One Sided Limit Error on the Prime

[chazzs]

Not sure if this bug has been reported or not.

One-sided limits aren't being evaluated correctly. For instance: limit as x->1^+1 (from above) of sqrt(1-x^2) should no exist, but the Prime gives 0 (what the limit from below equals.) Any thoughts?

C

[Tim Wessman]

http://www.wolframalpha.com/input/?i=lim...+x+to+1%2B

Some food for thought to stir the discussion...

[chazzs]

That I new. I just assumed unchecking the Complex and i boxes in CAS would have resulted in not allowing complex values. I guess I'm not entirely sure what the Complex check box does besides allowing the factorization of x^2+4 (and finding complex solutions.) I assumed some consistency across the board, especially if HP wants to make its way back into the educational field, which I hope is the current train of thought.

[parisse]

Xcas complex mode (translated by Use i in the Prime CAS settings) does not mean that complex result are forbidden. For example sqrt(-1) returns i in real mode. It is used if there is something ambiguous, as in the example you cite: factor(x^2+4), but also for sqrt(x^2).
I decided to do that after my experience with the HP49 CAS, where I found it was much too annoying to switch modes. The idea behind is that you should almost never have to work in complex mode (you can use cfactor or csolve to get complex factorization and roots in real mode). It's the same as for exact/approx mode : for example you don't want to get an error if you add a fraction and and approx number or if you call fsolve with exact data.
My experience with students using Xcas is that it's much easier that way (try to explain to a student on a hp49/50 that after each parametric plot he must switch complex mode off and exact mode on).

[leprechaun]

To have a dedicated cfactor is cool. I won't keep i switched on. It does not show up in the catalogue or the help screen though. Does it? Maybe worth adding the command in the next firmware?
There seem to be many hidden cas commands that hp was not aware of? Really interessting stuff thanks for sharing your knowledge.

[Terje Vallestad]

(04-15-2015 07:23 AM)leprechaun Wrote:  It does not show up in the catalogue or the help screen though.

What version do you run? If you look in the on-calculator "Catlg" for the functions and press help, both cFactor and cSolve are included.

Code:


Syntax: 
cFactor(Expr) 
Returns an expression factorized over the complex field (on Gaussian integers if there are more than two). 
Example: 
cFactor(x2*y+y) ➔ (x+i)*(x-i)*y 
cFactor(x2*y2+y2+2*x2+2)

Syntax: 
cSolve(Expr,Var) 
Returns the solutions, including complex solutions, of Expr, for Var. If Expr is an expression, solves the equation Expr=0. 

Example: 
cSolve(x^4=1,x) ➔ {-1, i,1, −i } 
cSolve(u*v-u=v and v2=u,[u,v]) ➔ {[0.,0.],[2.61803,1.61803],[0.38196,−0.618033]}

Hope this helps,

Cheers, Terje

[leprechaun]

Sorry that was unclear. I meant the toolbox. There I find factor but no cfactor. Also the help screen (i use that extensively) does not give a hint for cfactor.
Thanks a lot

Edit. Help on the command gives cas help. It is 6975 from 2014 12 3. is there new firmware available?

[rprosperi]

(04-15-2015 05:41 PM)leprechaun Wrote:  Sorry that was unclear. I meant the toolbox. There I find factor but no cfactor. Also the help screen (i use that extensively) does not give a hint for cfactor.
Thanks a lot

Edit. Help on the command gives cas help. It is 6975 from 2014 12 3. is there new firmware available?

The Help system does indeed include the function cFactor(), however you must use a capital F in the spelling. "cfactor()" - No, "cFactor()" - Yes.

And yes, this is annoying to me too.

[compsystems]

I can not get this result

cSolve(u*v-u=v and v2=u,[u,v]) ➔ {[0.,0.],[2.61803,1.61803],[0.38196,−0.618033]}

cSolve(u*v-u=v and v2=u,[u,v]) ➔ {[v2,v2/(v2-1)]} ➔ v2 and v2/(v2-1)

[parisse]

(c)solve([u*v-u=v,v^2=u],[u,v])
-> [[0,0],[(sqrt(5)+3)/2,(sqrt(5)+1)/2],[(-(sqrt(5))+3)/2,(-(sqrt(5))+1)/2]]