Hello again,

I want to maximize a function u(k,x) with the following form

u := (k, x) -> (1 - theta(sP, sL))((p + sP)*q(x) - w(k)*x + sL) + theta(sP, sL)*b(k)

where theta, q, b, w have previously being defined and (sP,sL) are parameters. I want to maximize u and therefore,

with(Optimization):
Maximize(u(k, x), variables = {k, x}, k = 0 .. 1);

My question is how to tell Maple that I want my optimal solution, (k*,x*) to be expressed as a function of (sP,sL)?

First, I want to find the set of solutions of this system and then find the steady state vector.

I know that I can find an approximation of the steady state vector ''directly'' if I calculate P^k for big k values (one column of P^k will give me an approximation), but it's not what I want to do. I need the complete set of solutions with a free parameter.

LinearSolve() doesn't give me the set of solutions. See the picture below. Here Q is the transition matrix.

I hope my question is clear (:

Please answer the questions posed in the body of the uploaded worksheet.

The worksheet employs the command DirectSearch[SolveEquations]. Responders must establish their own connection to the DirectSearch package.

Invert_Torus.mw

When i enter  Physics:-Version() I see the output

The "Physics Updates" version "859" is installed but is not active. The active version of Physics is within the library

   C:\Program Files\Maple 2020\lib\maple.mla, created 2020,  March 4, 20:36 hours

I tried to install it using Maple Cloud. The installation is stuck as seen below. Also i deleted the text file in the toolbox 2020 folder, maybe in the hope of starting from scratch.
 

Can someone please explain what to do to manually add the physics update, step by step. I am not that computer savvy as some of the users appear in other posts , I did try reading some.
I tried to download the physics update manually but I keep ending up with the same maple worksheet that says you need to use maplecloud.

In case you cannot read the text in the image

Version: Maple 2020.1

When i set the color for the gridlines it only seems to be applied for the major-tick gridlines as the following trivial example shows:

plot(sin(t), t = 0 .. Pi, axes = frame, background = "#303030", color = "Orange", axis = [gridlines = [color = "#707070", linestyle = dot]])

I assume it must also be possible to also specify the color for the minor tick-marks gridlines?

The obvious (?) variant "axis=[gridlines = [color = ["#707070", "#707070"] , ... " just seems to crash maple (nothing happens when the plot() expression is evaluated).

I'm unable to find anything in the documentation regarding this and it only seems to imply that the color should be applied to both major & minor gridlines which is not the case.

?

Hi everyone! Currently I'm studying magnetism, and I was thinking that maybe seeing represented the helix movement of an atom with a vector v parallel to the Magnetic Field B subject to the Force of Lorentz and the Hysteresis cycle created in the magnetazation of a ferromagnetic material could help me understand it more. I tried to create the plots in Maple 2015 but I couldn't.. anyone can help me by creating those two plots?

I notice that when I enter ?convert or ?convertininto the maple prompt, the help window opens once and then ceases to function.

Update. It seems that the problem is not restricted to a specific command, this occurs for any command. To replicate, open help using F1, exit maple help, then open help again using F1. Maple help won't open again. I have to do a hard exit to get it to work again.

Platform details:

Hello,

Recently I switched from Mathematica to Maple. I have the following code 

solve({pf'(e)- psi'(e) - tau - mu*pi(tau)/(1 - pi(tau)) = 0}, {tau}) assuming 0 < p, 0 < tau, 0 < mu, 0 <= pi< 1

and I am getting a result of 

RootOf(-D(pf)(e)*pi(_Z) - mu*pi(_Z) + _Z*pi(_Z) + 2*pi(_Z) + D(pf)(e) - _Z - 2)

I have to questions: (a) what does that _Z means? (b) is it possible to express the above solution in a more "readable" way?

Thanks in advance

/Mrs.,

How can I plot "log scale base 2" instead of "log scale base 10" (plot "log2plot(x,x=0..10)" instead of "logplot(x,x=0..10)")? 

I would appreciate if you make me some help with this situation.

faithfully,

I am trying to apply assumptions to the solution set of an equation. I've tried assume and assuming (see attached) to no avail. What am I missing? How can I achieve this?assume.mw
 

Download assume.mw

I am generating splines using CurveFitting[Spline] command, which produces piecewise functions. I would like to extract the different "pieces" of the spline for use elsewhere. How do I do that? In the attached worksheet, for example, I would like to extract (59*x^2)/756, -1/84*x^2 + 17/63*x - 17/84, and -19/504*x^2 + 19/36*x - 61/72. There has to be a way to do this, but I'm coming up short.

spline.mw
 

Download spline.mw

I want to plot some oscillating function (function involve sin and cos) as a function to time (t). And when I try a large interval like t=0..1000, it is going to take forever to plot the graph and the system becomes a little laggy. Is there any way I can do to make it compute quickly?

Thank you all

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Hello

I am trying to use Threads in my procedures as much as possible.  However, one of them returned different results when compared to map or Grid:-Map (I have checked if the used functions are threadsafe (perhaps I miss something)).  Here is the procedure (optimization of the code is most welcome).

searchMonomialsEqns:=proc(conds::set,Eqns::list,Vars::list,poolofeqns::list(list))
description "Find if a set of monomials in an equation can be found in a pool of monomials and returns the condition when it is true":
local A:=Array(1..0),
      C,
      i,
      res,
      n:=numelems(Eqns):
#  Find the monomials of Eqns
res:=subs(conds,Eqns):
for i from 1 to n do
    C:= coeffs(expand(lhs(res[i])-rhs(res[i])),Vars, 'M'):
    A,={M}:
end do:
ifelse(member([seq(A)],poolofeqns)=false,NULL,conds):
end proc:

1) Threads:-Map

ans1:=CodeTools:-Usage(Threads:-Map(w->searchMonomialsEqns(w,eqns[1..2],vars[2..3],validYZeqnMon),conds5)):nops(ans1);

returns

memory used=0.58GiB, alloc change=139.56MiB, cpu time=40.23s, real time=11.12s, gc time=1.01s

                              8613

2) map

ans2:=CodeTools:-Usage(map(w->searchMonomialsEqns(w,eqns[1..2],vars[2..3],validYZeqnMon),conds5)):nops(ans2);

returns

memory used=0.57GiB, alloc change=-4.00MiB, cpu time=22.48s, real time=21.55s, gc time=1.70s

                              8637

3) Grid:-Map

ans3:=CodeTools:-Usage(Grid:-Map(w->searchMonomialsEqns(w,eqns[1..2],vars[2..3],validYZeqnMon),conds5)):nops(ans3);

return

memory used=23.29MiB, alloc change=21.88MiB, cpu time=3.77s, real time=2.25s, gc time=3.14s

                              8637

Although the number of elements is the same, Grid:-Map returns the result with set function mentioned in my previous post. (I am aware that CodeTools:-Usage is pointless here).

4) Threads:-Seq

ans4:=CodeTools:-Usage([Threads:-Seq](searchMonomialsEqns(conds5[i],eqns[1..2],vars[2..3],validYZeqnMon),i=1..nops(conds5))):nops(ans4);

returns

memory used=0.58GiB, alloc change=0 bytes, cpu time=33.99s, real time=8.68s, gc time=644.74ms

                              8622

What am I missing?   

Many thanks

Ed