So you mean the sign of sin(x), x in the Reals - a "square wave"?

de:=rhs(eq1pp);
DE:=convert(de, D);
coeff(DE, D(theta)(t));
#coeff(DE, (D@@2)(theta)(t));

                      Ctheta sin(theta[0] + phi)
                      --------------------------
                              a sin(phi)

Be aware, that 'coefficients' - like for polynomials - may
need to expand the expression first.

PS: do not hesitate to use line breaks for longer formulae :-)

convert(%, expln) gives an answer as well.

Using 'gfun' it turns out to be a root of 56*x^3 - 42*x - 13

'proof':

  RootOf(56*x^3-42*x-13, index=1) / cos(arccos(13/14)/3) = 1;
  allvalues(%); convert(%, expln); evala(%); is(%);

                    true

g:= x -> BesselJ(0,x);
plot(g(x), x = -4 .. 4);

Summarising the discussion and argumentations in a sheet ...

MP_int_products_sinc.mws
MP_int_products_sinc.pdf

DTEdt:=aE*qE*A/(alpha+TR_SS)-muE*TE+rE TE   (1-TE/TEmax);

DTEdt:=aE*qE*A/(alpha+TR_SS)-muE*TE+rE*TE * (1-TE/TEmax);

You may want to use 'else' as last statement. I even type it always before writing 'end if' in any case - before filling the body, just as a frame.

For clarity I prefer a 'return' in the if-branches (not needed), it depends on the 'language' you use and not all programming languages behave the same way on constructions.

A suggestion for clarity: do not use the same name beta for different things.

If you mean a function then name it p, for example, like p(0.787*beta)

Then it makes it clear, that you have to tell us what p stands for,
it does not make much sense to say 'can be any value'

Those sheets in Standard Mode are very unhandily, so I use the better interface :-)

Find a sheet attached, the value for i=53 is 0.606852403708179e-2

MP_2dim-Int-numerica.mws

One may try to investigate closer for x0:=12236889.2928742 (having Digits=15) due to

  eps:=1e-5;
  m/10^24;
  plot([Re(%), Im(%)], x= x0*(1-eps) .. x0*(1+eps), color=[red,blue]);

I suggest that, after studying asympt(m, x, 1) and piecwise and some scaling, 
v:= m/( (1000 + 10000*I)*x^3*exp(0.4e-7*x) ) and some 'Brent Zero Finder'

Try a polynomial, degree = 7 (since there are 8 equations), now solve it

If have a Standard sheet or you open as such, then you can export as pdf.

You almost always can save as html, which can be handled by Word, where
input can be maintained, outputs a graphics.

And you generally can install some pdf or ps printer on your machine, which
can print as device anyway.

Some Linear Algebra (had to refresh it): you consider IR^7 ---) IR^14, x ---) A.x
and it is better to use A:= map(convert,A, rational) etc.

The command Rank(A) returns '7', so that is a monomorphism. Likewise you can ask
for NullSpace(A), which returns {} (I guess, that the zero vector is meant).

In words: if there is any solution for the equation A.x = y, then it is unique.

The command LinearSolve(A,y) returns with an error, which tells that there is no
solution (I would prefer that as result, not as an error ...).

To understand it use the commands "ColumnSpace(A): evalf[100](%): evalf[3](%);"

If you have set "interface(rtablesize=infinity)" as Preben Alsholm did, then you
see the base vectors for the image of the map: in the first 7 coordinates you will
see something like the 'canonical' base, while for the last coordinates you will
see entries of magnitude ~ 10^15.

Now your y has zeros in the last coordinates and non-zeros in the first coordinates.
But the representation (and injectivity or rank) says: the first 7 already uniquely
determine a pre-image x. And that does not map to zeros in the last ones.

IIRC least square is unique in this sitaution, so it does not make (direct) sense
to ask for a better one (except in other norms, but those are equivalent, hence
also unique)


If CS:=ColumnSpace(A) and y:= y:=convert(Y, Vector), then add(y[j].CS[j], j=1 .. 7)
is the exact vector in the image, which has coordinates of y in the first 7 ccordinates
(as you can see by %[1 .. 7] and looking at y).

The 2-Norm of that - y is ~ 6300, add(y - y[j].CS[j], j=1 .. 7):  Norm(%,2); evalf(%); 

Usually I was off *.mw sheets ...

That seems to have crashed my standard printer, which is a pdf-printer.
Printing just hangs up. The only thing which worked was printing to file
in the printer menu - but that seems to print postscript command code
(to be inspected with a proper editor), however it was possible to read
it with a postscript viewer (like ghostview) and to convert that to pdf.
My printer has its own, independent postscript system.

So I guess that file damaged the postscript for the printer.

I had to de-install and re-install the printer, which now works again.

Also had some strange entries in my registry, displaying non-Ascii,
it looked like chinese or so - non-readable for me.

Very strange ...

PS: I am using Win7

I think it is Pi^2/2 - arctan(sqrt(8))*Pi, which at least gives the correct numerical value 1.06762913815971

Have to clean up my ugly sheet to post it later.