50g

Does anyone have a program written for the HP 50G that will give all
complex roots of a number?  For example,the cube roots of -1 are
{[1+sqrt(3)]/2, -1, and [1-sqrt(3)]/2  } but the HP 50G will give only
the first.  Trying to evaluate the cube root of 2+11i it chokes
altogether though the answers are clearly {2+i, -1.866+1.232i
(approx), -0.1340-2.232i (approx)}. 

Joe

Make sure you're in complex & approx modes, then SOLVEX the equation x^3 + 1 = 0

For the other case, SOLVEX the equation x^3-2-11*i=0


--- On Wed, 12/31/08, joecolannino <joecolannino@...> wrote:

> From: joecolannino <joecolannino@...>
> Subject: [50g] Complex Roots
> To: 50g@yahoogroups.com
> Date: Wednesday, December 31, 2008, 1:15 PM
> Does anyone have a program written for the HP 50G that will
> give all
> complex roots of a number?  For example,the cube roots of
> -1 are
> {[1+sqrt(3)]/2, -1, and [1-sqrt(3)]/2  } but the HP 50G
> will give only
> the first.  Trying to evaluate the cube root of 2+11i it
> chokes
> altogether though the answers are clearly {2+i,
> -1.866+1.232i
> (approx), -0.1340-2.232i (approx)}. 
> 
> Joe

Here is a little program for finding the  approximate nth roots of a
Gaussian integer:

 

%%HP: T(3)A(R)F(.);

\<< OVER ABS OVER XROOT UNROT SWAP ARG 0 PICK3 1 -

  FOR j 2 \pi * j * OVER + i * PICK3 / EXP 4. PICK * 4. ROLLD

  NEXT DROP NIP \->LIST

  \<< \->NUM

  \>> MAP

\>>

 

It takes z and n from the stack and returns a list of values for z^ (1/n)

 

Jeremy

 

  _____  

From: 50g@yahoogroups.com [mailto:50g@yahoogroups.com] On Behalf Of
joecolannino
Sent: 31 December 2008 21:16
To: 50g@yahoogroups.com
Subject: [50g] Complex Roots

 

Does anyone have a program written for the HP 50G that will give all
complex roots of a number? For example,the cube roots of -1 are
{[1+sqrt(3)]/2, -1, and [1-sqrt(3)]/2 } but the HP 50G will give only
the first. Trying to evaluate the cube root of 2+11i it chokes
altogether though the answers are clearly {2+i, -1.866+1.232i
(approx), -0.1340-2.232i (approx)}. 

Joe

Don, that was really helpful.  It will be easy enough to write a program to
do this automatically.  When I do so, I'll share it with the group.  Thanks
again!

 

Joe

 

  _____  

From: 50g@yahoogroups.com [mailto:50g@yahoogroups.com] On Behalf Of Don Hart
Sent: Wednesday, December 31, 2008 10:56 PM
To: 50g@yahoogroups.com
Subject: Re: [50g] Complex Roots

 

Make sure you're in complex & approx modes, then SOLVEX the equation x^3 + 1
= 0

For the other case, SOLVEX the equation x^3-2-11*i=0

--- On Wed, 12/31/08, joecolannino <joecolannino@
<mailto:joecolannino%40sbcglobal.net> sbcglobal.net> wrote:

> From: joecolannino <joecolannino@ <mailto:joecolannino%40sbcglobal.net>
sbcglobal.net>

> Subject: [50g] Complex Roots
> To: 50g@yahoogroups. <mailto:50g%40yahoogroups.com> com
> Date: Wednesday, December 31, 2008, 1:15 PM
> Does anyone have a program written for the HP 50G that will
> give all
> complex roots of a number? For example,the cube roots of
> -1 are
> {[1+sqrt(3)]/2, -1, and [1-sqrt(3)]/2 } but the HP 50G
> will give only
> the first. Trying to evaluate the cube root of 2+11i it
> chokes
> altogether though the answers are clearly {2+i,
> -1.866+1.232i
> (approx), -0.1340-2.232i (approx)}. 
> 
> Joe

Hello Joe, if you want to get the n root of a number b, you have to 
solve the equation x^n-b=0, to solve this you have to use the command 
PROOT which needs as argument a vector with the coefficients, in this 
case [1 0...0 -b] and you get back a vector with all the roots, How 
many zeros do you need in your vector? n-1 zeros. If you enter first b 
and then n, your program can be something like this:
<<
    -> n
    << 1 SWAP NEG
         2 n
         START
           0 SWAP
         NEXT
         n 1 + ->ARRY PROOT
    >>
>>

b can be real or complex and n an integer grater than 1.

Everybody in the group have a nice year.

Also note that if you've set the 'exact' mode, the 
solution to x^2+1=0 will give the results in an algebraic 
form.

And you don't have to have the '=0' part. I put it in to 
make it easier to see what's going on.

--- In 50g@yahoogroups.com, "Joe Colannino" 
<joecolannino@...> wrote:
>
> Don, that was really helpful.  It will be easy enough 
to write a program to
> do this automatically.  When I do so, I'll share it 
with the group.  Thanks
> again!
> 
>  
> 
> Joe
> 
>  
> 
>   _____  
> 
> From: 50g@yahoogroups.com [mailto:50g@
yahoogroups.com] On Behalf Of Don Hart
> Sent: Wednesday, December 31, 2008 10:56 PM
> To: 50g@yahoogroups.com
> Subject: Re: [50g] Complex Roots
> 
>  
> 
> Make sure you're in complex & approx modes, then 
SOLVEX the equation x^3 + 1
> = 0
> 
> For the other case, SOLVEX the equation x^3-2-11*i=0
> 
> --- On Wed, 12/31/08, joecolannino <joecolannino@
> <mailto:joecolannino%40sbcglobal.net> sbcglobal.net> 
wrote:
> 
> > From: joecolannino <joecolannino@ 
<mailto:joecolannino%40sbcglobal.net>
> sbcglobal.net>
> > Subject: [50g] Complex Roots
> > To: 50g@yahoogroups. <mailto:50g%40yahoogroups.com> 
com
> > Date: Wednesday, December 31, 2008, 1:15 PM
> > Does anyone have a program written for the HP 50G 
that will
> > give all
> > complex roots of a number? For example,the cube 
roots of
> > -1 are
> > {[1+sqrt(3)]/2, -1, and [1-sqrt(3)]/2 } but the HP 
50G
> > will give only
> > the first. Trying to evaluate the cube root of 
2+11i it

> > chokes
> > altogether though the answers are clearly {2+i,
> > -1.866+1.232i
> > (approx), -0.1340-2.232i (approx)}. 
> > 
> > Joe
>