MaplePrimes Questions

I'm doing something wrong again in the attached file. Please advise.

test.mw

Hi everyone,

I'm having some trouble with plotting in Maple and was hoping to get some help here. I'm trying to create a plot for a specific function, but I'm not sure if I'm using the right commands or parameters. Here’s what I’m trying to do:

To plot the line plot(E3,nu=10^13..4.5*10^18);

and 

plot(E1(nu),nu=10^13..4.5*10^18); 

you can look around my calculus please advise.

Could someone please explain what might be going wrong with my approach? Any suggestions or examples of correct usage would be greatly appreciated.

Thanks in advance for your help!PLanckPh.mw

Hi,

I am trying to create a series of exercises ( Generate Similar) with a table layout (2x3), but my approach is not optimal. Any suggestions? Thanks

GenerateSimilar_Test.mw

So, MaplePrimes is now accessible again after an unprecedented 5-day outage. What happened? There was no announcement of the outage beforehand, making it seem like an accident. How could it take 5 days to recover from an accident? I don't see any differences yet, so it doesn't seem as if the software that runs MaplePrimes was being updated. There's usually some official announcement of these things, but I don't see any.

Is it possible to reduce the space between the plot title and the 3dplot in the attached file?

Plot_title_too_high.mw

I am trying to do something that was recommended in

https://math.stackexchange.com/questions/4583857/how-to-use-recursion-to-define-a-number-series-in-maple

but can't get the desired sequnce. See for example my code

v := proc(m) option remember; return m; end proc;
k := 5:
v(k + 1) := 0:
v(k):=1:
for i from k - 1 by -1 to 1 do
    v(i);
end do;

I get the output 1,1,1,1

I don't get it.

When I write the following code, I get an error and I cannot plot the graph. 

Please, I would appreciate your support

 

restart;                                                                                                                                              with(plots):                                                                                                                                            h:=(u)->sin((0.3)*u^2);                                                                                                                                         K:=(r,v,u)-> (factorial(2*r+3)*v^r*u^(r+2))/(factoral(r)*factoral(r+2)*(v+u)^(2*r+4));                                         w:=(r,j,a,u)->(u^j-1)/((1+u)^(r+j-1))*((a*u/(1+u))*binomial(r+j-1,j)-(1-a)*(1+u)*binomial(r+j-3,j-2)+(1-a)*u*binomial(r+j-1,j));                                                                                                                                 B:=(r,a,u)->sum(w(r,j,a,u)*h(j/r),j=0..infinity);                                                                                                  H:=(r,a,u)->int(K(r,v,u)*B(r,a,v),v=0..infinity);                                                                                                  p1:=plot(h(u),u=-1.5*Pi..1.5*Pi,color=blue):                                                                                                    p2:=plot(B(10,0.9,u),u=-1.5*Pi..1.5*Pi,color=red):                                                                                        p3:=plot(H(10,0.9,u),u=-1.5*Pi..1.5*Pi,color=brown):                                                                                    display([p1,p2,p3]);

This is problem from INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014 ,  Chapter 2. First Order Equations. Exercises 2.4, page 57, problem 39

Maple 2024.2 can't solve it. But solution is arctan(t)-t*y(t)^2 = 0 which Maple verifies correct

restart;

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1848 and is the same as the version installed in this computer, created 2025, March 11, 16:9 hours Pacific Time.`

restart;

ode:=(1/(1+t^2)-y(t)^2)-(2*t*y(t))*diff(y(t),t)=0;
IC:=y(0)=0;

1/(t^2+1)-y(t)^2-2*t*y(t)*(diff(y(t), t)) = 0

y(0) = 0

sol:=dsolve([ode,IC])

mysol:=arctan(t)-t*y(t)^2 = 0;

arctan(t)-y(t)^2*t = 0

odetest(mysol,[ode,IC])

[0, 0]

 

 

Download can_not_dsolve_march_12_2025.mw

Any one has suggestion how to help dsolve find this solution?

Hey guys, 

I am solving many systems of polynomial equations. Sometimes I get the same solution, just in a diffrent are, so for example the first solution is for y between 0 and 1 and the second solution is for y between 1 and 2. So now I want to take those solutions intervals and combine them so I can make one solution out of two. However I am struggeling with working with intervals in Maple. It is not that easy how I expected it to be.

I wrote an own program which works quite nice unless there is a single solution which would meen an interval like [1,1] meaning y=1working_with_intervals.mw

restart; sets := [{1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]; intervals := [RealRange(Open(1), Open(infinity)), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]; correct_form := [y::(RealRange(Open(1), Open(infinity))), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]; Sol := solve(`~`[convert](Or(op(correct_form)), relation))

[{1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]

 

[RealRange(Open(1), infinity), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]

 

[y::(RealRange(Open(1), infinity)), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]

 

RealRange(Open(0), Open(1)), RealRange(Open(1), infinity)

(1)

restart; sets := [{1}, {1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]; intervals := [[1, 1], RealRange(Open(1), Open(infinity)), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]; correct_form := [y::[1, 1], y::(RealRange(Open(1), Open(infinity))), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]; Sol := solve(`~`[convert](Or(op(correct_form)), relation))

[{1}, {1 < y}, {y <= 1/2, 0 < y}, {1/2 < y, y < 1}]

 

[[1, 1], RealRange(Open(1), infinity), RealRange(Open(0), 1/2), RealRange(Open(1/2), Open(1))]

 

[y::[1, 1], y::(RealRange(Open(1), infinity)), y::(RealRange(Open(0), 1/2)), y::(RealRange(Open(1/2), Open(1)))]

 

RealRange(Open(0), Open(1)), RealRange(Open(1), infinity)

(2)
 

NULL

Download working_with_intervals.mw

In the attached file you can see my problem. When I add the intervall [1,1] the solution should become (0,infty), but it seems like Maple does not understand what I mean by [1,1], so the 1 is not part of the solution "Sol".

