Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

This crashes the kernel each and everytime. I was testing a solution which is most likely wrong. But this does not mean Maple should just crash like this. ps. I do not remember if I reported this before or not for this exact example, hard to search Mapleprimes. If I did report this exact example before in the past, then it is still not fixed.

Does this happen in Maple 2025?


Worksheet below. Make sure to save all your work first.

maple_server_crash_on_odetest_march_15_2025.mw

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

Plot_title_too_high.mw

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

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 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

Hello everyone,

I have created a Maple worksheet titled "ΕΜΒΑΔΟΝ ΕΠΙΠΕΔΟΥ ΧΩΡΙΟΥ", designed to help my students prepare for their final exams as they qualify for university. This worksheet focuses on area calculations in plane geometry, using Maple to visualize and solve problems efficiently.

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I would love to hear your thoughts and feedback!

Have you used Maple for similar exam preparation?
εμβαδόν_χωρίου.mw

I believe I found I bug.

The 'next' statement for loop control will not work in 2D Input but it does in Code Edit Region.

From the documentation on 'next', I copied the following code into a 2D input in a document. 

Running it results in Error, invalid expression for eval; id=54 which is a missing help page.

for i to 4 do
    for j to 4 do
       print([i, j]);
         if i = j then next i;
        end if;
   end do;
end do

However 'next' without a following integer/name works fine in both 2D Input and Code Edit Region.

So is there only a subset of Maple code that will work in 2D Input?

I have calculated an expression which depends on functions. I would now like to calculate the derivative withe respect to a function  but when I try to do so I get the error “Deriving a functional ”Error, invalid input: diff received fA(r), which is not valid for its 2nd argument. There is no help page available for this error, so maybe someone knows what I am doing wrong .

I get this is because die diff function might not be able to handel a function as an argument, but how would I do it? 

L := -r^2*((-fA(r)^4+(-2*fB(r)^2-2*fC(r)^2+2)*fA(r)^2+4*(D(fB))(r)*fA(r)*fC(r)*r-fB(r)^4+(-2*fC(r)^2+2)*fB(r)^2-4*fB(r)*fC(r)*(D(fA))(r)*r-2*r^2*(D(fA))(r)^2-1-2*r^2*(D(fB))(r)^2)/(2*g^2*r^4)+(r*(fB(r)^2+(1/2)*fC(r)^2+fA(r)^2-2*fA(r)+1)*H(r)^2+(-(D(K))(r)*r^2*fC(r)-2*K(r)*fB(r)*r)*H(r)+(1/2)*K(r)^2*fC(r)^2*r+(D(H))(r)*K(r)*r^2*fC(r)+r*((fB(r)^2+fA(r)^2)*K(r)^2+(1/2)*r^2*((D(H))(r)^2+(D(K))(r)^2)))*v^2/(r^2)^(3/2)-lambda((1/2)*(K(r)^2+H(r)^2-1)*v^2)^2)

-r^2*((1/2)*(-fA(r)^4+(-2*fB(r)^2-2*fC(r)^2+2)*fA(r)^2+4*(D(fB))(r)*fA(r)*fC(r)*r-fB(r)^4+(-2*fC(r)^2+2)*fB(r)^2-4*fB(r)*fC(r)*(D(fA))(r)*r-2*r^2*(D(fA))(r)^2-1-2*r^2*(D(fB))(r)^2)/(g^2*r^4)+(r*(fB(r)^2+(1/2)*fC(r)^2+fA(r)^2-2*fA(r)+1)*H(r)^2+(-(D(K))(r)*r^2*fC(r)-2*K(r)*fB(r)*r)*H(r)+(1/2)*K(r)^2*fC(r)^2*r+(D(H))(r)*K(r)*r^2*fC(r)+r*((fB(r)^2+fA(r)^2)*K(r)^2+(1/2)*r^2*((D(H))(r)^2+(D(K))(r)^2)))*v^2/(r^2)^(3/2)-lambda((1/2)*(K(r)^2+H(r)^2-1)*v^2)^2)

(1)

diff(L, fA(r))

Error, invalid input: diff received fA(r), which is not valid for its 2nd argument

 
 

``

Download test_funtion.mw

Hello, an interesting issue about set equivalence.

