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

Hello :)

So what I was trying to find Galois group for quartic polynomials in a form f=x^+a_3*x^3+a_2*x^2+a_1*x+a_0, where 0<=a_i<=2 and a_0 <>0. I get polynomials and galois groups - that's not an issue. Lets say I specifically need polynomials with group D_4 so I run script

restart;
A := {seq(0 .. 2)};
A0 := A minus {0};
m := numelems(A)^3*(numelems(A) - 1);
a := Iterator:-CartesianProduct(A0, A $ 3);
s := seq(x^4 + add(v[i]*x^(i - 1), i = 1 .. 4), v = a);
for k to m do
if irreduc(s[k]) = 'true' then print(f[k] = s[k], galois(s[k])); end if end do;

This one gives all list of polynomalias and their galois group.

for k to m do
    if irreduc(s[k]) = 'true' then if galois(s[k]) = ("4T3", {"D(4)"}, "-", 8, {"(1 3)", "(1 2 3 4)"}) then print(f[k] = s[k], galois(s[k])); end if; end if;
end do;

This one gives me a list of D_4 specifically. 
When 0<=a_i<=2 - there are not many polynomials so I cant count it by hand, but if I make a sequence larger there are too many polynomials to count them manually. So the question is how to count how many polynomials there are with a group D_4? Or lets say how do I count how many polynomials are in each group?
Thank you

Please help me solve the following problem about complex numbers with Maple: w= (3+zi)/(2+z) whose geometric representation in the "oxy" plane is a straight line. Calculate module of z. Thank you so much.

Hi,

I have a code (see below) for the following number sequence and want to produce a graph as well as the numerical data, please advise how to do it.

Sequence definition: Lexicographicaly least sequence of nonnegative integers commencing 1,3,5,7 such that any four  consecutive terms are mutually coprime.

The code I have so far is: 

ina := proc (n) false end :

a := proc (n) option remember; local k;

if n < 5 then k := 2*n-1

else for k from 2 while ina(k) or igcd(k, a(n-1)) <> 1 or igcd(k, a(n-2)) <> 1 or igcd(k, a(n-3)) <> 1

do  od 

fi; ina(k) := true; k

end proc;

seq(a(n), n = 1 .. 100);
1, 3, 5, 7, 2, 9, 11, 13, 4, 15, 17, 19, 8, 21, 23, 25, 16, 27, 

  29, 31, 10, 33, 37, 41, 14, 39, 43, 47, 20, 49, 51, 53, 22, 35, 

  57, 59, 26, 55, 61, 63, 32, 65, 67, 69, 28, 71, 73, 45, 34, 77, 

  79, 75, 38, 83, 89, 81, 40, 91, 97, 87, 44, 85, 101, 93, 46, 

  95, 103, 99, 52, 107, 109, 105, 58, 113, 121, 111, 50, 119, 

  127, 117, 62, 115, 131, 123, 56, 125, 137, 129, 64, 133, 139, 

  135, 68, 143, 149, 141, 70, 151, 157, 153

I have tried listplot but for some reason cant get the correct format

Hope you can help

Best regards

David.

eqs.mw

Download eqs.mw

#im tryin to solve 9 equation having 9 varibales but the fsolve doesnt solve for C1 to R4, what i am doing wrong??

I am working on a sequence: seq([seq([a[i,j],b[?]],i=1..3)], j=1..3)], it has in total 9 output of a such as a[1,1],a[2,1],a[3,1],a[1,2],a[2,2],a[3,2],a[1,3],a[2,3],a[3,3], yet I need to the output of b like b[1],b[2],b[3],b[4],b[5],b[6],b[7],b[8],b[9]. I have tried to put something like seq([seq([a[i,j],b[f]],i=1..3,f=1..9)] j=1..3)] but it does not work...

Could someone help me?

Greatly appreciated!