FYI: I wrote a program which is able to convert "sets" into "intervals" into "correct_form" using RealRange, but it is not necesarry for my problem. 

So my questions are: Why doesnt Maple recognize [1,1] as an interval containing only the 1? Is there a way I can rewrite the intervall so I can use it for the solve process in "Sol"? I also thought about making two diffrent sets with the same intervals than adding [1,2) to the one set and (1,2) to the other set and than make an intersection but I seems to be very complicated for a seemingly easy problem. Is there a easier way to work with intervals? 

Regards and thank you

Felix

Hi,

In order to obtain an algebraic system, one must set the coeffcients of (H + G′/G2)i to zero. Solve the obtained algebraic system.

But the expressions were not arranged correctly, but no answer was obtained, while the answer was as follows:

 

``NULL

restart

with(PDEtools):
df:= diff(diff(G(xi), xi)/(G(xi)^2), xi)= A+B*(diff(G(xi), xi)/(G(xi)^2))^2+ c*(diff(G(xi), xi)/(G(xi)^2));

(diff(diff(G(xi), xi), xi))/G(xi)^2-2*(diff(G(xi), xi))^2/G(xi)^3 = A+B*(diff(G(xi), xi))^2/G(xi)^4+c*(diff(G(xi), xi))/G(xi)^2

(1)

a := [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10]:

 

NULL

p:= -2: q:= 2:

Y1 :=xi -> (add(a[i+3]*(H+(diff(G(xi), xi)/(G(xi)^2)))^i, i = p .. q)):

NULL

eq1 := -4*(k^2)*m*diff(Y1(xi), xi,xi) - 4*l*(Y1(xi)^2)+(4*(nu^2)-4*nu*n+n^2-4)*Y1(xi):

eq2:=subs(df,eq1);

-4*k^2*m*(6*a0*(A+B*(diff(G(xi), xi))^2/G(xi)^4+c*(diff(G(xi), xi))/G(xi)^2)^2/(H+(diff(G(xi), xi))/G(xi)^2)^4-2*a0*((diff(diff(diff(G(xi), xi), xi), xi))/G(xi)^2-6*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^3+6*(diff(G(xi), xi))^3/G(xi)^4)/(H+(diff(G(xi), xi))/G(xi)^2)^3+2*a1*(A+B*(diff(G(xi), xi))^2/G(xi)^4+c*(diff(G(xi), xi))/G(xi)^2)^2/(H+(diff(G(xi), xi))/G(xi)^2)^3-a1*((diff(diff(diff(G(xi), xi), xi), xi))/G(xi)^2-6*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^3+6*(diff(G(xi), xi))^3/G(xi)^4)/(H+(diff(G(xi), xi))/G(xi)^2)^2+a3*((diff(diff(diff(G(xi), xi), xi), xi))/G(xi)^2-6*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^3+6*(diff(G(xi), xi))^3/G(xi)^4)+2*a4*(A+B*(diff(G(xi), xi))^2/G(xi)^4+c*(diff(G(xi), xi))/G(xi)^2)^2+2*a4*(H+(diff(G(xi), xi))/G(xi)^2)*((diff(diff(diff(G(xi), xi), xi), xi))/G(xi)^2-6*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^3+6*(diff(G(xi), xi))^3/G(xi)^4))-4*l*(a0/(H+(diff(G(xi), xi))/G(xi)^2)^2+a1/(H+(diff(G(xi), xi))/G(xi)^2)+a2+a3*(H+(diff(G(xi), xi))/G(xi)^2)+a4*(H+(diff(G(xi), xi))/G(xi)^2)^2)^2+(n^2-4*n*nu+4*nu^2-4)*(a0/(H+(diff(G(xi), xi))/G(xi)^2)^2+a1/(H+(diff(G(xi), xi))/G(xi)^2)+a2+a3*(H+(diff(G(xi), xi))/G(xi)^2)+a4*(H+(diff(G(xi), xi))/G(xi)^2)^2)

(2)

simplify(eq2):

fin1:=simplify(numer(%)):

``

for i from 0 to degree(fin1,H+(diff(G(xi), xi)/(G(xi)^2))) do EQ[i]:=simplify(coeff(fin1,H+(diff(G(xi), xi)/(G(xi)^2)),i)); end do;