Logically, the two sets are equivalent by derivation.

The first principal case, for set A, k=0, the element values ​​are Pi/6 and 5*Pi/6, which corresponds to the case of k=0 (element value is Pi/6) and k=1 (element value is 5*Pi/6) in set B. Obviously, the k value is not one-to-one correspondence, but just a letter representing a positive integer. As for the second general case, it is the same steps I thought.

So, how to verify that the two sets are equivalent? I know Maple cannot do it in one step, but I don't know how to do it?

A := solve(sin(x) = 1/2, allsolutions = true)

(1/6)*Pi+2*Pi*_Z5, (5/6)*Pi+2*Pi*_Z5

(1)

A := `assuming`([`union`({(1/6)*Pi+2*k*Pi}, {Pi-(1/6)*Pi+2*k*Pi})], [k::integer])

{(1/6)*Pi+2*k*Pi, (5/6)*Pi+2*k*Pi}

(2)

B := `assuming`([{k*Pi+(1/6)*(-1)^k*Pi}], [k::integer])

{k*Pi+(1/6)*(-1)^k*Pi}

(3)

is(A = B)

false

(4)

restart

alpha = 'alpha'

alpha = alpha

(5)

solve(sin(x) = alpha, x, allsolutions = true)

2*Pi*_Z1+arcsin(alpha), -arcsin(alpha)+Pi+2*Pi*_Z1

(6)

A := `assuming`([`union`({arcsin(alpha)+2*k*Pi}, {Pi-arcsin(alpha)+2*k*Pi})], [k::integer])

{arcsin(alpha)+2*k*Pi, Pi-arcsin(alpha)+2*k*Pi}

(7)

B := `assuming`([{k*Pi+(-1)^k*arcsin(alpha)}], [k::integer])

{k*Pi+(-1)^k*arcsin(alpha)}

(8)

is(A = B)

false

(9)
 

NULL

Download verify_set_A_and_set_B_is_equivalent.mw

I have Maple 2024 and successfully loaded the FeynmanIntegral package with:

with(Physics); with(FeynmanIntegral);

Maple confirms that FeynmanIntegral is loaded by displaying:

[Evaluate, ExpandDimension, FromAbstractRepresentation, Parametrize, Series, SumLookup, TensorBasis, TensorReduce, ToAbstractRepresentation, epsilon, varepsilon]

However, when I attempt to evaluate a Feynman integral, Maple only displays the unevaluated expression instead of computing it:

Delta(q); %FeynmanIntegral(1/p^2*1/(p + q)^2, p);

And explicitly calling Evaluate() does not compute the result:

Evaluate(Delta(q));

  1. Using Evaluate() explicitly:

    FeynmanIntegral:-Evaluate(1 / (p^2 * (p + q)^2), p);

    Result: No evaluation, only displays the input.

  2. Assigning the integral to a variable before evaluating:

    I := FeynmanIntegral(1 / (p^2 * (p + q)^2), p); Evaluate(I);

    Result: Still does not evaluate.

  3. Using dimension= instead of d= when specifying the spacetime dimension:

    FeynmanIntegral:-Evaluate(1 / (p^2 * (p + q)^2), p, dimension = 4 - 2*epsilon);

    Result: No evaluation.

  4. Checking if FeynmanIntegral functions exist:

    showstat(FeynmanIntegral);

    Result: The package seems loaded, but it does not execute calculations.

I expect FeynmanIntegral:-Evaluate(...) to automatically compute the dimensional integral using Feynman rules and return a result.

  1. Is FeynmanIntegral:-Evaluate() broken in Maple 2024?
  2. Are there additional setup steps needed to enable full functionality?
  3. Has anyone successfully used FeynmanIntegral for automatic dimensional integration?
  4. Are there alternative Maple functions/packages for computing Feynman integrals in dimensional regularization?

