MaplePrimes Questions

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

 

 

 
 
 
 
 

Hello, I'm using free 15 day trial Maple 2019.2 on my Macbook (Macos 10.15.3).

I can't work Maple. I enter some inputs (2+3) and press enter. It works. But when I write plot, version(), f, sin.. or something else it didn't works. And no response. When I click enter, nothind happen. What is the problem? Please help me.. 

   I download one  file about  all 5 connected graphs of graph6  (total 21 graphs). format from http://users.cecs.anu.edu.au/~bdm/data/graphs.html,and I want to import it in Maple. Since platform restrictions , I can not attach the file .   Please download it by yourself,very thanks to you ! 

   I put the file  in the installation path of  Maple in my computer:D:\\ Program Files\Maple 2019. (my computer system is Window 10 )  And I import it like following: 

  But it  only imports the graph of  the first row in the file. How to import all graphs in a file of graph6 format one time?

 

I get quite an annoying "bug" that messes up all the presentation aspect of my document.

I want to assume some variable is real so that calculation are simplified at several parts of the document.

 

But I get this:

 

Whener I use U__LL I always end up with this ugly form that would make anybody think U__LL is multiplied by itself.

How do I get around this?

I'd like to populate a listbox from elements of a matrix, but need some help.

I created an empty listbox with name ListBox0, and try to add a name from the matrix.

DataSet := Matrix(3, 3, [[Tim, 21, 80], [Tom, 23, 86], [Tinker, 25, 90]])

with*DocumentTools

SetProperty("ListBox0", DataSet[1, 1])

Hi,

I want to optimize a function f(g(e(x),x))  where g(x) is interpolated and e(x) is not known when the interpolation object is created. I found the intpolation Methods of Maple 2018 very helpful to quickly change the inpterpolation method.

Unfotunately the optimization fails when the interpolation object receives an expression as input.

It works if I just use x. Do you know my the first approach fails?

Is there maybe a way to convert the interpolation object to a piecewise function?

 

Thank you for your help
 

# Optimize with Interpolation Object


points :=  <<0.4000|  10.0000>,
            <0.7000|   10.0000>,
            <1.0000|   10.0000>,
            <0.3000|   30.0000>,
            <0.4000|   30.0000>,
            <0.5000|   30.0000>>;

Data := <0617,0767,0220,0444,0692,0789>*0.001;

intmethod := LinearInterpolation;

g := Interpolation[intmethod](points(1..-1,1),Data):

Matrix(6, 2, {(1, 1) = .4000, (1, 2) = 10.0000, (2, 1) = .7000, (2, 2) = 10.0000, (3, 1) = 1.0000, (3, 2) = 10.0000, (4, 1) = .3000, (4, 2) = 30.0000, (5, 1) = .4000, (5, 2) = 30.0000, (6, 1) = .5000, (6, 2) = 30.0000})

 

Vector[column](%id = 18446884324022199230)

 

LinearInterpolation

(1)

plot(g(x),x=0..1)

 

e := x/sqrt(2);

(1/2)*x*2^(1/2)

(2)

f := 5+g(e)*x^2

"5+(module() ... end module)(module() ... end module,1/2 x sqrt(2)) x^2"

(3)

f_simple := 5+g(x)*x^2

"f_simple:=5+[[["a linear interpolation object"],["with 6 points in 1-D"]]](x) x^2"

(4)

op_f := Optimization[Minimize](f(x),x=0 .. 1);

Error, (in Optimization:-NLPSolve) non-numeric result encountered

 

op_f_simple := Optimization[Minimize](f_simple(x),x=0 .. 1);

[HFloat(4.999979117244145), [x = HFloat(0.028901647183245588)]]

(5)

 

NULL


 

Download convert_interpolation_object.mw

 

 

I received an (automated) email, which called attention to an update.

Where can I find the update?

Thank you, Jan Drösler

 

Hi there,

I have been using Maple for a while now.

I installed Maple on my Desktop PC, but I am experencing horrendous loading times, and just in general, a slow client. When I look in Task Manager I can see Java Platform SE Binary run at 0% CPU or close to 0% CPU. It uses about 600 MB of ram. I think this is the issue. On my laptop it runs much higher, and I experience no issues. My Desktop PC is significantly better than my laptop. I am running a i7-7700k with a RTX 2080, so there shouldn't be any hardware worries. 

Does anyone know what is causing this? Simple math like 1+1 takes time to execute. It is very slow.

Hope someone knows what to do.

Thanks,

Kritix.

Hi everybody

My question comes back to singularities within a differential equation.

Consider a Non-Linear differential equation of y(x), say Eq1.

When we solve this with dsolve ({Eq1, ICs}, type=numeric) we can extract the value of y(x) for each independent variable x.

Now if Eq.1 admits a singularity (for example at x=x0) that can not be removed the following message appears:

Error, (in unknown) cannot evaluate the solution further left (right) of x0, probably a singularity.

By left(right) Maple means that the solution cannot be evaluated for x<x0 (x>x0).

However, in some situations, the Linear form of Eq.1 behaves regularly for all of the values of x, I call the Linear equation as Eq.2.

Now my question is:

How can I make a conditional expression with proc and for commands that do the following requirements: 

1. Detect the singular point x0 by running a loop over x for the numerical solution of Eq.1 and write the value of x0 for different initial conditions , since the value of x0 depends on initial conditions.

2. Find the value of y(x=x0) by solving Eq.2 as the linear equation is no longer singular at x=x0.

I want to find out the suitable algorithm through which I can perform the above procedures.

Thank you very much and best regards.

Hadi

Hope that no one minds a beginners question.   How do I enter non-null k=0 robertson-walker tetrad in the physics package?  Not the tensor package as that has depreciated or the differential geometry package as notation is different there.

why is  the figure  so weird ? How can I get the smooth trajectories of the ode system?


