[CAS] arc sine of a complex number
12-17-2014, 02:45 AM
Post: #1
 compsystems Senior Member Posts: 1,262 Joined: Dec 2013
[CAS] arc sine of a complex number
[home mode]

ASIN(4.0+i) => 1.31861691808+2.09659645729*iok

[CAS mode]

ASIN(4.0+i) => "Error: Bad Argument Value" why the argument is a bad
12-17-2014, 03:07 AM
Post: #2
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
What are your flag settings? I get, in CAS, ASIN(4+i) unevaluated, and ASIN(4.+i) 1.31... + 2.09...*i, no problem.
12-17-2014, 03:17 AM
Post: #3
 compsystems Senior Member Posts: 1,262 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
[CAS mode] and use i (set)

ASIN(4.0+i) => 1.31861691808+2.09659645729*i ok

I think that instead of showing the error message "Error: Bad Argument Value" , should say set flag "use i"

"use i" says use i to factor polynomials

that relation has polynomials with complex numbers?
12-17-2014, 03:24 AM
Post: #4
 Han Senior Member Posts: 1,820 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
(12-17-2014 03:17 AM)compsystems Wrote:  [CAS mode] and use i (set)
that relation has polynomials with complex numbers?

Perhaps the CAS interprets (4+i) as a polynomial (of degree 0) with complex coefficients. (Just a guess on my part)

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12-17-2014, 03:25 AM (This post was last modified: 12-17-2014 03:28 AM by Helge Gabert.)
Post: #5
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
I see what you are suggesting, but it could be very exhausting to come up with precise error messages for every eventuality a user could encounter. Yes, here you need to check "Use i."
12-17-2014, 03:45 AM (This post was last modified: 12-17-2014 03:53 AM by compsystems.)
Post: #6
 compsystems Senior Member Posts: 1,262 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
Messages that launches the hpprime are truly disappointing. =(

entry is a valid complex number.

or should I ask switch flag to answer complex, as it does in the HP50

asin("hello") => "Error: Bad Argument Value" OK but not
ASIN(4.0+i) => "Error: Bad Argument Value" :~(
12-17-2014, 03:50 AM
Post: #7
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
I don't disagree . . . flag switching like in the HP50G might be more desirable in this case.
12-17-2014, 06:53 AM
Post: #8
 parisse Senior Member Posts: 1,121 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
i is complex mode, I'm not responsible for the way it is described on the HP settings screen.
I'll have a look, perhaps I can improve the error message.
12-17-2014, 07:51 AM
Post: #9
 parisse Senior Member Posts: 1,121 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
Well, I will probably remove the error, since it is only present on the Prime, not in Xcas.
12-17-2014, 04:20 PM (This post was last modified: 12-17-2014 04:57 PM by compsystems.)
Post: #10
 compsystems Senior Member Posts: 1,262 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
(12-17-2014 06:53 AM)parisse Wrote:  i is complex mode
What is the difference between the flags "Complex" and "use I"?

The message that launches the hpprime (asin(4.0+i) => "Error: Bad Argument Value" ) makes losing all the computational power of xcas

(12-17-2014 07:51 AM)parisse Wrote:  Well, I will probably remove the error

Return the same input when the flag is disabled, suggests you can not solve. :~(
asin(4.0+i) => asin(4.0+i) =(

ideally show a dialog box saying that if you want to change a complex mode, this is already implemented in the CAS of HP50, what involution? must extract the best from the past

HP50G

are you agree with this request? +1 or -1 or indifferent, please vote

solve(x^2+2*x+3 = 0,x) "use i [OFF]" => [] ok no real results
solve(x^2+2*x+3 = 0,x) "use i [on]" => {√(2)*i-1,-√(2)*i-1}

solve(x^2+2*x+3 = 0,x) "use i [OFF]" => great if also generates a message to change the flag, if the user does not want to change return []

PD: Please Parisse can improve the output of the expression, ordered the real part first

solve(x^2+2*x+3 = 0,x) "use i [on]" => {-1+ √(2)*i, -1 - √(2)*i-1 }

Naturally mathematical texts show real part + imaginary part , a+b*I, also for easy reading when the output expression is very large

other request is to label the output only for the purpose of observing a more didactic output, this may be adding a new flag in configuration of the CAS

solve(x^2+2*x+3 = 0,x) "use i [on] and tag[on]" => { x1:-1+ √(2)*i, x2:-1 - √(2)*i-1 }

Thanks
12-17-2014, 06:56 PM
Post: #11
 parisse Senior Member Posts: 1,121 Joined: Dec 2013
RE: [CAS] arc sine of a complex number
"Use i for factoring" is more restrictive than what complex mode does. For example, if complex mode is on, sqrt(x^2) returns x instead of |x|. On the HP port of giac, some functions like ln were returning errors if the argument would return a complex answer (like domain error on the TI) in non real mode. This was later removed, but I did not check everything, and functions that are not used often like asin/acos have the check.

For the mode switch, my experience with the hp49/50/40 convinced me it was not such a good idea because it requires manual mode switchs after. For example if you make a parametric plot on the 50g, you end up in complex approx mode, and you must switch back to real exact for normal CAS operations (there are shortcuts to do that but non-geeks will not learn them).
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