Any help would be greatly appreciated!

this function i have is so long and my parameter are twenty they are two much when i make a change in explore i the change is so slow and i can't see some of this parameter how act to figure when i change becuase the placement of parameters i want some of parameter being in right  and some of them being in right  and figure be in the middle for see them together can we do something like that?

figure.mw

Hi everyone,

I'm trying to compute the cohomology group of some Lie algebras using the LieAlgebra package, but it appears that the Cohomology command doesn't provide the correct basis for the higher dimensional cohomology group, instead repeating up to the correct dimension only one element.

For example, with the following Lie algebra

L1:=_DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 2], 1], [[1, 2, 3], -1], [[4, 6, 5], 1], [[4, 5, 6], -1]]])
DGSetup(L1)

the command

C := RelativeChains([])

does provide the correct k-forms on Alg1, but then

H := Cohomology(C)
provides
[[theta4,theta1],[theta1 &w theta4, theta1 &w theta4, theta1 &w theta4],[theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3], [theta1 &w theta2 &w theta3 &w theta4,theta1 &w theta2 &w theta3 &w theta4,theta1 &w theta2 &w theta3 &w theta4],[theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6, theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6], [theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6]

A similar thing does happen for the examples provided in the online help (e.g. example 1 from https://de.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/LieAlgebras/Cohomology). Is the command broken?

Any help is really appreciated.

when i use change maple to latex most of that equation when i want to change the place of term are change how i can fix that for example in (R) if watch in exponential the x is first term but after changing to latex are change which i have to change by hand how i can fix this issue?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

_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.

 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

NULL

declare(u(x, y, z, t))

u(x, y, z, t)*`will now be displayed as`*u

(2)

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

(3)

NULL

W := Lambda = k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

Lambda = k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

(4)

latex(W)

\Lambda = k_{i} \left(w_{i} t +y l_{i}+r_{i} z +x \right)+\eta_{i}

 

Lambda[1] := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

(5)

Q := f = 1+exp(Lambda[1])

f = 1+exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])

(6)

Q1 := subs(W, Q)

f = 1+exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])

(7)

latex(Q1)

f =
1+{\mathrm e}^{k_{i} \left(w_{i} t +y l_{i}+r_{i} z +x \right)+\eta_{i}}

 

eq15 := w[i] = (-1+sqrt(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1))/(2*mu)

w[i] = (1/2)*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu

(8)

latex(eq15)

w_{i} =
\frac{-1+\sqrt{-4 \beta  \mu  l_{i}-4 \delta  \mu  r_{i}-4 \mu  k_{i}^{2}-4 \alpha  \mu +1}}{2 \mu}

 

R := f(x, y, z, t) = 1+exp(k[i]*(x+l[i]*y+r[i]*z+(-1+sqrt(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1))*t/(2*mu))+eta[i])

f(x, y, z, t) = 1+exp(k[i]*((1/2)*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))*t/mu+y*l[i]+r[i]*z+x)+eta[i])

(9)

latex(R)

f =
1+{\mathrm e}^{k_{i} \left(\frac{\left(-1+\sqrt{-4 \beta  \mu  l_{i}-4 \delta  \mu  r_{i}-4 \mu  k_{i}^{2}-4 \alpha  \mu +1}\right) t}{2 \mu}+y l_{i}+r_{i} z +x \right)+\eta_{i}}

 
 

NULL

Download latex.mw

Hi everyone,

I am trying to visualize the integral of x3 over the interval x=−1 to x=1. I tried using:

with(plots):
display(
   plot(x^3, x = -1 .. 1, color = black, thickness = 2),
   shadebetween(x^3, 0, x = -1 .. 1, color = cyan)
);

This works, but I wondered if there’s a better or more elegant way to visualize definite integrals. For example:

  • Can I add transparency to the shaded region?
  • Is there a built-in function that directly plots definite integrals with shading?
  • Any tips for improving the aesthetics of such plots?

Thanks in advance for any help!

Download εμβαδόν_χωρίου.mw

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