S:=[solve(n*p*(1-p)=(sigma)^(2), p)];
eval(k, p=S[1]);

or

T:=[solve(n*p*(1-p)=(sigma)^(2), {p})];
eval(k, T[1]); # simplify(%);

Denote your last expression by F. Then the following gives you a guess:

Digits:=14;

plot(abs(F), n=1+0.1 .. 2-0.01);
plot(abs(F), n=2+0.01 .. 3-0.01);

fsolve(F, n= 1.2);
                           1.2808546834442

fsolve(F, n= 2.9);
                           2.9814974080718

eval(F, n = %); evalf(%);  # check it - indicates, you need better precision

That is quite rude (I am note used to properties of the fct and one should
use ranges instead of simple start values (please check the help for the

fsolve command) and for more and exact values (+ "yes, they must be Reals")
you may have to invest some thoughts.

That's what Maple is doing to you :-)

if rep = ... then proceed else display info and ask the user again

I do not know, whether you can do that through code (or some settings), but 'mark' the plot with the mouse and then you can resize.

Also had troubles for the whole interval ...

However played with Brent's minimizer (both with older code due to Devore
and my own version in Excel), which only finds local minima.

The Maple version gets problems, while the Excel (~ original code) version
finds it - if working with -f(-x) on -1.0 ... 1.4, since Brent seems to
start from the left.

One can observe similar 'orientation' thing in Maple:

Optimization[NLPSolve](f(x), x= -1.4 .. 1,
  method=branchandbound,   maximize, evaluationlimit=10^2, nodelimit=100);

Optimization[NLPSolve](f(-x), x= -1 .. 1.4,
  method=branchandbound,   maximize, evaluationlimit=10^2, nodelimit=100);

returns the left boundary point in both cases. 

Finally tried to transform to -1 ... +1 and then to global (by arctan).
And then it works to approach the 'boundaries', selecting the correct one.

It is not an error, but Maple's way to "umpf ...", i.e. it does not find a solution.

I played a bit (Digits:=14, EQs:=convert ({ ... eq ...}, rational) - or better: for your Matrices), but that did not help.

And at least you need 0 < T (as you have log(T)).

I think you have to invest some (manual) work for your K[i] =10^(CFC[i,1]*ln(T/1000)+CFC[i,2]/T+CFC[i,3]+CFC[i,4]*T+CFC[i,5]*T^2) by 10^T = t etc.

But even then it is not clear, whether Maple will find a solution (and as there may be many: whether it finds a desired/expected solution).

sptype:="Saddle";

[{x = 2, y = 1}, {x = 2, y = -1}, {x = -2, y = 1}, {x = -2, y = -1}];
s[i]:=convert(%, string);

cat( "Stationary point ", s[i], " is a ", sptype);

  "Stationary point [{x = 2, y = 1}, {x = 2, y = -1}, {x = -2, y =\
         1}, {x = -2, y = -1}] is a Saddle"

Not sure what your motivation is, but switch to logarithm:

  log2:=log[2];
  d:=log2(10);

  'd*k = log2(10^k)'; 
  simplify(%) assuming k::integer: #combine(%);
  is(%);
                                        k
                           d k = log2(10 )

                                 true

May be some overloading is possible, so instead of 1ek you write dk
for its log2, i.e. 1ek = 2^(dk).

Even then you again will find limits for the system, where it will give up.

And I would not expect Maple to do all what can be written down in
Math, and as a task for you: how many pages with 60 lines and each
of line length 80 are needed to write down your number before the
decimal point?

.

You should use reasonable Digits (not 10), perhaps even rationals (not floats) and without looking closer it is a typical behaviour for branch cuts at the negative line. And if you want to locate the problem then omit the factor in front of exp.

I looked at it. Periodics usually have no 'good' solutions.

  restart; Digits:=14;
 (tan(Pi/18)=(2*cot(b)*((3.4^2)*sin(b^2)-1))/((3.4^2)*(1.4+cos(2*b))+2));
  lhs(%) - rhs(%);
  eq:=convert(%, rational);

and the following 'shows', that at least you have to decide for ranges

  discont(eq, b);
  plot(eq, b=1e-2 .. 10
  # , discont=true
  );

Even then it is far from being clear what one can even expect from Math
(besides desires, for any software):

  plot(eq, b= 1e-2 .. Pi -1e-1);
  plot(eq, b= 2*Pi+ 1e-2 .. 3*Pi -1e-1);


So I doubt any statement about 'the solution' without specification.

That one is 'just' a statement (as pagan shows), it does not inform the system obout your desire :-)

If I understand you correctly then you have 2 functions U(x,m) and V(y,m)

P:= t -> [ U(t,floor(t)), V(t,floor(t)) ] seems to be what you are looking for

Well, certainly also a matter of taste ... and having M 12 on Win XP
that are more or less my settings.

- which are not obvious to find, the default is different: document mode

- Featuring the Java interface that way leads (new) users to use that
and meanwhile made me to ignore those sheets. There are lots of good
arguments why the input behaviour is messy. And personally I hate the
ambiguous ways for code.

- For me the classical interface is *much* faster (may be it is better
now in newer version) anf for me that's more worth then nicer graphics.

- There is an odd behaviour with fonts: I do not want to see italics
and switch it of, saving as 'default style sheet'. However opening a
new (or old) sheet again shows all italics (mostly keywords or variables).
And one can not simply 'click off italics', one has to activate and
the deactivate again. Everytime after opening a sheet. And if I execute
one statement, the displayed out put agian in italics ...

- Floats are presented different, I see 1.234 10^20 versus 0.1234 10^21

- sqrt sign is broken, integral sign is blurred, no spacing between sum
sign and summen (they are glued together), Pi bad to read, all the Greek
alphabet difficult to read and blured (especially epsilon is messy) etc.

- If I print (as pdf) the zoom seems always to be set to 100%, which
is not what I want.

- sometimes I try sheets in older versions (say 9.5) or want to send
it to somebody have those and if it is not a classical that will not
work, since one can not save / convert as such.

Some of the above are certainly bugs and may vanish, other stuff may
be intended, will remain and are not my taste and do not have to face
it in the classical interface.


So why should I use it? The only advantage (for me) are nicer graphics
(except strange behaviour for 3 d axes) and in the rare cases that I
need those - just open as Java and done.

Otherwise said: may be Maple has maintainance reasons to switch, but
it still after years (it was introduced in M10) does not work properly.
And I will not spend money to try it :-) (OK, beta tester would be a way).

The mouse wheel is no reason for me (for example it does not work in
MS Excel, if you are in code modules, so what ...)
 

You mean 'echelon form' (like stairs), a diagonal matrix would
have its eigenvalues already in the field.

  restart;
  with(LinearAlgebra[Modular]);

  p:=5;

  M:=Matrix(4,4,[[0, 1, 1, 4], [1, 0, 1, 0], [1, 1, 0, 1], [4, 0, 1, 0]]);
  A:=Mod(p, M, integer[]);          # now we are over Z/pZ

  B := Copy(p,A):                   # work with a copy of A
  RowReduce(p,B,4,4,0,0,0,0,0,0,0); # does not output directly, works on B

  B;                                # show the result
  convert(%, matrix);               # in 'readable' form

                          [1    0    1    0]
                          [                ]
                          [0    1    1    4]
                          [                ]
                          [0    0    1    4]
                          [                ]
                          [0    0    0    1]