Using Casios for finding roots using Deflation
11-13-2022, 07:01 AM
Post: #1
 Matt Agajanian Senior Member Posts: 1,083 Joined: Dec 2013
Using Casios for finding roots using Deflation

In calculus there is a method for finding several roots of a function called deflation.

When a root is found, that’s root one, r1.

To find the next root, the function becomes f(x)/(x-r1). If a root is found, that’s root two, r2.

To find the next root, the function to solve is (f(x)/(x-r1))/(x-r2)

My question is, to make this repetitive process easier, I’d like to just modify the function accordingly to find successive root. Problem is that after I find a root, I can’t just store the result in a variable and keep the function intact so I can continue editing it for finding the next root.

The way I need to exit the solver, erases the function I’m evaluating.

How can I retain the function so I can edit it to find successive roots on the 991EX Classwiz, fx-991ES Plus, and fx-115ES Plus?

Thanks
11-14-2022, 09:32 AM
Post: #2
 Csaba Tizedes Senior Member Posts: 608 Joined: May 2014
RE: Using Casios for finding roots using Deflation
(11-13-2022 07:01 AM)Matt Agajanian Wrote:  The way I need to exit the solver, erases the function I’m evaluating.
How can I retain the function

First evaluate your function with CALC, with this step your function stored in History.
Then use SOLVE
When your root is on the screen (x=...; L-R=0) press STO A
Go up to your stored equation, bracket it () and press fraction button: with this step your function goes to fraction numerator and you can add (x-A) into denominator

From here same as above:

Evaluate your function with CALC, type for x any value which is not equal A
SOLVE
.... STO B
.... (x-B)
....

Next root is same as above again:
....
.... STO C
.... (x-C)
....

and so on...

Enjoy!
Cs.
11-15-2022, 11:05 PM
Post: #3
 Csaba Tizedes Senior Member Posts: 608 Joined: May 2014
RE: Using Casios for finding roots using Deflation
Here a cubic equation:

Cs.
11-16-2022, 03:04 AM (This post was last modified: 11-16-2022 04:16 AM by Matt Agajanian.)
Post: #4
 Matt Agajanian Senior Member Posts: 1,083 Joined: Dec 2013
RE: Using Casios for finding roots using Deflation
Although the keystrokes were kinda blocked due to hands covering the keyboard, your description of the keystrokes helped!

Now, let’s see if the Sharp cooperates.

And yes it does!!

The trick, after a root is found, exit by pressing ON/C. This brings up the equation with the cursor at the end of the equation. Press =
Then, store X into A (first root)
Move back up to the equation. Editing is enabled. So, bracket the equation in parentheses and add /(x-a).
Press SOLVER.
Enter an initial guess.
Press =
Once a root is found, Press ON/C
The cursor is at the end of f(x), press =. This will add f(x) to the history list.
Recall X and store in B as this is the second root.
Move back up the history to edit the f(x) you solved. Bracket it and add / (x-b).
Press SOLVER.

Repeat the above steps.
11-16-2022, 05:57 AM
Post: #5
 Thomas Klemm Senior Member Posts: 2,147 Joined: Dec 2013
RE: Using Casios for finding roots using Deflation
(11-15-2022 11:05 PM)Csaba Tizedes Wrote:

Off topic, but I noticed the analemma in the cover of your calculator.
Are you into sundials?
11-16-2022, 08:41 AM (This post was last modified: 11-16-2022 08:44 AM by Csaba Tizedes.)
Post: #6
 Csaba Tizedes Senior Member Posts: 608 Joined: May 2014
RE: Using Casios for finding roots using Deflation
(11-16-2022 05:57 AM)Thomas Klemm Wrote:  analemma - Are you into sundials?

Not really, but I use it for sunrise-noon-sunset calculations.

And a video about the calculation + how you can insert the analemma into calculator case (video timing set to 40:15, but Youtube not enough clever to understand... Damn...):

Cs.
11-16-2022, 11:38 AM
Post: #7
 Thomas Klemm Senior Member Posts: 2,147 Joined: Dec 2013
RE: Using Casios for finding roots using Deflation
(11-16-2022 08:41 AM)Csaba Tizedes Wrote:  Not really, but I use it for sunrise-noon-sunset calculations.

This old forum article might interest you: Sunrise and Sunset
11-16-2022, 11:51 AM
Post: #8
 Thomas Klemm Senior Member Posts: 2,147 Joined: Dec 2013
RE: Using Casios for finding roots using Deflation
(11-16-2022 08:41 AM)Csaba Tizedes Wrote:  video timing set to 40:15, but Youtube not enough clever to understand...

But in the embedded iframe the following URL is used:

Either YouTube doesn't allow the use of a timestamp in that case or then it could also be a limitation of MyBB.
11-19-2022, 11:23 PM
Post: #9
 Eddie W. Shore Senior Member Posts: 1,606 Joined: Dec 2013
RE: Using Casios for finding roots using Deflation
Great thread - help tips with the Solver function.
11-20-2022, 12:11 AM
Post: #10
 Matt Agajanian Senior Member Posts: 1,083 Joined: Dec 2013
RE: Using Casios for finding roots using Deflation
(11-19-2022 11:23 PM)Eddie W. Shore Wrote:  Great thread - help tips with the Solver function.