Re: An exact simplification challenge - 61 (arctan)

1787 schrieb:
>
> Is Derive (6.1) currently available for download and use on MS Windows
XP?
> Thank you.

Google "derive 6 download" (without the quotes). Presumably all
download offers are time-limited trial versions (vbox protected). As
far as I know Texas Instruments acquired the company in 1999 and
stopped selling Derive around 2007.

I should perhaps mention that, being a very recent and still
incomplete addition to Derive, the display of simplification steps is
somewhat buggy. Thus, the step after those I showed for Vladimir's
simplification challenge fails in version 6.10. Let's make use of a
time warp and see how Derive 7.0 handles the remaining simplification:

  pi/2+ATAN((2*SQRT(5*SQRT(2)+1)/7-SQRT(2)/7+SQRT(2*SQRT(2)-2)-10/7)/
(~
  1-(SQRT(2*SQRT(2)-2)-1)*(2*SQRT(5*SQRT(2)+1)/7-SQRT(2)/7-3/7)))/2-
AT~
  AN(-SQRT(2*SQRT(2)-2)+1)/2

  " (taking on SQRT(2*SQRT(2)-2) * 2*SQRT(5*SQRT(2)+1)/7 in the
denomi~
  nator) "

  " If x>y>0, SQRT(x-y) -> SQRT((x+SQRT(x^2-y^2))/2)-SQRT((x-SQRT(x^2-
~
  y^2))/2) "

  pi/2+ATAN((3*SQRT(10*SQRT(2)+2)/7-SQRT(2)/7-10/7)/(1-(2*(-
SQRT(2)+4)~
  /7+SQRT(2*SQRT(2)-2)*(-SQRT(2)/7-3/7)-(2*SQRT(5*SQRT(2)+1)/7-
SQRT(2)~
  /7-3/7))))/2-ATAN(-SQRT(2*SQRT(2)-2)+1)/2

  " 1/(z+w) -> (z-w)/(z^2-w^2) "

  pi/2+ATAN((SQRT(34*SQRT(2)+46)/7-SQRT(2)/
7+4/7)*(3*SQRT(10*SQRT(2)+2~
  )/7-SQRT(2)/7-10/7)/((SQRT(34*SQRT(2)+46)/7)^2-(SQRT(2)/7-4/7)^2))/
2~
  -ATAN(-SQRT(2*SQRT(2)-2)+1)/2

  " If x>y>0, SQRT(x+y) -> SQRT((x+SQRT(x^2-y^2))/2)+SQRT((x-SQRT(x^2-
~
  y^2))/2) "

  pi/2+ATAN((3*SQRT(2)*SQRT(2)*(6*SQRT(2)+11)/
(7*7)+SQRT(34*SQRT(2)+46~
  )*(-SQRT(2)/7-10/7)/7+(3*SQRT(10*SQRT(2)+2)/7-SQRT(2)/7-10/7)*(-
SQRT~
  (2)/7+4/7))/((SQRT(34*SQRT(2)+46)/7)^2-(SQRT(2)/7-4/7)^2))/2-ATAN(-
S~
  QRT(2*SQRT(2)-2)+1)/2

  " 1/(z+w) -> (z-w)/(z^2-w^2) "

  pi/2+ATAN(7*(6*SQRT(2)/7-4/7)*(-4*SQRT(5*SQRT(2)+1)/7+6*SQRT(2)/7+4/
~
  7)/8)/2-ATAN(-SQRT(2*SQRT(2)-2)+1)/2

  " (a final trivial step) "

  pi/2

Comments in parentheses are by me.

Martin.