CAS: approx. sqrt?

[Helge Gabert]

I happened to run across this some time ago

sqrt(1+i) gets approximated right away in CAS, with the message:

"Warning, converting to approx. sqrt." ? Why?

But no automatic approximation with the 3-root or 4-root of 1+i.

   

[pwarmuth]

Is your CAS configured to use complex numbers in the CAS settings?

[Helge Gabert]

Return exact symbolic result is checked, of course - -

Or do you mean include complex results in variable? That doesn't seem to matter.

What do you get?

[parisse]

I have recently disabled exact sqrt for complex numbers on the Prime when they lead to complicated expressions that would take too much time to simplify (especially when mixed with other expressions) and are difficult to interrupt (because C++ exceptions are disabled on the Prime).

[Helge Gabert]

Thanks for the explanation,

but what about the 3-root and 4-root expressions? They stay in exact form. Why not have sqrt(complex #) simply also rewritten as e^(1/2*ln(complex number)? Or just leave it as sqrt(Complex #)? Will that really lead to too complicated, exact expressions further on?

If so, flashing the warning makes sense (as a suggestion), but the user can always hit the approx key anyway (at any time). I don't think that the CAS system should approximate by default - - the beauty of CAS is to enable exact computations.

[parisse]

There are limitations on a calculator, as explained above, aborting a too complex computation is sometimes not possible on the Prime because I can not compile with C++ exceptions enabled here.

[Helge Gabert]

OK, I understand.

[Helge Gabert]

Not to beat a dead horse, but has this been reported before?

CAS: (sqrt(x-1))^i and the Prime hangs.

There definitely are some issues with square roots and complex numbers
(Rev 8151).

[parisse]

I can not reproduce. Have you non default settings?

[Helge Gabert]

It happens if you don't add the parenthesis (sorry I typed that wrong in the above post)

just sqrt(x-1)^i,

and also if you hit simplify().

My settings are standard, except "use i" is checked, and simplify: "minimum."

The emulator hangs as well.

[parisse]

This has probably been fixed since last firmware release, as you can check with the latest version of Xcas.

[Helge Gabert]

Yes,

Xcas is OK, but this hasn't been fixed in the Prime firmware yet.