4*k^2*(H*G(xi)^2+diff(G(xi), xi))*(-2*(diff(G(xi), xi))^4*a4-G(xi)^2*(8*H*a4+a3)*(diff(G(xi), xi))^3-3*G(xi)^4*H*(4*H*a4+a3)*(diff(G(xi), xi))^2+G(xi)^6*(-8*H^3*a4-3*H^2*a3+a1)*(diff(G(xi), xi))+G(xi)^8*(-2*H^4*a4-H^3*a3+H*a1+2*a0))*m*G(xi)^4*(diff(diff(diff(G(xi), xi), xi), xi))-24*(diff(G(xi), xi))*k^2*(H*G(xi)^2+diff(G(xi), xi))*(-2*(diff(G(xi), xi))^4*a4-G(xi)^2*(8*H*a4+a3)*(diff(G(xi), xi))^3-3*G(xi)^4*H*(4*H*a4+a3)*(diff(G(xi), xi))^2+G(xi)^6*(-8*H^3*a4-3*H^2*a3+a1)*(diff(G(xi), xi))+G(xi)^8*(-2*H^4*a4-H^3*a3+H*a1+2*a0))*m*G(xi)^3*(diff(diff(G(xi), xi), xi))-4*a4*(12*k^2*m*G(xi)^2+2*B^2*m*k^2+a4*l)*(diff(G(xi), xi))^8-8*G(xi)^2*(3*k^2*m*(10*H*a4+a3)*G(xi)^2+a4*((4*B^2*k^2*m+4*a4*l)*H+2*c*B*m*k^2+a3*l))*(diff(G(xi), xi))^7-16*(6*H*k^2*m*(5*H*a4+a3)*G(xi)^2+(3*B^2*a4*k^2*m+7*a4^2*l)*H^2+(7/2)*((8/7)*c*B*m*k^2+a3*l)*a4*H+(m*(B*A+(1/2)*c^2)*k^2+(1/2)*l*a2-(1/4)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(1/4)*a3^2*l)*G(xi)^4*(diff(G(xi), xi))^6-64*G(xi)^6*(-(3/8)*k^2*m*(-20*H^3*a4-6*H^2*a3+a1)*G(xi)^2+((1/2)*k^2*m*B^2*a4+(7/2)*a4^2*l)*H^3+(21/8)*((4/7)*c*B*m*k^2+a3*l)*a4*H^2+((m*(B*A+(1/2)*c^2)*k^2+(3/4)*l*a2-(3/8)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(3/8)*a3^2*l)*H+((1/4)*c*A*m*k^2+(1/8)*a1*l)*a4+(1/8)*a1*B^2*k^2*m+(1/8)*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*(diff(G(xi), xi))^5-8*G(xi)^8*(-6*k^2*m*(-5*H^4*a4-2*H^3*a3+H*a1+a0)*G(xi)^2+(B^2*a4*k^2*m+35*a4^2*l)*H^4+35*((8/35)*c*B*m*k^2+a3*l)*a4*H^3+(((12*A*B+6*c^2)*m*k^2+15*l*a2-(15/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(15/2)*a3^2*l)*H^2+((8*A*c*k^2*m+5*a1*l)*a4+a1*B^2*k^2*m+5*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H+(A^2*k^2*m+a0*l)*a4+(3*B^2*a0+2*B*a1*c)*m*k^2+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*(diff(G(xi), xi))^4-32*G(xi)^10*(-(3/4)*H*k^2*m*(-2*H^4*a4-H^3*a3+H*a1+2*a0)*G(xi)^2+7*H^5*a4^2*l+(35/4)*((2/35)*c*B*m*k^2+a3*l)*a4*H^4+((m*(2*A*B+c^2)*k^2+5*l*a2-(5/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(5/2)*a3^2*l)*H^3+(((5/2)*a1*l+3*c*A*m*k^2)*a4+(5/2)*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^2+((A^2*k^2*m+a0*l)*a4+(1/2)*k^2*m*B*a1*c+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H+(1/2)*((B*A+(1/2)*c^2)*a1+3*B*a0*c)*m*k^2+((1/4)*a0*a3+(1/4)*a1*a2)*l-(1/8)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*(diff(G(xi), xi))^3-48*((7/3)*H^6*a4^2*l+(7/2)*H^5*a3*a4*l+(((1/3)*m*(B*A+(1/2)*c^2)*k^2+(5/2)*l*a2-(5/4)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(5/4)*a3^2*l)*H^4+(((5/3)*a1*l+(4/3)*c*A*m*k^2)*a4+(5/3)*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^3+((A^2*k^2*m+a0*l)*a4+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H^2+((1/3)*(B*A+(1/2)*c^2)*a1*m*k^2+((1/2)*a0*a3+(1/2)*a1*a2)*l-(1/4)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*H+(1/3)*m*(A*a1*c+3*(B*A+(1/2)*c^2)*a0)*k^2+((1/6)*a0*a2+(1/12)*a1^2)*l-(1/12)*(nu-(1/2)*n-1)*a0*(nu-(1/2)*n+1))*G(xi)^12*(diff(G(xi), xi))^2-8*(4*a4^2*H^7*l+7*a3*a4*H^6*l+((6*l*a2+3*nu*n-3*nu^2-(3/4)*n^2+3)*a4+3*a3^2*l)*H^5+((2*A*c*k^2*m+5*a1*l)*a4+5*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^4+((4*A^2*k^2*m+4*a0*l)*a4+(4*a1*a3+2*a2^2)*l-2*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H^3+((3*a0*a3+3*a1*a2)*l-(3/2)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*H^2+(2*k^2*m*A*a1*c+(2*a0*a2+a1^2)*l-(nu-(1/2)*n-1)*a0*(nu-(1/2)*n+1))*H+A*m*(A*a1+6*a0*c)*k^2+a1*l*a0)*G(xi)^14*(diff(G(xi), xi))-8*G(xi)^16*((1/2)*H^8*a4^2*l+H^7*a3*a4*l+((l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(1/2)*a3^2*l)*H^6+(a1*a4*l+a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^5+((A^2*k^2*m+a0*l)*a4+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H^4+((a0*a3+a1*a2)*l-(1/2)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*H^3+(((1/2)*a1^2+a0*a2)*l-(1/2)*(nu-(1/2)*n-1)*a0*(nu-(1/2)*n+1))*H^2+a1*(A^2*k^2*m+a0*l)*H+(1/2)*a0^2*l+3*k^2*m*A^2*a0)

