Further work on TMS, TIMESIN and PLUSIN



I have prepared to commit the reported changes to TMS, TIMESIN and
PLUSIN. I would like to summarize sum of the results and problems.

The following bugs are related to the changes and will vanish:

   BUG ID: 721575 2/sqrt(2) doesn\'t simplify
   BUG ID 2029041 a*sqrt(2)/2 unsimplified
   BUG ID 1923119 1/sqrt(8)-sqrt(8)/8
   BUG ID 1927178 integrate(sin(t),t,%pi/4,3*%pi/4) 
   BUG ID: 1480562 2*a*2^k isn't simplified to a*2^(k+1)
   BUG ID: 1853191 rat(2/sqrt(2)),algebraic doesn't cancel
   BUG ID: 1996354 unsimplifed result from expand

Already closed as won't fix, but now works too:

   BUG ID: 1379761 nusum leaves unsimplified product 2*3

The changes do not help to simplify something like the following:

   BUG ID: 1639678 3*sqrt(2)/sqrt(3)/sqrt(6) != 1

We will have again two problems. The following bug was closed, but will
not work again:

   ID: 1884711 bug when adding fractions involving square roots

The reason is, that sqrt(2)/6 and 2*sqrt(2)/6 simplify to different
expressions:

   (%i27) sqrt(2)/6-2*sqrt(2)/6;
   (%o27) 1/(3*sqrt(2))-sqrt(2)/3

To get a more simple expression, the result has to be factored:

   (%i28) factor(%);
   (%o28) -1/(3*sqrt(2))

But for this case it works:

   (%i29) sqrt(3)/12-5*sqrt(3)/12;
   (%o29) -1/sqrt(3)

The following bug report was closed too, but will not work again:

   ID: 657382 defint/limit infinite loop

This is the integral which will loop endlessly again:
   
   integrate(1/(x^5-1),x,1,inf)

Should we ignore the two problems and go on to commit the improvements?

Dieter Kaiser