@FormatB 

SolveTools[SemiAlgebraic] command was introduced in Maple 16.
You could try   solve([sys, l>0], [alpha], parameters=[l]);  but it probably will not work in Maple 15 (because it is calling SemiAlgebraic).

@litun 

I do not have your (very old) version to check. You could:
- check the entries of the matrix AB. Are they correct?
- LinearSolve has several options. Maybe one of them works for you.

Also, your system seems to be consistent but has n+1 equations (n=the number of unknowns).
You should try to eliminate one of them. Or, try LinearAlgebra[LeastSquares].

@litun 

Here is the executed worksheet. I have changed the line  V = ~Vsol seeing that you use Maple 12.

solntosystem-1.mw

1 / %;            

@tomleslie 

Carl has changed the code and now it does not work because q is no longer necessarily a prime.

@Carl Love 

Of course for <128 bit Maple cracks easily the RSA:

p1,q1:=expand([op(ifactor(n))])[];
d1:=1/e mod ilcm(p1-1, q1-1);

The prefered form of the answer is "culture-dependent". E.g. in my country (Romania) a teacher definitely expects sqrt(2)/2; in universities it does not matter.

Anyway, an option for this (if any) should be part of Typesetting. However, I would prefer Maplesoft effort  directed towards maths rather than typesetting.

@tomleslie 

Why didn't you respect OP's special request?   :-)

@Jsevillamol 

Why don't you post an executable worksheet . Use the green arrow to upload it.

Download gi.mw

@Axel Vogt 

For the last limit it's a "semi-bug" because with assuming a>1 it works. And also with assuming a>0,a<=1.

P.S. Many limits are computed by series, not by f/g, L'Hospital or such.

CommonPeriod:=(T1::Not(0),T2::Not(0)) -> `if`(type(T2/T1,rational), abs(numer(T2/T1)*T1), infinity);

PER:=proc(f::algebraic,x::name)
description "The period of a fumction f = g(sin(...),cos(...),...)";
local v:=indets( f, specfunc({sin,cos})), T,t,i;
T:=2*Pi/~ (diff(op~(v),x) minus {0});
if T={} then 
   if depends(f,x) then error "Improper expr" else WARNING("Constant expr"); return 0 fi
fi;
if depends(subs(v=~{seq(t[i],i=1..nops(v))}, f), x) or depends(T,x) 
   then  error "Improper expr" fi ;
t:=op(1,T);
for i in T do 
   t:=CommonPeriod(t,i);
   if t=infinity then return t   fi;
od;
t
end:

PER(a*cos(2*x/3+4) + b*sin(5*x/2)*cos(x), x);
PER(sin(x)+cos(Pi*x), x);
                             12 Pi
                            infinity

@Axel Vogt 
It's not normal that Maple does not know

limit(GAMMA(a,x), x=0,right) assuming a>0;

Note that MultiSeries:-limit  knows it. Same for x=infinity and series. Probably in the near future MultiSeries will be part of "regular" Maple.

@Carl Love 

- The compilation could be done via an auxiliary procedure obtained with ToInert or subs. The problem is whether it is worth the effort.

- But you have recursion in Binomial (using thisproc). Of course it has not a serious impact on performance in our case.

@torabi 

You must give the general form of your function because it would be difficult (time consumming) to consider the period of an arbitrary function.