(3)

 

NULL

for i from 0 to degree(fin1,H+(diff(G(xi), xi)/(G(xi)^2))) do EQ[i]:=simplify(coeff(fin1,H+(diff(G(xi), xi)/(G(xi)^2)),i)); end do;

4*k^2*(H*G(xi)^2+diff(G(xi), xi))*(-2*(diff(G(xi), xi))^4*a4-G(xi)^2*(8*H*a4+a3)*(diff(G(xi), xi))^3-3*G(xi)^4*H*(4*H*a4+a3)*(diff(G(xi), xi))^2+G(xi)^6*(-8*H^3*a4-3*H^2*a3+a1)*(diff(G(xi), xi))+G(xi)^8*(-2*H^4*a4-H^3*a3+H*a1+2*a0))*m*G(xi)^4*(diff(diff(diff(G(xi), xi), xi), xi))-24*(diff(G(xi), xi))*k^2*(H*G(xi)^2+diff(G(xi), xi))*(-2*(diff(G(xi), xi))^4*a4-G(xi)^2*(8*H*a4+a3)*(diff(G(xi), xi))^3-3*G(xi)^4*H*(4*H*a4+a3)*(diff(G(xi), xi))^2+G(xi)^6*(-8*H^3*a4-3*H^2*a3+a1)*(diff(G(xi), xi))+G(xi)^8*(-2*H^4*a4-H^3*a3+H*a1+2*a0))*m*G(xi)^3*(diff(diff(G(xi), xi), xi))-4*a4*(12*k^2*m*G(xi)^2+2*B^2*m*k^2+a4*l)*(diff(G(xi), xi))^8-8*G(xi)^2*(3*k^2*m*(10*H*a4+a3)*G(xi)^2+a4*((4*B^2*k^2*m+4*a4*l)*H+2*c*B*m*k^2+a3*l))*(diff(G(xi), xi))^7-16*(6*H*k^2*m*(5*H*a4+a3)*G(xi)^2+(3*B^2*a4*k^2*m+7*a4^2*l)*H^2+(7/2)*((8/7)*c*B*m*k^2+a3*l)*a4*H+(m*(B*A+(1/2)*c^2)*k^2+(1/2)*l*a2-(1/4)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(1/4)*a3^2*l)*G(xi)^4*(diff(G(xi), xi))^6-64*G(xi)^6*(-(3/8)*k^2*m*(-20*H^3*a4-6*H^2*a3+a1)*G(xi)^2+((1/2)*k^2*m*B^2*a4+(7/2)*a4^2*l)*H^3+(21/8)*((4/7)*c*B*m*k^2+a3*l)*a4*H^2+((m*(B*A+(1/2)*c^2)*k^2+(3/4)*l*a2-(3/8)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(3/8)*a3^2*l)*H+((1/4)*c*A*m*k^2+(1/8)*a1*l)*a4+(1/8)*a1*B^2*k^2*m+(1/8)*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*(diff(G(xi), xi))^5-8*G(xi)^8*(-6*k^2*m*(-5*H^4*a4-2*H^3*a3+H*a1+a0)*G(xi)^2+(B^2*a4*k^2*m+35*a4^2*l)*H^4+35*((8/35)*c*B*m*k^2+a3*l)*a4*H^3+(((12*A*B+6*c^2)*m*k^2+15*l*a2-(15/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(15/2)*a3^2*l)*H^2+((8*A*c*k^2*m+5*a1*l)*a4+a1*B^2*k^2*m+5*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H+(A^2*k^2*m+a0*l)*a4+(3*B^2*a0+2*B*a1*c)*m*k^2+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*(diff(G(xi), xi))^4-32*G(xi)^10*(-(3/4)*H*k^2*m*(-2*H^4*a4-H^3*a3+H*a1+2*a0)*G(xi)^2+7*H^5*a4^2*l+(35/4)*((2/35)*c*B*m*k^2+a3*l)*a4*H^4+((m*(2*A*B+c^2)*k^2+5*l*a2-(5/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(5/2)*a3^2*l)*H^3+(((5/2)*a1*l+3*c*A*m*k^2)*a4+(5/2)*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^2+((A^2*k^2*m+a0*l)*a4+(1/2)*k^2*m*B*a1*c+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H+(1/2)*((B*A+(1/2)*c^2)*a1+3*B*a0*c)*m*k^2+((1/4)*a0*a3+(1/4)*a1*a2)*l-(1/8)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*(diff(G(xi), xi))^3-48*((7/3)*H^6*a4^2*l+(7/2)*H^5*a3*a4*l+(((1/3)*m*(B*A+(1/2)*c^2)*k^2+(5/2)*l*a2-(5/4)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(5/4)*a3^2*l)*H^4+(((5/3)*a1*l+(4/3)*c*A*m*k^2)*a4+(5/3)*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^3+((A^2*k^2*m+a0*l)*a4+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H^2+((1/3)*(B*A+(1/2)*c^2)*a1*m*k^2+((1/2)*a0*a3+(1/2)*a1*a2)*l-(1/4)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*H+(1/3)*m*(A*a1*c+3*(B*A+(1/2)*c^2)*a0)*k^2+((1/6)*a0*a2+(1/12)*a1^2)*l-(1/12)*(nu-(1/2)*n-1)*a0*(nu-(1/2)*n+1))*G(xi)^12*(diff(G(xi), xi))^2-8*(4*a4^2*H^7*l+7*a3*a4*H^6*l+((6*l*a2+3*nu*n-3*nu^2-(3/4)*n^2+3)*a4+3*a3^2*l)*H^5+((2*A*c*k^2*m+5*a1*l)*a4+5*a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^4+((4*A^2*k^2*m+4*a0*l)*a4+(4*a1*a3+2*a2^2)*l-2*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H^3+((3*a0*a3+3*a1*a2)*l-(3/2)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*H^2+(2*k^2*m*A*a1*c+(2*a0*a2+a1^2)*l-(nu-(1/2)*n-1)*a0*(nu-(1/2)*n+1))*H+A*m*(A*a1+6*a0*c)*k^2+a1*l*a0)*G(xi)^14*(diff(G(xi), xi))-8*G(xi)^16*((1/2)*H^8*a4^2*l+H^7*a3*a4*l+((l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1))*a4+(1/2)*a3^2*l)*H^6+(a1*a4*l+a3*(l*a2-(1/2)*(nu-(1/2)*n-1)*(nu-(1/2)*n+1)))*H^5+((A^2*k^2*m+a0*l)*a4+(a1*a3+(1/2)*a2^2)*l-(1/2)*(nu-(1/2)*n-1)*a2*(nu-(1/2)*n+1))*H^4+((a0*a3+a1*a2)*l-(1/2)*(nu-(1/2)*n-1)*a1*(nu-(1/2)*n+1))*H^3+(((1/2)*a1^2+a0*a2)*l-(1/2)*(nu-(1/2)*n-1)*a0*(nu-(1/2)*n+1))*H^2+a1*(A^2*k^2*m+a0*l)*H+(1/2)*a0^2*l+3*k^2*m*A^2*a0)

