Maple 2020 Questions and Posts

These are Posts and Questions associated with the product, Maple 2020

I'm trying to solve a coupled inductor problem.  All I'm trying to do is solve for the currents (which I could do), then solve for resonance by setting the imaginary part of I1 to 0 and solving for omega.  I then want to plug this resonant frequency back into I1 and evaluate it for some component values and coupling coefficient.

The problem is that even though I define the various variables as real,  Maple doesn't seem to recognize them as such.  I suspect I've failed to define one of them, and that is why it is responding like it is, but I can't find it.  

I'm also getting some weird behavior.....for example if I type :  wres0, I get the value I assigned to it --that's fine.  But then, when I type : wres0/(2*pi), I get an error, "Error, unable to parse 'mverbatim"   --- what does this mean?

This should be a pretty straight forward calculation on Maple, but at this point, I think I may be better off doing it by hand!  I appreciate any help you can provide.  Thank you.

reflected_load.mw

This worksheet animates part of the motion of the classic ladder sliding down a wall.

Please answer the two questions posed in the opening text.

Respondents will need to establish their own link to the DirectSearch package

Slide_Ladder.mw

Hello all, 

Would you allow me to ask this one question?
[moderator: See also this previous question]

Is there any possible way to treat the differentiation operator (e.g., 'D') as an ordinary coefficient of a polynomial?

For example, as described in the attached worksheet, I was wondering if there is a way to re-write the LHS of the expression 'eq_e5_9b' as the expression 'desired'. 

In Kwon Park 

restart;

with(DEtools):

eq_e5_9b := psi__d0*Delta__delta(t) + psi__q0 * D(Delta__delta(t))/omega__0 = p_(Delta__psi__d(t))/omega__0 - Delta__psi__q(t);

psi__d0*Delta__delta(t)+psi__q0*D(Delta__delta(t))/omega__0 = p_(Delta__psi__d(t))/omega__0-Delta__psi__q(t)

(1)

collect(lhs(eq_e5_9b), Delta__delta(t));

psi__d0*Delta__delta(t)+psi__q0*D(Delta__delta(t))/omega__0

(2)

desired := Delta__delta(t) * (psi__d0 + psi__q0 * D/omega__0);

Delta__delta(t)*(psi__d0+psi__q0*D/omega__0)

(3)

 

Download Q20220404.mw

I am trying to decide O of times fo a computer process. I thought it was n^2*log(N) or something like that.

With 12  points, it may be hard to determine if O(N^4), etc.

See big-o.mw

The uploaded worksheet attempts to determine arc lengths of an ellipse by two methods. Why do their results differ?

ArcLength_of_Ellipse.mw

I want to integrate the function int(1/(A^2 - B^2*cos(t))^(1/2), t = 0 .. 2*Pi), I get the correct solution, but I want to prevent all the "if" statements from appearing. I have tried to use "assume" but the if statement still does not disappear.  

Download Plot.mw

Is there any way to save "explore plot" in such a way that the slider of constants should appear in the extension file?

So that I can see the constant changing in the extension file too.

For example for an ellipsoid with principal axes 3, 2 and 1 along the x, y and z coordinate axes respectively, with center at the origin and truncated at x equals 1.

What math will reveal its center of mass and its moment of inertia for an axis of revolution through the center of mass and parallel to the y axis?

Hi

I wanted to know how to search a list of permutations given criteria: print the permutation(s) If the 4th element of each perm was equal to [C,Z} and the seventh was equal to [B,Y]

perm.mw

I tried to simplify this equation:

where Ts,Cf,Rf,Lg & L are Variables to equivelent equation in the form of:

                                                         (.....)Z3+(....)Z2+(.....)Z+(.........)      /   (.....)Z3+(....)Z2+(.....)Z+(.........)
                                                         

Hi professors,

Please can someone help me 
i want code of  function in maple to calculate values  of B(t), 

i have this matlab code

randn('state',100)          
T = 1; N = 5; dt = T/N;

dW = sqrt(dt)*randn(1,N);   
W = cumsum(dW)

but does not calculate B(0.25) and B(0.5)

Thanks,

Hi

Say I have 3 players on 2 teams. The teams play each other and there are 9 single [[A[s], B[s]], [A[s], B[m]], [A[s], B[w]], [A[m], B[s]], [A[m], B[m]], [A[m], B[w]], [A[w], B[s]], [A[w], B[m]], [A[w], B[w]]]matchups.

A, B, C & X, Y, Z. are the players. A and X are the strongest players, C and Z are the weakest.

Here's one: [[A,X],[B,Y],[C,Z],[A,Y],[B,Z],[C,X],[A,Z],[B,X],[C,Y]]

So i'm looking for some code to display all such permutations.

Carl came up with some code a while back which 'kind of' does it

P:= [A,B]:  S:= [s,m,w]:
[seq(rtable((1..nops(S)) $ nops(P), ()-> index~(P, S[[args]]), order= C_order))];
[[A[s], B[s]], [A[s], B[m]], [A[s], B[w]], [A[m], B[s]], [A[m], B[m]], [A[m], B[w]], [A[w], B[s]], [A[w], B[m]], [A[w], B[w]]]

I am trying to define a sum which is obtained from linked functions (which also contain the sum command). 

