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From: Wes on 15 Apr 2008 14:23
Here's a strange CAS bug I ran across in class this week.

Set the calculator in EXACT, REAL, RECTANGULAR modes
Put the following on the stack:

4: 0
3: pi
2: 'SIN(X)^3'
1: 'X'

Do a definite integral (RS-TAN). You should get 4/3 which is the
correct answer.

Press UNDO and switch the mode from RECTANGULAR to either CYLINDRICAL
(Polar) or SPHERICAL and do the definite integral again. I get 3/2,
and REAL mode has changed to COMPLEX.

Press UNDO again redo the same integral without changing anything and
you get 4/3 again. The difference seems to be that the calculator in
now in COMPLEX mode.

Interestingly, it does not have this behavior when using the symbolic
expression 'integral(0,pi,SIN(X)^3,X)' or entering it in ALG mode.


If using RISCH or INTVX on 'SIN(X)^3', you get a different symbolic
result for each of the four combinations of REAL/COMPLEX mode and RECT/
CYLIN mode. Three of the four are equivalent and are correct, but the
REAL/CYLIN combination gives a different, incorrect result.

Anybody know what's going on here?

-wes
From: Bill Markwick on 17 Apr 2008 09:49
On Apr 15, 2:23 pm, Wes <wjltemp...(a)yahoo.com> wrote:
> Set the calculator in EXACT, REAL, RECTANGULAR modes
> Put the following on the stack:
>
> 4: 0
> 3: pi
> 2: 'SIN(X)^3'
> 1: 'X'
>
> Do a definite integral (RS-TAN).  You should get 4/3 which is the
> correct answer.

Interesting, but I can't duplicate this on my 49G+ with v2.09. The
calc switches to approximate mode and I get 1.33... in all versions
except complex. Are there some flag settings that might be affecting
this?

Regards,
Bill

From: Wes on 17 Apr 2008 11:28
On Apr 17, 4:49 pm, Bill Markwick <bd...(a)torfree.net> wrote:
> On Apr 15, 2:23 pm, Wes <wjltemp...(a)yahoo.com> wrote:
>
> > Set the calculator in EXACT, REAL, RECTANGULAR modes
> > Put the following on the stack:
>
> > 4: 0
> > 3: pi
> > 2: 'SIN(X)^3'
> > 1: 'X'
>
> > Do a definite integral (RS-TAN). You should get 4/3 which is the
> > correct answer.
>
> Interesting, but I can't duplicate this on my 49G+ with v2.09. The
> calc switches to approximate mode and I get 1.33... in all versions
> except complex. Are there some flag settings that might be affecting
> this?
>
> Regards,
> Bill

I've got the same ROM on my 50g. I get the same results with EMU48
with the 2.09 emulator ROM. I don't have my 50g in front of me, but
my EMU flags are:

{ # 700000820521CFF0h # 101h # 89010020A000000h # 0h }

-wes
From: Bill Markwick on 17 Apr 2008 19:04
On Apr 17, 11:28 am, Wes <wjltemp...(a)yahoo.com> wrote:
> On Apr 17, 4:49 pm, Bill Markwick <bd...(a)torfree.net> wrote:
>
>
>
>
>
> > On Apr 15, 2:23 pm, Wes <wjltemp...(a)yahoo.com> wrote:
>
> > > Set the calculator in EXACT, REAL, RECTANGULAR modes
> > > Put the following on the stack:
>
> > > 4: 0
> > > 3: pi
> > > 2: 'SIN(X)^3'
> > > 1: 'X'
>
> > > Do a definite integral (RS-TAN).  You should get 4/3 which is the
> > > correct answer.
>
> > Interesting, but I can't duplicate this on my 49G+ with v2.09.  The
> > calc switches to approximate mode and I get 1.33... in all versions
> > except complex.  Are there some flag settings that might be affecting
> > this?
>
> > Regards,
> > Bill
>
> I've got the same ROM on my 50g.  I get the same results with EMU48
> with the 2.09 emulator ROM.  I don't have my 50g in front of me, but
> my EMU flags are:
>
> { # 700000820521CFF0h # 101h # 89010020A000000h # 0h }
>

Hi. I installed your flags and managed to duplicate the oddity.
However, it turned out that it wasn't the flags at all - it was the
fact that I had entered pi as a number, which made the calc revert to
Approximate mode. Once I changed it to a symbol it behaved as you
described it.

I'm not sure what's going on. I'll experiment with it tonight.

Bill
From: Bill Markwick on 19 Apr 2008 09:11
After some tinkering, I found you could boil it down to the fact that
in cylindrical or spherical mode (plus Real mode), you get different
answers from the stack version and the algebraic expression version.
Another symptom is that the calculator doesn't switch from Real to
Complex until the calculation is over. If you switch to Complex before
you start, the problem doesn't come up.

And just to confuse things further, it only happens if the exponent of
SIN(X) is an odd number. Try it with any even exponent and it works
fine.

This is a peculiar one.

Bill
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