(4)

Eqs:={seq(EQ[i],i=0..12)}:

 

sol:=solve(Eqs,{a0, a1, a2, a3, a4, H, nu},explicit)

(5)
 

 

Download GGGGGGG2.mw

Hi!

I am studying Burger's equation, and I would like to see the steps that Maple takes to solve this.  "ShowSteps" doesn't seem to work.

Unfortunately, I am unable to share the worksheet I made.

Server Error - MaplePrimes

 
 

MaplePrimes
 
 
 
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i don't know where is issue?

p-not.mw

restart

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

 

t := 0

0

(1)

M := -(2*(-(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/(a[1]+I*b[1])+((6*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta)+(6*(a[4]+I*b[4]))*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2*beta)-(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/(a[1]+I*b[1]))*exp((a[2]+I*b[2])*(-((a[2]+I*b[2])^2*(a[4]+I*b[4])+alpha*(a[4]+I*b[4])+beta)*t/(a[4]+I*b[4])+(a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta^2*(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2)-(6*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta*conjugate(a[1]+I*b[1]))-(6*(a[4]+I*b[4]))*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))*(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2*beta*(a[1]+I*b[1]))+(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta))*(a[2]+I*b[2])*exp((a[2]+I*b[2])*(-((a[2]+I*b[2])^2*(a[4]+I*b[4])+alpha*(a[4]+I*b[4])+beta)*t/(a[4]+I*b[4])+(a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta)+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2*beta)-(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/(a[1]+I*b[1]))*exp(conjugate(a[2]+I*b[2])*(-(conjugate(a[2]+I*b[2])^2*conjugate(a[4]+I*b[4])+alpha*conjugate(a[4]+I*b[4])+beta)*t/conjugate(a[4]+I*b[4])+conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+(36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta^2*(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)-6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta*conjugate(a[1]+I*b[1]))-6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))*(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2*beta*(a[1]+I*b[1]))+(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta))*conjugate(a[2]+I*b[2])*exp(conjugate(a[2]+I*b[2])*(-(conjugate(a[2]+I*b[2])^2*conjugate(a[4]+I*b[4])+alpha*conjugate(a[4]+I*b[4])+beta)*t/conjugate(a[4]+I*b[4])+conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+(-(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/(a[1]+I*b[1])+(6*(a[4]+I*b[4]))*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2*beta)+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2*beta)+(6*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta)+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta))*((-(3*(a[2]+I*b[2]))*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-(2*(-3*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])*(1/2)+beta))*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*exp((a[2]+I*b[2])*(-((a[2]+I*b[2])^2*(a[4]+I*b[4])+alpha*(a[4]+I*b[4])+beta)*t/(a[4]+I*b[4])+(a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(-(conjugate(a[2]+I*b[2])^2*conjugate(a[4]+I*b[4])+alpha*conjugate(a[4]+I*b[4])+beta)*t/conjugate(a[4]+I*b[4])+conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-(3*(a[2]+I*b[2]))*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-(2*(3*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])*(1/2)+beta))*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)+((alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))-((6*(a[4]+I*b[4]))*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2*beta)+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2*beta))*(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/(a[1]+I*b[1])-((6*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta)+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta)+36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta^2*(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2)+36*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta^2*(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2)+(36*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta^2*(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)+36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta^2*(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2))*((-(3*(a[2]+I*b[2]))*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-(2*(-3*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])*(1/2)+beta))*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*exp((a[2]+I*b[2])*(-((a[2]+I*b[2])^2*(a[4]+I*b[4])+alpha*(a[4]+I*b[4])+beta)*t/(a[4]+I*b[4])+(a