Hello everybody!! Can you please help me figure it out. I wrote the code, but for some reason I have an infinite loop going on, it counts normally to the cycle, as the cycle reaches, then everything is infinite

restart;
with(plots):
f:=unapply(2*x-4*cos(x)-0.6,x); #the equation itself
f1:=unapply(diff(f(x),x),x); #its derivative
a:=-0.5; b:=1.5; eps:=0.001: #interval and accuracy
 
 
phi:=unapply((4*cos(x)-0.6)/2,x); #solving the equation with respect to x
x[0]:=1; #I take any point from the interval
x[1]:=evalf(phi(x[0]));
L:=evalf(abs(phi(b)-phi(a))/abs(b-a)); 
L1:=evalf(abs(phi(x[1])-phi(x[0]))/abs(x[1]-x[0])); 
psi:=unapply(abs(diff(phi(x),x)),x);
plot([psi(x),1],x=a..b,color=[red,green]);
 
n:=1:
while abs(evalf(x[n]-x[n-1])) > eps do
n:=n+1:
x[n]:=evalf(phi(x[n-1]));
od;
fsolve(f(x)=0,x=a..b);

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

v2i2v_circuit.msim

I try to design a circuit to make a voltage-current-voltage translation. In my assumption, probe1.v is equal to probe2.v and it will generate a current(probe2.v / R4) through NMOS. The NMOS acts as a closed switch. Probe3.v is equal to CV3 and i can get "Probe4.v = CV1 + CV3". However, when the circuit operates, probe3.v isn't equal to CV3 and probe1.v isn't equal to probe2.v. I have tried to rise the differential input resistance and differential amplifier to make the Uin+ close to Uin- in op amp, but it doesn"t work effectively.
In addition, the closed resisitance of NMOS is also taken into consideration and i try to make it pretty below Kohm.

Could you help me fix the problem? 

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