try_IG.mw

The following codes is a part of my program for computing ING at several points of r between -1 and 1 (by a step of for example 0.1 or even smaller for a better pointplot of ING(r) ):

H:=(r, teta) -> h(r, zn, teta) # h is a complicated function of (r, z, teta) (referred to the attached maple file) and   zn is a given number

F:= r -> int(H(r, teta), teta= 0…alpha)

I ‘d like to compute something as follows at certain r and z, but first I must compute the integral and then substituting the r and z values.

A(r, z) = int( f(r,z, teta), teta=0..0.78)

But the problem: f is a complicated function of the 3 variables (including BesselJ(0,..), sin & root square functions, ..!!) thus a simple int command...

I want to have a solve command in a loop like this: for j from 0 to 10 do s[j]:=solve( {f[j]=0 , g[j]=0},[ a[j] , b[j] ]); od; where f[j] and g[j] are complex exponential functions of j and a[j]& b[j] e.g in a very simple case: f[j]:=a[j]*exp(I*2*j)+b[j] after such a loop Maple just solve s[0] and for other j's a warning message appears saying: "solutions may have been lost". And amazingly this warning seems very correct for when I put the solve command outside the loop,like solve({f[2]=0,g[2]=0},[a[2],b[2]]); it simply solves it! I don't know how I can overcome this problem?!

Suppose I've plotted 3 functions:

Now I'd like to have these 3 plots following one after another (in a successive manner) in 1 plot like diagram. How can I perform such a task?

 

Another question:

How can I have a plot in reverse range? For example instead of plot(x^2,x=0..1), I'd like to have sth as plot(x^2,x=1..0), i.e. the horizontal range begins from 1 and ends to zero (also the vertical range is from (1)^2=1 to (0)^2=0).

for having just the real solutions in the output of the solve command is it enough to use the RealDomain Package?Is there any other way for extracting only the real solutions?