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(-(conjugate(a[2]+I*b[2])^2*conjugate(a[4]+I*b[4])+alpha*conjugate(a[4]+I*b[4])+beta)*t/conjugate(a[4]+I*b[4])+conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-(3*(a[2]+I*b[2]))*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-(2*(3*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])*(1/2)+beta))*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)))/((alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta)+(36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta^2*(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2)-(6*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta*conjugate(a[1]+I*b[1]))-(6*(a[4]+I*b[4]))*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))*(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2*beta*(a[1]+I*b[1]))+(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta))*exp((a[2]+I*b[2])*(-((a[2]+I*b[2])^2*(a[4]+I*b[4])+alpha*(a[4]+I*b[4])+beta)*t/(a[4]+I*b[4])+(a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta^2*(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)-6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta*conjugate(a[1]+I*b[1]))-6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))*(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2*beta*(a[1]+I*b[1]))+(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta))*exp(conjugate(a[2]+I*b[2])*(-(conjugate(a[2]+I*b[2])^2*conjugate(a[4]+I*b[4])+alpha*conjugate(a[4]+I*b[4])+beta)*t/conjugate(a[4]+I*b[4])+conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+((alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/((a[1]+I*b[1])*conjugate(a[1]+I*b[1]))-((6*(a[4]+I*b[4]))*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2*beta)+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2*beta))*(alpha*t*(a[1]+I*b[1])-y*(a[1]+I*b[1])^2+beta*t-x*(a[1]+I*b[1]))/(a[1]+I*b[1])-((6*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta)+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta))*(alpha*t*conjugate(a[1]+I*b[1])-y*conjugate(a[1]+I*b[1])^2+beta*t-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])+(6*(a[1]+I*b[1]))*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2*beta)+36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta^2*(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2)+36*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta^2*(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2)+(36*(a[4]+I*b[4]))*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-a[4]-I*b[4])^2*beta^2*(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)+36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/((a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2*beta^2*(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2))*((-(3*(a[2]+I*b[2]))*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-(2*(-3*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])*(1/2)+beta))*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*exp((a[2]+I*b[2])*(-((a[2]+I*b[2])^2*(a[4]+I*b[4])+alpha*(a[4]+I*b[4])+beta)*t/(a[4]+I*b[4])+(a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(-(conjugate(a[2]+I*b[2])^2*conjugate(a[4]+I*b[4])+alpha*conjugate(a[4]+I*b[4])+beta)*t/conjugate(a[4]+I*b[4])+conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-(3*(a[2]+I*b[2]))*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-(2*(3*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])*(1/2)+beta))*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2))

NULL

lprint(indets(M,name));

{beta, x, y, a[1], a[2], a[3], a[4], b[1], b[2], b[3], b[4]}

 

G := proc(alpha,beta,a__1,a__2,a__3,a__4,b__1,b__2,b__3,b__4) global last; last := [[:-alpha=alpha, :-beta=beta, :-a[1]=a__1 , :-a[2]=a__2, :-a[3]=a__3,:-a[4]=a__4,:-b[1]=b__1,:-b[2]=b__2,:-b[3]=b__3,:-b[4]=b__4], eval(M, [:-alpha=alpha, :-beta=beta,:-a[1]=a__1,:-a[2]=a__2 ,:-a[3]=a__3,:-a[4]=a__4,:-b[1]=b__1,:-b[2]=b__2,:-b[3]=b__3,:-b[4]=b__4])]; plot3d(eval(M), y = -100 .. 100, x = -100 .. 100, view = -100 .. 100, grid = [150, 150], color = blue, style = surface, adaptmesh = false, size = [500, 500]); end proc;

proc (alpha, beta, a__1, a__2, a__3, a__4, b__1, b__2, b__3, b__4) global last; last := [[:-alpha = alpha, :-beta = beta, :-a[1] = a__1, :-a[2] = a__2, :-a[3] = a__3, :-a[4] = a__4, :-b[1] = b__1, :-b[2] = b__2, :-b[3] = b__3, :-b[4] = b__4], eval(M, [:-alpha = alpha, :-beta = beta, :-a[1] = a__1, :-a[2] = a__2, :-a[3] = a__3, :-a[4] = a__4, :-b[1] = b__1, :-b[2] = b__2, :-b[3] = b__3, :-b[4] = b__4])]; plot3d(eval(M), y = -100 .. 100, x = -100 .. 100, view = -100 .. 100, grid = [150, 150], color = blue, style = surface, adaptmesh = false, size = [500, 500]) end proc