Dear all

I have a power series, the genral term contains sign(sin(n)), 
everything is well defined, but when I apply summation to the general term, i can not see sign(sin(n)), its dropped.. why 

and how deduce the the limit to get the radius of convergence 

Cauchy_criteria.mw

thank you for any help 

Hello,

I'm trying to solve a differential equation with boundary conditions using dsolve. However dsolve return nothing. Any help to understand what's happening?

Thank you!

Here's my code:

eq1:=diff(psi(s),s,s)=t*sin(psi(s))-r*cos(psi(s));
eq2:=diff(x(s),s)=cos(psi(s));
eq3:=diff(y(s),s)=sin(psi(s));

cond1:=x(0)=0;
cond2:=x(1)=d+1;
cond3:=y(0)=0;
cond4:=psi(0)=0;
cond5:=D(psi)(0)=0;
cond6:= y(1)=0;

dsolve({eq1,eq2,eq3,cond1,cond2,cond3,cond4,cond5,cond6});
 

Dear all

I  compute the radius of convergence of power series using maple, 

but the code does not give any result

radius_convergence_PSeries.mw

thank you for any help 

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

Hi, I am very new in maple. I want to create a list of 54 quartic polynomials f=x^4 + a_3*x^3 + a_2*x^2 + a_1*x + a_0 with coefficients 0<=a_i<=2 and a_0 <> 0 . 

f := x ->  x^4 + add(a[i]*x^i, i = 0 .. 3);
for m to 54 do
    pol[m] := f(x);
end do;

How do I incorporate conditions 0<=a_i<=2 and a_0 <> 0 into this cycle so I can get 54 different combinations of coefficients? Thank you.

restart;
u := (H(x, t, z)+sqrt(R))*exp(I*R*x);
                /              (1/2)\           
                \H(x, t, z) + R     / exp(I R x)

I*(Diff(u, z))+Diff(u, `$`(x, 2))+Diff(u, `$`(t, 2))+(abs(u)*abs(u))*u-((abs(u)*abs(u))*abs(u)*abs(u))*u;
  / d  //              (1/2)\           \\
I |--- \\H(x, t, z) + R     / exp(I R x)/|
  \ dz                                   /

     / 2                                   \
     |d  //              (1/2)\           \|
   + |-- \\H(x, t, z) + R     / exp(I R x)/|
     \                                     /

     / 2                                   \                    
     |d  //              (1/2)\           \|                  2 
   + |-- \\H(x, t, z) + R     / exp(I R x)/| + (exp(-Im(R x)))  
     \                                     /                    

                       2                                    
  |              (1/2)|  /              (1/2)\              
  |H(x, t, z) + R     |  \H(x, t, z) + R     / exp(I R x) - 

                                        4                       
                 4 |              (1/2)|  /              (1/2)\ 
  (exp(-Im(R x)))  |H(x, t, z) + R     |  \H(x, t, z) + R     / 

  exp(I R x)
value(%);
  / d            \              / d  / d            \\           
I |--- H(x, t, z)| exp(I R x) + |--- |--- H(x, t, z)|| exp(I R x)
  \ dz           /              \ dx \ dx           //           

         / d            \             
   + 2 I |--- H(x, t, z)| R exp(I R x)
         \ dx           /             

     /              (1/2)\  2           
   - \H(x, t, z) + R     / R  exp(I R x)

     / d  / d            \\                             2 
   + |--- |--- H(x, t, z)|| exp(I R x) + (exp(-Im(R x)))  
     \ dt \ dt           //                               

                       2                                    
  |              (1/2)|  /              (1/2)\              
  |H(x, t, z) + R     |  \H(x, t, z) + R     / exp(I R x) - 

                                        4                       
                 4 |              (1/2)|  /              (1/2)\ 
  (exp(-Im(R x)))  |H(x, t, z) + R     |  \H(x, t, z) + R     / 

  exp(I R x)
simplify(%);
  / d            \              / d  / d            \\           
I |--- H(x, t, z)| exp(I R x) + |--- |--- H(x, t, z)|| exp(I R x)
  \ dz           /              \ dx \ dx           //           

         / d            \                 2                      
   + 2 I |--- H(x, t, z)| R exp(I R x) - R  exp(I R x) H(x, t, z)
         \ dx           /                                        