 

with(DEtools)

with(DEtools)

with(plots)

with(plots, implicitplot)

[implicitplot]

(1)

with(MatrixTools)

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received MatrixTools

 

with(LinearAlgebra)

with(VectorCalculus)

R := PolynomialRing([x, y])

PolynomialRing([x, y])

(2)

``

p1 := phaseportrait([diff(x(t), t) = x(t)*(1-x(t)^2-y(t)^2)+y(t)*(y(t)^2+(x(t)^2-1)^2), diff(y(t), t) = y(t)*(1-x(t)^2-y(t)^2)-x(t)*(y(t)^2+(x(t)^2-1)^2)], [x(t), y(t)], t = 0 .. 50, [[x(0) = -3, y(0) = .5], [x(0) = 4, y(0) = 2]], x = -4 .. 4, y = -4 .. 4, dirgrid = [13, 13], stepsize = 0.5e-1, axes = BOXED)

 

p2 := pointplot([[1, 0], [-1, 0], [0, 0]], symbolsize = 20, symbol = solidcircle, color = black)

 

``

 

display(p1, p2)

 

solve({x*(-x^2-y^2+1)+y*(y^2+(x^2-1)^2), y*(-x^2-y^2+1)-x*(y^2+(x^2-1)^2)}, {x, y})

{x = 0, y = 0}, {x = RootOf(_Z^8-6*_Z^6+11*_Z^4-6*_Z^2+2), y = RootOf(_Z^8-6*_Z^6+11*_Z^4-6*_Z^2+2)^5-3*RootOf(_Z^8-6*_Z^6+11*_Z^4-6*_Z^2+2)^3+RootOf(_Z^8-6*_Z^6+11*_Z^4-6*_Z^2+2)}, {x = 1, y = 0}, {x = -1, y = 0}, {x = RootOf(_Z^2-2), y = RootOf(_Z^2+1)}

(3)

subs({x = .5, y = -.5}, x*(-x^2-y^2+1)+y*(y^2+(x^2-1)^2))

-.15625

(4)

sys := [x*(-x^2-y^2+1)+y*(y^2+(x^2-1)^2), y*(-x^2-y^2+1)-x*(y^2+(x^2-1)^2)]

[x*(-x^2-y^2+1)+y*(y^2+(x^2-1)^2), y*(-x^2-y^2+1)-x*(y^2+(x^2-1)^2)]

(5)

A := Jacobian(sys, [x, y])

Matrix(%id = 18446746647299284134)

(6)

latex(Matrix(2, 2, {(1, 1) = -2, (1, 2) = 0, (2, 1) = 0, (2, 2) = 0}))

 \left[ \begin {array}{cc} -2&0\\ \noalign{\medskip}0&0\end {array}
 \right]

 

A1 := subs([x = 1, y = 0], A)

Matrix(%id = 18446746647299319918)

(7)

A2 := subs([x = -1, y = 0], A)

Matrix(%id = 18446746647176545934)

(8)

A3 := subs([x = 0, y = 0], A)

Matrix(%id = 18446746647213830142)

(9)

r1, e1 := Eigenvectors(A1)

Vector[column](%id = 18446746647213811102), Matrix(%id = 18446746647213811582)

(10)

r2, e2 := Eigenvectors(A3)

Vector[column](%id = 18446746647299291126), Matrix(%id = 18446746647299291246)

(11)

``


 

Download as22a.mw

Dear Sir/Madam, I am new in maple and willing to use an old (yet tested) Maple V code. The program first evaluates two integrals numerically, which depend on the values of "d" and "s" (user-defined), and then computes the values of a cumulative distribution function. The problem is that, when running the code on Maple 2018, the evalf(Int) of the first integrand (named "ex1") results in "Float (undefined)". I would really appreciate your help. Thank you in advance.

 

#Maple V program

assume(x, real, y, real, c1, real, c2, real);
d := 3:
s := .9:
ex1:=(1-exp(-(d-y)*I*x))/I/x*exp(y*I*x/(1-I*x)):
ex1:=simplify(Re(evalc(ex1))):
f1:= unapply(ex1,x,y):
ex2:=(1-exp(-(d-y)*I*x))/I/x*exp(y*I*x/(1-I*x))/(1-I*x):
ex2:=simplify(Re(evalc(ex2))):
f2:=unapply(ex2,x,y):
t1:=evalf(Int(f1(x,s),x=-infinity..infinity));
t2:=evalf(Int(f2(x,s),x=-infinity..infinity));
cumulativeprob:=evalf(subs(c1=1/2,c2=1/2,1-((c1*t1+c2*t2)/(2*Pi)+c1*exp(-s)/2)));

cumulativeprob:=.2503779941

 

I get the same result here where I expected a difference to be acknowledged by the split command. Is there a more efficient way of handling this problem other than the substitution for another character, followed by executing the split  command, then substituting the substituted character with the original ?(here ":")




 

StringTools['Split']("fdsg543656fgh:576fghs:dsfg::657ufdgdsg", "::")

["fdsg543656fgh", "576fghs", "dsfg", "", "657ufdgdsg"]

(1)

StringTools['Split']("fdsg543656fgh:576fghs:dsfg::657ufdgdsg", ":")

["fdsg543656fgh", "576fghs", "dsfg", "", "657ufdgdsg"]

(2)

``


 

Download split_help.mw

 

How can I set Maple 2019 so that all inputs are of the color red?

I am using a Lenovo Notebook 64-bit.

 

Thank you, Jan Drösler

 

Plot the "moment curve" f(t)=(t,t^2,t^3) over the interval 1≤t≤2 and a tangent line at the point when t=1. Include both plots in the same display, with the moment curve red and the tangent line blue.
 

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