(2)

last := 'last'; Explore(G(alpha, beta, a__1, a__2, a__3, a__4, b__1, b__2, b__3, b__4), alpha = -5.000000001 .. 5.000000001, beta = -5.000000001 .. 5.00000010, a__1 = -5.000000001 .. 5.00000010, a__2 = -5.000000001 .. 5.00000010, a__3 = -5.000000001 .. 5.00000010, a__4 = -5.000000001 .. 5.00000010, b__1 = -5.000000001 .. 5.00000010, b__2 = -5.000000001 .. 5.00000010, b__3 = -5.000000001 .. 5.00000010, b__4 = -5.000000001 .. 5.00000010, placement = right)

Warning, expecting only range variables [y, x] in expression -2*(-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])+(6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1]))*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2-6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta/conjugate(a[1]+I*b[1])-6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*(a[2]+I*b[2])*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1]))*exp(conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+(36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2-6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta/conjugate(a[1]+I*b[1])-6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*conjugate(a[2]+I*b[2])*exp(conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+(-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])+6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta+6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta)*((-3*(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(-3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-3*(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)+((-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])-(6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta)*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])-(6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta)*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta+36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2+36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)*((-3*(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(-3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-3*(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2))/((-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta+(36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2-6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta/conjugate(a[1]+I*b[1])-6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2-6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta/conjugate(a[1]+I*b[1])-6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*exp(conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+((-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])-(6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta)*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])-(6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta)*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta+36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2+36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)*((-3*(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(-3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-3*(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)) to be plotted but found names [beta, a[1], a[2], a[3], a[4], b[1], b[2], b[3], b[4]]

 

Warning, expecting only range variables [y, x] in expression -2*(-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])+(6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1]))*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2-6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta/conjugate(a[1]+I*b[1])-6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*(a[2]+I*b[2])*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1]))*exp(conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+(36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2-6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta/conjugate(a[1]+I*b[1])-6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*conjugate(a[2]+I*b[2])*exp(conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+(-(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])-(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])+6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta+6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta)*((-3*(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(-3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-3*(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)+((-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])-(6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta)*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])-(6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta)*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta+36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2+36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)*((-3*(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(-3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-3*(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2))/((-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta+(36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2-6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta/conjugate(a[1]+I*b[1])-6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3])+(36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2-6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta/conjugate(a[1]+I*b[1])-6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta/(a[1]+I*b[1])+(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta)*exp(conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))+((-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/(a[1]+I*b[1])/conjugate(a[1]+I*b[1])-(6*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2/beta)*(-y*(a[1]+I*b[1])^2-x*(a[1]+I*b[1]))/(a[1]+I*b[1])-(6*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta+6*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta)*(-y*conjugate(a[1]+I*b[1])^2-x*conjugate(a[1]+I*b[1]))/conjugate(a[1]+I*b[1])+6*(a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[1]+I*b[1]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[1]+I*b[1]))^2/beta+36*(a[4]+I*b[4])^2*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*conjugate(a[4]+I*b[4])*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(a[4]+I*b[4]+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-a[4]-I*b[4])^2+36*(a[4]+I*b[4])*(a[1]+I*b[1])*(a[4]+I*b[4]+a[1]+I*b[1])*conjugate(a[4]+I*b[4])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-a[4]-I*b[4])^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2+36*conjugate(a[4]+I*b[4])^2*(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+a[1]+I*b[1])*conjugate(a[1]+I*b[1])*(conjugate(a[4]+I*b[4])+conjugate(a[1]+I*b[1]))/(a[1]+I*b[1]-conjugate(a[4]+I*b[4]))^2/beta^2/(conjugate(a[1]+I*b[1])-conjugate(a[4]+I*b[4]))^2)*((-3*(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(-3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]-conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)*exp((a[2]+I*b[2])*((a[4]+I*b[4])*y+x)+a[3]+I*b[3]+conjugate(a[2]+I*b[2])*(conjugate(a[4]+I*b[4])*y+x)+conjugate(a[3]+I*b[3]))/((-3*(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*(a[4]+I*b[4])^2-2*(3/2*conjugate(a[2]+I*b[2])*(a[2]+I*b[2]+conjugate(a[2]+I*b[2]))*conjugate(a[4]+I*b[4])+beta)*conjugate(a[4]+I*b[4])*(a[4]+I*b[4])+beta*conjugate(a[4]+I*b[4])^2)) to be plotted but found names [beta, a[1], a[2], a[3], a[4], b[1], b[2], b[3], b[4]]

 

i have an equilibrium, i want to simplify SEkuil_End[1] but with R0 eq in the simplify, how can i do that?

restart

with(VectorCalculus):

with(linalg):

with(DETools):

with(DynamicSystems):

_local(I):

I

 

Warning, The imaginary unit, I, has been renamed _I

 

dS := VectorCalculus:-`+`(VectorCalculus:-`+`(Lambda, VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(alpha, S), P))), VectorCalculus:-`-`(VectorCalculus:-`*`(mu, S)));

-P*S*alpha-S*mu+Lambda

 

alpha*S*P-(-T*eta+1)*beta*E-theta*E-mu*E

 

(-T*eta+1)*beta*E-delta*I-gamma*I-mu*I

 

E*theta+I*gamma-R*mu

 

