytically, then considered the stream function, did some steps, and plotted the streamline. It is different from the stream function, which has been obtained directly by using the numeric method. I have assigned the values to the parameters that I used during the analytical plot. I put x=0 and did not get the answer. Besides,  I am uploading the graph as a reference, which I have obtained by considering the stream function. This plot is similar to my flow direction, and I expect the same results from the numeric method.

streamline_Help.mw

dr := draw([Tr(t3), AP(cbl), BP(cbl), CP(cbl)]),
textplot([coordinates(A)[], "A"], [coordinates(B)[], "B"], [coordinates(C)[], "C"], align = {above, right});
Error, (in plots:-textplot) unexpected options: [[0, 0, "B"], [13, 0, "C"]]
Why the coordinates are unrecognized ? Thank you.

Hi! I'm trying to find out if i can construct a sequence fn that generates all the (positive) rational numbers as n goes to infinity.

This is, the sequence shows to be an injective homomorphism fn: N -> Q+ . This sequence was constructed by cantor in his proof of rationals being countably infinite, and can really be helpful in evaluating expressions using rational numbers, but i do not knoww if it is implemented in maple, or how to construct it myself. 

Any help would be very appreciated. 

The equal sign ":=" in my document sign has changed to a "d".  The equal sign "=" has not changed.  Is there a setting I need to change?

Thank you in advance.

Hello

I need to share some results with a colleague who is not a user of Maple, and a way to do this is by using the Tabulate (plain command and not from DocumentTools) function to format them. In the worksheet, the output looks good, but when I try to print it or save it as a PDF, only a few lines are printed. It appears that Maple is not able to break the tables into multiple pages for printing.

The output is a table with 77 rows and 30 columns.   

I welcome alternative solutions to the problem of displaying the results. 

Many thanks

I am trying to find the value of y4 at t=infinity and t=-infinity when lambda1>lambda2 or lambda1<lambda2. But every time I got the same answer. For example, if we do it by hand then the terms which are responsible for making the indeterminate form can be extracted and canceled (see Fig.). 

But in limit.mw y4 is too lengthy-expression and very difficult to do it manually.

Hi,

 I'm looking for a simpler code to generate random proportional tables, like k*x type? Thanks for your suggestions.

TabPropQ.mw

Hey!

I am working on a 2-dimensional real curve gamma, that is being deformed by a real 2x2 matrix A and translated by some shift vector s. Both the matrix A and the vector s depend on two real parameters alpha and beta, which vary between 0 and 1. My goal is to create an animated plot that shows the curve depending on the parameters alpha and beta (ideally with some sort of slider, so I can play with different values of alpha and beta). I am having a hard time animating this, also because I am unsure if this is actually possible in Maple. The code I am working with is so far:

with(plots);
with(LinearAlgebra);
f := x -> exp(2*I*Pi*x);
CDFT := Matrix(3, 3, [[1, 1, 1], [1, f(1/3), f(2/3)], [1, f(2/3), f(1/3)]]);

al := 10/100;
be := 10/100;
lam1 := f(al);
lam2 := f(be);
lam3 := f(-al - be);
coef := (1/3*HermitianTranspose(CDFT)) . (Vector[column](3, [lam3, lam2, lam1]));
a := coef[1];
b := coef[2];
c := coef[3];

gam := t -> MatrixVectorMultiply(Matrix(2, 2, [[Re(a^2 + b*c), -Im(a^2 - b*c)], [Im(a^2 + b*c), Re(a^2 - b*c)]]), Vector[column](2, [cos(2*t) - 2*cos(t), sin(2*t) + 2*sin(t)])) + 3*Vector[column](2, [Re(b*c), Im(b*c)]);
P1 := plot([cos(2*t) - 2*cos(t), sin(2*t) + 2*sin(t), t = 0 .. 2*Pi], color = [blue]);
P2 := plot([gam(t)[1], gam(t)[2], t = 0 .. 2*Pi], color = [purple]);
plots:-display([P1, P2]);

Note that you can basically ignore everything up to the definition of the curve gam (short for gamma), apart from the definition of the parameters al and be (alpha and beta). The plot P1 corresponds to the "unperturbed curve", i.e. when we multiply the curve by the identity, which happens for alpha=beta=0. The plot P2 is now the deformed curve. The output is then:

My goal is now to animate this plot such that I can play with different values of alpha and beta, without having to manually insert them. How do I do this?

Here is an example where evalf[n] doesn't operate on the argument of the undefined function f.

x := rand(0. .. 1.)()
                          0.2342493224
y := x+f(x):
evalf[4](y)
                    0.2342 + f(0.2342493224)

# but, as soon as f is a known function:
evalf[4](cos(x))
                             0.9727


Here is a way to force evalf[4](f(x)) to return f(0.2342)?

I found only two ways to do this:
First: declare interface(displayprecision=4) 

interface(displayprecision=4):
y;
                 0.2342 + f(0.2342)

Or: do this (which is relatively cumbersome)

Evalf := proc(expr, n)
  local i := [indets(evalf[n](expr), numeric)[]]:
  eval(expr, i =~ evalf[4](i))
end proc:

Evalf(y, 4)
                 0.2342 + f(0.2342)

Thanks in advance.

PS:  I do not like setting displayprecision to some value because its effect is remnant: if you execute again the same worksheet (begining with a restart), the value of displayprecision is not reset to 10 but keeps the value you gave it previously, somewhere in the worksheet.

This worksheet animates the motion of an object (say, a cube which slides frictionlessly) on a rotating carousel. The cube is not self-propelled.

How can the worksheet be modified to handle the combination of the carousel motivated motion and the cube's own generated motion, caused by, say, by a few strategically placed thrusters?

The cube's own generated path could be a straight line, or a curve such as an ellipse. The cube's own motion could have a constant velocity or be accelerating.

Carousel_dynamics.mw

Hi,

How can two specular equations generate two nonspecular (i.e., very different in length and form) solutions? I attach my script with two questions at the bottom: 

specular_equations_nonspecular_solutions.mw

Thank you.

Maple seems to give me very inaccurate results for this computation, I'm wondering if this is a known issue and if there's a way to fix it? Worksheet:

Exact commands I ran:
with(combinat):
B := (n, i, p) -> binomial(n, i)*(p^i)*(1-p)^(n-i)/i;

F:=(n,p)->sum(B(n,i,p),i=1..n);
F(2,1);

This outputs 0, when it should output 1/2. See image attached:

 

Is there a fix for this?

xA := 4;
yA := 10;
xB := 0;
yB := 0;
xC := 13;
yC := 0;
Mat := matrix(3, 3, [xA, xB, xC, yA, yB, yC, 1, 1, 1]);
phi := (x, y) -> 1/Mat &x [x, y, z];
phi(4, 18/2);
phi(4, 10);
phi(13, 0);
Why the results are not calculated ? Thank you.

Hello everyone,

I wrote a very simple shooting method and I don't know why it doesn't go through the for loop.
Please help, I have no idea why it doesn't work.

Simple_ODE_Met_1.mw

Hello,

How to add the arrow or symbol for the flow function ( psi[1] and psi[2]). I do not know how to use from fieldplot with the option of arrows = SLIM

please see the attached figure.

Thanks so much

h1_h2_ok_ac_2020_8_ac_(1).mw

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