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Display more than just one root
06-29-2015, 02:43 PM (This post was last modified: 06-29-2015 03:00 PM by conrad8.)
Post: #1
Display more than just one root
Hi,

I have an equation which has one variable Y2 but two instances of it, ignore Y1 as have numbers to plug in for those.

Basically I know all variables except Y2

[Image: 97f7681927b90991bd9382732f6562c7.png]

Anyhow - when I use the HP Prime SOLVE APP to find a solution
it does solve the the Y2 variable but only puts out ONE solution of the the 3
I know that exist.. my friend sitting next to me has a Ti Nspire and his has 3 root solutions.... and we need all 3 to move ahead with these conjugate problems... driving me mad!!!!

how do I get the HP prime to list ALL the solutions.. I've managed to play around with the plot range and got the a valid different one solution but thats trial and error...

Please help if you can.. Thanks Smile

Here is a quick image link from the internet of a random hp prime solve page but with multivariable being solved... can this type of page display the two positive and one negative values of Y??????
[Image: 80762i8683F4FF47882DB9?v=mpbl-1]

Heres a link to the kind of equations Im having to solve (scroll down to Conjugate Depths in a Rectangular Channel):
[url=https://en.wikipedia.org/wiki/Momentum-
depth_relationship_in_a_rectangular_channel]https://en.wikipedia.org/wiki/Momentum-depth_relationship_in_a_rectangular_channel[/url]
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06-29-2015, 05:09 PM
Post: #2
RE: Display more than just one root
If you type in a guess near the root you want it should fine the exact solution. I believe that solver uses either bi-section or Newton's method as a solve routine. Both work best with a starting guess close to the root.

For Q=1, G=2, and Y1=3 Y2=0 when I solve for Y2 I get 0.107
For Q=1, G=2, and Y1=3 Y2=-5 when I solve for Y2 I get -3.107

The 3rd root is always going to be Y1, 3 in the example above. Screen shots are below:

   
   
   
   

Road
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06-30-2015, 05:36 PM
Post: #3
RE: Display more than just one root
Hello,

The solve application is a purely numerical solver. It will only give you the nearest unique answer from your initial guess. You can use the PLOT key which can show you nearby results as well.

For example, type X^3+3*X^2-1=Y in your solve. Press NUM and type 0 for your Y. Type 1 for X. Now when you press solve, it uses the initial value for X and iterates to find the root. If you started at -10, it would give you a different result. Press PLOT and you'll see intersections of your lines.


Now if you are wanting to get results all together, you can also do this - just by doing it the same way as what your friend is doing.

Go to the CAS screen, type your equation, and use the TOOLBOX->CAS->Solve -> Numerical Solve command. You should see something like:

fsolve(x^3+3*x^2-1) [ENTER] [-1, -1.618... .618...]

There are your three results. Note that since this is a numeric solver, you cannot always guarantee that ALL possible results have been returned for many types of systems. You can however specify ranges. For example:


fsolve(x^3+3*x^2-1,x,0..1) [ENTER] [.618...] (from range 0 to 1)

fsolve(x^3+3*x^2-1,x,-1..1) [ENTER] [ -1, .618...] (from range -1 .. 1)


So basically, on the nspire you have the "solve" command. If it can't symbolically solve something, it will automatically drop back to numeric solving. On Prime, you have separate numeric and symbolic commands (fsolve, solve).

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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07-01-2015, 05:58 AM
Post: #4
RE: Display more than just one root
Hello,

>The solve application is a purely numerical solver.
>It will only give you the nearest unique answer from your initial guess.

Actually, a slightly incorrect answer.
It is numerical and uses a variety of methods to 'zero in' on the solution.
These method can cause it, depending on the shape of the curve to find a solution that is NOT the nearest to the initial guess in some cases.

Cyrille
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11-10-2015, 08:20 PM
Post: #5
RE: Display more than just one root
(06-30-2015 05:36 PM)Tim Wessman Wrote:  ..
Go to the CAS screen, type your equation, and use the TOOLBOX->CAS->Solve -> Numerical Solve command. You should see something like:
fsolve(x^3+3*x^2-1) [ENTER] [-1, -1.618... .618...]
...

If I may correct a little thing from all this, the equation in the example is probably the following one x^3+2*x^2-1 if the roots where -1, -1.618 and 0.618.

But it is just a small detail. I am sure every ones understood the main points of the answer.

Denis.

Denis Bisson
Little electronic technician loving calculators
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11-17-2015, 02:00 PM
Post: #6
RE: Display more than just one root
With the Solve App you will only find real solutions, so for X^2-3x+5=0 you will receive "Error: Extremum found"

fsolve in CAS will try to find also complex solutions, so if "Use i" is checked in CAS Settings fsolve(x^2-3*x+5=0) will return:
[1.5-1.65831239518*i,1.5+1.65831239518*i]
which are numerical solutions and not exact solution like with solve(x^2-3*x+5=0) which will return
{1/2*(√11*i+3),1/2*(-√11*i+3)}
cfsolve(x^2-3*x+5=0) give the same answer independently of the "Use i" setting.
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