-P*T*sigma+I*xi-P*tau

 

r*T*(1-T/K)-phi*T

(1)

SEkuil := solve({dE, dI, dP, dR, dS, dT}, {E, I, P, R, S, T}):

SEkuil_End := SEkuil[4]:

R0 := VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(Lambda, alpha), beta), r), xi), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, eta), r), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, eta), phi))), VectorCalculus:-`-`(r))), 1/VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(mu, VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, phi), sigma), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, r), sigma))), VectorCalculus:-`-`(VectorCalculus:-`*`(r, tau)))), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, beta), eta), phi), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, beta), eta), r))), VectorCalculus:-`*`(beta, r)), VectorCalculus:-`*`(mu, r)), VectorCalculus:-`*`(r, theta))), VectorCalculus:-`+`(VectorCalculus:-`+`(delta, gamma), mu)));

Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r)/(mu*(K*phi*sigma-K*r*sigma-r*tau)*(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)*(delta+gamma+mu))

(2)

SEkuil_End[1]

E = (K^2*beta*delta*eta*mu*phi^2*sigma-2*K^2*beta*delta*eta*mu*phi*r*sigma+K^2*beta*delta*eta*mu*r^2*sigma+K^2*beta*eta*gamma*mu*phi^2*sigma-2*K^2*beta*eta*gamma*mu*phi*r*sigma+K^2*beta*eta*gamma*mu*r^2*sigma+K^2*beta*eta*mu^2*phi^2*sigma-2*K^2*beta*eta*mu^2*phi*r*sigma+K^2*beta*eta*mu^2*r^2*sigma+K*Lambda*alpha*beta*eta*phi*r*xi-K*Lambda*alpha*beta*eta*r^2*xi-K*beta*delta*eta*mu*phi*r*tau+K*beta*delta*eta*mu*r^2*tau-K*beta*eta*gamma*mu*phi*r*tau+K*beta*eta*gamma*mu*r^2*tau-K*beta*eta*mu^2*phi*r*tau+K*beta*eta*mu^2*r^2*tau+K*beta*delta*mu*phi*r*sigma-K*beta*delta*mu*r^2*sigma+K*beta*gamma*mu*phi*r*sigma-K*beta*gamma*mu*r^2*sigma+K*beta*mu^2*phi*r*sigma-K*beta*mu^2*r^2*sigma+K*delta*mu^2*phi*r*sigma-K*delta*mu^2*r^2*sigma+K*delta*mu*phi*r*sigma*theta-K*delta*mu*r^2*sigma*theta+K*gamma*mu^2*phi*r*sigma-K*gamma*mu^2*r^2*sigma+K*gamma*mu*phi*r*sigma*theta-K*gamma*mu*r^2*sigma*theta+K*mu^3*phi*r*sigma-K*mu^3*r^2*sigma+K*mu^2*phi*r*sigma*theta-K*mu^2*r^2*sigma*theta+Lambda*alpha*beta*r^2*xi-beta*delta*mu*r^2*tau-beta*gamma*mu*r^2*tau-beta*mu^2*r^2*tau-delta*mu^2*r^2*tau-delta*mu*r^2*tau*theta-gamma*mu^2*r^2*tau-gamma*mu*r^2*tau*theta-mu^3*r^2*tau-mu^2*r^2*tau*theta)/((K*eta*phi-K*eta*r+r)*xi*beta*(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)*alpha)

(3)
 

``

Download end.mw

I am trying to set up a new tensor expression (r^hat is my unit vector):  

Can someone show me how to do it and/or point me to the right help page? 

The first part of the equation works but the rest does not. How do I get around the problem with the different indices? Another problem I have is that KroneckerDelta is no longer a tensor. Is there a way to define it as such?

with(Physics); Setup(mathematicalnotation = true)

with(Vectors)NULL

Setup(spacetimeindices = greek, spaceindices = lowercaselatin, su2indices = uppercaselatin, signature = `- - - +`, coordinates = cartesian)

[coordinatesystems = {X}, signature = `- - - +`, spaceindices = lowercaselatin, spacetimeindices = greek, su2indices = uppercaselatin]
````

(1)

Define(A[mu, a] = (1-fA(r))/(g*r)*(LeviCivita[a, nu, mu, 4]*X[nu]/r))

{R, A[mu, a], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-gamma_[a, b], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(2)

A[]

A[mu, a] = Matrix(%id = 36893490522608139428)

(3)

Define(V[mu, a] = (1-fA(r))/(g*r)*(LeviCivita[a, nu, mu, 4]*X[nu]/r)-fB(r)*(KroneckerDelta[i, j]-X[i]*X[j]/r^2)/gr+fC(r)*X[i]*X[j]/(gr*r^2))

Error, (in Physics:-Define) found different free indices in different operands of a sum; in operand 1: [], in operand 2: [i, j], in `+`(Physics:-KroneckerDelta[i,j],-Physics:-SpaceTimeVector[i](x,y,z,t)*Physics:-SpaceTimeVector[j](x,y,z,t)/r^2)

 

NULL

Download V_Tensor.mw

I am trying to draw the Poincare section diagram related pendulum problem, article is shared below. I can not understand and code gives error, can you help me to draw Poincare section Fig. 4 of attached article?7._Energy_distribution_in_intrinsically_coupled_system [moderator: URL changed to respect IP, as per Mapleprimes Terms of Use]

pendulum.mw

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