      (5/2)              / d  / d            \\           
   - R      exp(I R x) + |--- |--- H(x, t, z)|| exp(I R x)
                         \ dt \ dt           //           

                                                  2           
                             |              (1/2)|            
   + exp(-2 Im(R x) + I R x) |H(x, t, z) + R     |  H(x, t, z)

                                                  2       
                             |              (1/2)|   (1/2)
   + exp(-2 Im(R x) + I R x) |H(x, t, z) + R     |  R     

                                                  4           
                             |              (1/2)|            
   - exp(-4 Im(R x) + I R x) |H(x, t, z) + R     |  H(x, t, z)

                                                  4       
                             |              (1/2)|   (1/2)
   - exp(-4 Im(R x) + I R x) |H(x, t, z) + R     |  R     
collect(%, exp(I*R*x));
 /  (5/2)       / d            \      2           
 |-R      + 2 I |--- H(x, t, z)| R - R  H(x, t, z)
 \              \ dx           /                  

        / d            \   / d  / d            \\
    + I |--- H(x, t, z)| + |--- |--- H(x, t, z)||
        \ dz           /   \ dx \ dx           //

      / d  / d            \\\           
    + |--- |--- H(x, t, z)||| exp(I R x)
      \ dt \ dt           ///           

                                                   2           
                              |              (1/2)|            
    + exp(-2 Im(R x) + I R x) |H(x, t, z) + R     |  H(x, t, z)

                                                   2       
                              |              (1/2)|   (1/2)
    + exp(-2 Im(R x) + I R x) |H(x, t, z) + R     |  R     

                                                   4           
                              |              (1/2)|            
    - exp(-4 Im(R x) + I R x) |H(x, t, z) + R     |  H(x, t, z)

                                                   4       
                              |              (1/2)|   (1/2)
    - exp(-4 Im(R x) + I R x) |H(x, t, z) + R     |  R     
 

restart;
H := a__1*exp(I*(-Omega*t+k*x+z*k[1]))+a__2*exp(-I*(-Omega*t+k*x+z*k[1]));
I*(diff(H, z))+diff(H, x, x)+diff(H, t, t)+R*(H+conjugate(H))+R^2*(H+conjugate(H))*H;
value(%);
simplify(%);

Download m18bs.mw

Hi,

I'm trying to solve the attached system but I don't know how to proceed.

Any ideas?

Thanks very much in advance.

Best regards,

Download maple_problem.mw

I run Maple 2021 under Ubuntu 20.04 on a new Lenovo laptop with 32Gb of Ram. Every time I start Maple, it runs for a few minutes and then loses the "kernel connection". I have to save the worksheet and re-start Maple. In dmesg, I find:

[ 1436.724570] oom-kill:constraint=CONSTRAINT_NONE,nodemask=(null),cpuset=/,mems_allowed=0,global_oom,task_memcg=/user.slice/user-1000.slice/user@1000.service,task=mserver,pid=8037,uid=1000
[ 1436.724589] Out of memory: Killed process 8037 (mserver) total-vm:31723552kB, anon-rss:31289772kB, file-rss:60kB, shmem-rss:0kB, UID:1000 pgtables:61656kB oom_score_adj:0
[ 1437.151441] oom_reaper: reaped process 8037 (mserver), now anon-rss:0kB, file-rss:0kB, shmem-rss:0kB

indicating that Maple's virtual memory exceeded 30 Gb! This happens even if the only command I execute is, for instance, "resrart" or "A:=1" and nothing else. It also happens when no other applications are running and the "top" command indicates that around 30Gb of RAM is available.

In this state, Maple is utterly useless to me. This was a new install of Maple and a fresh install of Ubuntu on a new laptop, surely I am not the only one seeing this?

I have tried setting a 30Gb limit in "kerneloptions" for "stacklimit" but that di not make a difference.

If you have seen any behaviour like this, please respond. Is there some bug in Maple that leads to oncontrolled and unprovoked memory grabbing?