MaplePrimes Questions

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.
 

Plot the boundary of the rectangle with bounds 1≤x≤4 and 2≤y≤3 by parametrizing and plotting all four boundary segments in the same display

 

How do I simplify KdV equation in Maple by using =fxt))xx)?)


 

``

   I am by using =2*difffxtxx)
    My aim is to get the form
   diff((f*(diff(f, x, t))-(diff(f, x))*(diff(f, t))+f*(diff(f, x, x, x))-4*(diff(f, x, x, x))*(diff(f, x))+3*(diff(f, x, x))^2)/f^2, x) = 0

NULL

``

restart; with(PDEtools); with(DEtools)

``

alias(u = u(x, t)); declare(u(x, t)); alias(f = f(x, t)); declare(f(x, t))

u

 

` u`(x, t)*`will now be displayed as`*u

 

u, f

 

` f`(x, t)*`will now be displayed as`*f

(1)

KdV := diff(u, t)+6*u.(diff(u, x))+diff(u, x, x, x) = 0

diff(u, t)+6*(u.(diff(u, x)))+diff(diff(diff(u, x), x), x) = 0

(2)

KdV_f := eval(KdV, u = 2*(diff(ln(f), x, x)))

2*(diff(diff(diff(f, t), x), x))/f-2*(diff(diff(f, x), x))*(diff(f, t))/f^2-4*(diff(f, x))*(diff(diff(f, t), x))/f^2+4*(diff(f, x))^2*(diff(f, t))/f^3+6*((2*(diff(diff(f, x), x))/f-2*(diff(f, x))^2/f^2).(2*(diff(diff(diff(f, x), x), x))/f-6*(diff(diff(f, x), x))*(diff(f, x))/f^2+4*(diff(f, x))^3/f^3))+2*(diff(diff(diff(diff(diff(f, x), x), x), x), x))/f-10*(diff(diff(diff(diff(f, x), x), x), x))*(diff(f, x))/f^2+40*(diff(diff(diff(f, x), x), x))*(diff(f, x))^2/f^3-20*(diff(diff(diff(f, x), x), x))*(diff(diff(f, x), x))/f^2-120*(diff(diff(f, x), x))*(diff(f, x))^3/f^4+60*(diff(diff(f, x), x))^2*(diff(f, x))/f^3+48*(diff(f, x))^5/f^5 = 0

(3)

df := collect(KdV_f, f)

6*((2*(diff(diff(f, x), x))/f-2*(diff(f, x))^2/f^2).(2*(diff(diff(diff(f, x), x), x))/f-6*(diff(diff(f, x), x))*(diff(f, x))/f^2+4*(diff(f, x))^3/f^3))+(2*(diff(diff(diff(f, t), x), x))+2*(diff(diff(diff(diff(diff(f, x), x), x), x), x)))/f+(-2*(diff(diff(f, x), x))*(diff(f, t))-20*(diff(diff(diff(f, x), x), x))*(diff(diff(f, x), x))-4*(diff(f, x))*(diff(diff(f, t), x))-10*(diff(diff(diff(diff(f, x), x), x), x))*(diff(f, x)))/f^2+(60*(diff(diff(f, x), x))^2*(diff(f, x))+4*(diff(f, x))^2*(diff(f, t))+40*(diff(diff(diff(f, x), x), x))*(diff(f, x))^2)/f^3-120*(diff(diff(f, x), x))*(diff(f, x))^3/f^4+48*(diff(f, x))^5/f^5 = 0

(4)

factor(simplify(df, size))

2*(12*(((diff(diff(f, x), x))*f-(diff(f, x))^2)/f^2.(((diff(diff(diff(f, x), x), x))*f^2-3*(diff(diff(f, x), x))*(diff(f, x))*f+2*(diff(f, x))^3)/f^3))*f^5+f^4*(diff(diff(diff(f, t), x), x))+f^4*(diff(diff(diff(diff(diff(f, x), x), x), x), x))-f^3*(diff(diff(f, x), x))*(diff(f, t))-10*f^3*(diff(diff(f, x), x))*(diff(diff(diff(f, x), x), x))-2*f^3*(diff(f, x))*(diff(diff(f, t), x))-5*f^3*(diff(f, x))*(diff(diff(diff(diff(f, x), x), x), x))+30*f^2*(diff(diff(f, x), x))^2*(diff(f, x))+2*f^2*(diff(f, t))*(diff(f, x))^2+20*f^2*(diff(diff(diff(f, x), x), x))*(diff(f, x))^2-60*(diff(diff(f, x), x))*(diff(f, x))^3*f+24*(diff(f, x))^5)/f^5 = 0

(5)

``

``

``

``


 

Download KdV_simplify

Is there lifting function for polynomials or algebra use?

expect input a list univariate polynomial , then output a list of polynomials of two variables.

it should be the reverse operation of projection.

Which library has this function in maple 12 or maple 2015?

I am a beginner of MapleSim. I study the MapleSim User Guide. I follow the Tutor 8:Modeling Hydraulic System. But the following issue occurs, as shown in the picture. I bet I follow the guide carefully.

Also, I find that if I open the User's Guide example,Chapter 6, Analysis of Simple Hydraulic System Network, which is the standard example,I simulate it and it works well. But if I delete the probe, and attach a probe at the same place , selecting same values to measure, and simulate again, it failed, giving the same error description. I need your help,please.

problem_with_Analysis_of_Simple_Hydraulic_Network.msim

 

I am trying to write a metric in Maple 2019, using the Physics package in Cartesian coordinates. I know that there is already a pre-installed way in which to set the coordinates to Cartesian, namely, if we have something like 

Setup(coordinates=cartesian);

or similarly, using the Coordiantes calling sequence, such that we may define something like

Coordinates(A=cartesian);Setup(coordinates=A);

yet, if I am not mistaken, this gives the coordinates in the following form: {x,y,z,t}, yet I seek to define the metric in the following, perhaps more arbitrary coordinate system, {x1,x2,x3,t}. Is there any way to setup the coordinate system to read like the set I just described, such that I can then take a norm of these three spatial coordaintes to be |x|? Any help would be greatly appreciated. 

   It would seem that the option style = planar  of DrawGraph()    is  failure when some graphs are planar.
   For example: 

treeof5:=[NonIsomorphicGraphs(5,4,output= graphs,outputform=graph,restrictto = connected )]:
DrawGraph ~ (treeof5, stylesheet=[vertexborder=false,vertexpadding=20]);


 

We know tree is planar graph obviously. But when I add the option style = planar ,  drawing of the first tree of list displays an error :
Error, (in GraphTheory:-Graph) vertex 1 cannot be its own neighbour in list of neighbours

I did not find any reason to explain. 

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