The problem is: if I modify the first function p and rerun the worksheet (except fot the restart command), then the changes do not affect the result. Does anyone know why? Thank you very much.
 

I start with this

restart

p := proc (i, j) options operator, arrow; sum('cat(A, _, i, j, k)', 'k' = 1 .. 3) end proc

proc (i, j) options operator, arrow; sum('cat(A, _, i, j, k)', 'k' = 1 .. 3) end proc

(1)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(2)

r := sum('q(i)', 'i' = 1 .. 3)

A_331+A_332+A_333+A_321+A_322+A_323+A_311+A_312+A_313+A_231+A_232+A_233+A_221+A_222+A_223+A_211+A_212+A_213+A_133+A_123+A_131+A_132+A_121+A_122+A_111+A_112+A_113

(3)

If I modify p (I make it twice its initial value), then this does not affect the value of q and r

p := proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

(4)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(5)

r := sum('q(i)', 'i' = 1 .. 3)

A_331+A_332+A_333+A_321+A_322+A_323+A_311+A_312+A_313+A_231+A_232+A_233+A_221+A_222+A_223+A_211+A_212+A_213+A_133+A_123+A_131+A_132+A_121+A_122+A_111+A_112+A_113

(6)

Why?
Even if I  unassign p, q and r, this does not work, either.

unassign('p', 'q', 'r')

p := proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

(7)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(8)

r := sum('q(i)', 'i' = 1 .. 3)

A_331+A_332+A_333+A_321+A_322+A_323+A_311+A_312+A_313+A_231+A_232+A_233+A_221+A_222+A_223+A_211+A_212+A_213+A_133+A_123+A_131+A_132+A_121+A_122+A_111+A_112+A_113

(9)

Only if I restart, then I can modify p and change the rest of values

restart

p := proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

(10)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(11)

r := sum('q(i)', 'i' = 1 .. 3)

2*A_332+2*A_333+2*A_323+2*A_331+2*A_313+2*A_321+2*A_322+2*A_311+2*A_312+2*A_231+2*A_232+2*A_233+2*A_221+2*A_222+2*A_223+2*A_212+2*A_213+2*A_211+2*A_131+2*A_132+2*A_133+2*A_121+2*A_122+2*A_123+2*A_111+2*A_112+2*A_113

(12)

``

``


 

Download problem_with_sums.mw

Hello,

I'm struggling with following simple problem which I however cannot seem to implement easily in Maple:

  • I have 2 different periodic functions: f1 and f2, each time in  variables x and t.
  • On the second function f2 a duty cycle with period T and fraction q should need to be applied so that:
    • during the DUTY (=ON or 1) part of this period, so from 0 -> q*T, f2__DC=f2
    • during the remainder (=OFF or 0) part of this period, so from q*T->T, f2__DC=0
    • each subsequent DUTY part starts at the same point where it ended at the previous cycle, so as if f2 was 'froozen' during the OFF part (see code for more details, but basically this means that the t parameter needs to be constantly translated depending on which duty cycle we are in).
  • In the end I want to calculate f1*f2 in a simple way using ranges for both variables x and t so that e.g. plotting can easily be done.

I've tried implicit functions and procedures but keep getting stuck whenever I introduce a second variable.  Somehow, Maple does not seem to work straightforward with non-univariate stuff.  Such an examples can also not be found in the programming guide so I'm hoping that one of you knows how to tackle this.

Any help will be much appreciated!
 

restart;
with(plots):

f1 := (x, t) -> A * (1 + B * sin(a*x-b*t));

proc (x, t) options operator, arrow; A*(1+B*sin(a*x-b*t)) end proc

(1)

f2 := (x, t) -> C * (1 + E * sin(c*x-d*t));

proc (x, t) options operator, arrow; C*(1+E*sin(c*x-d*t)) end proc

(2)

A:=1: B:=0.5: a:=100: b:=1:
C:=1: E:=0.5: c:=10: d:=10:

densityplot(f1(x,t) * f2(x,t), x = 0..1, t = 0..10, style=patchnogrid);

 

#Duty cycle (DC) applied to f2
# ON state:      n*T <= t <(n+q)*T  : f2__DC(x,t)=f2(x,t-n*(1-q)*T)
# OFF state: (n+q)*T <= t < (n+1)*T : f2__DC(x,t)=0 (so all other cases)
# (n is a positive integer, zero included, and n=floor(t/T))

T:=1:
q:=0.3; #fraction of T where DC is 1=ON

#How to apply the above DC to f2(x,t) so that f2__DC is obtained and following command works:
densityplot(f1(x,t) * f2__DC(x,t), x = 0..1, t = 0..10, style=patchnogrid);

 


 

Download dutycycle_.mw

windows 11 maple 2020 I can load other packages but cannot load the student packages

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