Why does maple not simplify this expression any further:

-4*cos((1/5)*Pi)*m^3-4*cos((1/5)*Pi)*n^3-4*cos((1/5)*Pi)*p^3-4*cos((1/5)*Pi)*q^3+4*cos((2/5)*Pi)*m^3+4*cos((2/5)*Pi)*n^3+4*cos((2/5)*Pi)*p^3+4*cos((2/5)*Pi)*q^3-10*cos((1/5)*Pi)*p*q^2+10*cos((2/5)*Pi)*m^2*n+12*cos((2/5)*Pi)*m^2*p+12*cos((2/5)*Pi)*m^2*q+12*cos((2/5)*Pi)*m*n^2+10*cos((2/5)*Pi)*m*p^2+12*cos((2/5)*Pi)*m*q^2+12*cos((2/5)*Pi)*n^2*p+10*cos((2/5)*Pi)*n^2*q+12*cos((2/5)*Pi)*n*p^2+12*cos((2/5)*Pi)*n*q^2+12*cos((2/5...

How do I plot the imaginary or real part of a complex valued function

e.g.

E:=y^2+x^2=1

I tried:

E1:=eval(E,{y=y1+I*y2,x=x1+I*x2})

implicitplot3d(E1,x1=-3..3,x2=-3..3,y1=-3..3)

but which does not work

Hello I have the following system of equations and I want to solve for rho1 and z1

E := (1/2)*(1/rho1^2+1/rho1^2)-1/sqrt(z1^2+rho1^2)-1/sqrt((R-z1)^2+rho1^2)-1/sqrt(z1^2+rho1^2)-1/sqrt((R-z1)^2+rho1^2)+1/R+1/sqrt((2*rho1)^2+(R-2*z1)^2);

Er1 := diff(E, rho1);

Ez1 := diff(E, z1);

solve([Er1, Ez1], {z1, rho1});

The system is a function of R.

The solve command spits out Kernel lost after some time. So my question is how can I solve it ?

Is it possible when solving a differential equation to get the corresponding recurrence relation of the series expansion instead of the actual solution?

e.g.

ode:=y''=omega^2*y(x)

the solution is obviously exp(\pm omega*x)

But I want

a_(n+2) = omega^2/(n+1)(n+2) * a_n

or something like that

t0 := arccosh(lambda/(s*(1-lambda)))

f := int(sqrt(lambda-s*cosh(t)/(1+s*cosh(t))), t = -t0 .. t0)

s := 1/10

with(Student[Calculus1])

g := f-Pi*(0+1/2)

Roots(g, lambda = 0 .. 1, numeric)

Why does maple say:

Error, (in mod/Expand) too many levels of recursion?