@dharr how i can tell maple assuming  this is positive or negative ? you mention at there but there is any special code or just write down and in another code you did by squar dot (::) like that , i don't know this

@dharr I don't know how i can thank you, you are emazing thank you so much you helped me a lot thus day

@dharr we have a ode equation which we can finded R(xi) by it i explained in file

function_of_R(xi).mw

if dont undrestand mention i will send hole work for you

@dharr i saw your code is perfect like always but when i run your code not give me the same results as yours in my maple can you tell my why?

not_run_exactly_f12.mw

@dharr i get ode but because i add some part by hand i didn't post here in ode test my soluttion is correct by you are write in top picture there is something messing let me tell you in the file below

Download f12.mw

@acer  and can you solve my problem you have a great profile the top question is easy for you i am stuck

@acer  i am here for getting help  and most time i got email (was deleted by a moderator for the following reason: Spam. If you believe this was done in error, please contact Maplesoft customer service) if you can't help please don't delete my questions ...

@nm  how we can use this code for testing and find solution how i can test one by one of them if it is solution come out otherwise not

@dharr  swear to God this is the best code ever seen in my life, very nice and pretty

@vv  thank you so much
your code are great  i liked a lot yea i am at begining of learning machine learning and i have a lot idea but i can't do it with this pure skill in machin learning , this code not run in my maple but didn't give me any error , yea 4^8 is a lot of calculation but when this fuction outcome is done i use it in other equation must be satisfy which is i asked the question but they delete my post i will post in comment if you can help me with this i will be really appreciate... thanks any help

@vv 

restart;
phi := (p__1, p__2, p__3, p__4, q__1, q__2, q__3, q__4, xi) -> (p__1*exp(q__1*xi) - p__2*exp(q__2*xi))/(p__3*exp(q__3*xi) + p__4*exp(q__4*xi));
xi := x;
for p__1 in [1, -1, I, -I] do
    for p__2 in [1, -1, I, -I] do for p__3 in [1, -1, I, -I] do for p__4 in [1, -1, I, -I] do for q__1 in [1, -1, I, -I] do for q__2 in [1, -1, I, -I] do for q__3 in [1, -1, I, -I] do for q__4 in [1, -1, I, -I] do result1 := evalf(phi(p__1, p__2, p__3, p__4, q__1, q__2, q__3, q__4, xi)); print('phi'(p__1, p__2, p__3, p__4, q__1, q__2, q__3, q__4, xi) = result1); end do; end do; end do; end do; end do; end do; end do;
end do;

in one place stop and not continues when is zero how tell him not calculate that one which is equal to zero?

@vv  thank you so much ...

@mmcdara  i already use it but in first picture i crop the picture.

@Carl Love thanks a lot it is worked