Thread Subject: solving a 6th degree polynomial

I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.

On 11/22/2011 2:12 AM, dineo wrote:
> I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function
>of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic
>math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.

I did not think there is a solution for roots of 6th degree poly in terms of its coefficients?

I think Someone called Gaolis or is it Abel? said so if I remember.

May be you have to use numerics? (plug in a value for 't').

--Nasser

You can find roots numericly using function:
roots

t=...
r=roots([c1*t x2/t 1/t ...])

-----------------------------------------
Maxim Vedenev, MATLAB Custom Programming
vedenev@ngs.ru
http://simulations.narod.ru/

"Nasser M. Abbasi" <nma@12000.org> wrote in message <jafn85$bj7$1@speranza.aioe.org>...
> On 11/22/2011 2:12 AM, dineo wrote:
> > I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function
> >of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic
> >math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.
>
> I did not think there is a solution for roots of 6th degree poly in terms of its coefficients?

Yes and no; actually the solution can be expressed as hypergeometric functions:
http://library.wolfram.com/examples/quintic/main.html

Problem: to my knowledge, there is no *efficient* implementation of hypergeometric function in Matlab.

>
> I think Someone called Gaolis or is it Abel? said so if I remember.

Abel is the first, but Galois's theory go straight into the heart of the problem and explains "why".

>
> May be you have to use numerics? (plug in a value for 't').
>

That's the best option I guess.

Bruno

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <jafonr$9u8$1@newscl01ah.mathworks.com>...
> "Nasser M. Abbasi" <nma@12000.org> wrote in message <jafn85$bj7$1@speranza.aioe.org>...
> > On 11/22/2011 2:12 AM, dineo wrote:
> > > I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function
> > >of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic
> > >math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.
> >
> > I did not think there is a solution for roots of 6th degree poly in terms of its coefficients?
>
> Yes and no; actually the solution can be expressed as hypergeometric functions:
> http://library.wolfram.com/examples/quintic/main.html
>
> Problem: to my knowledge, there is no *efficient* implementation of hypergeometric function in Matlab.
>
> >
> > I think Someone called Gaolis or is it Abel? said so if I remember.
>
> Abel is the first, but Galois's theory go straight into the heart of the problem and explains "why".
>
> >
> > May be you have to use numerics? (plug in a value for 't').
> >
>
> That's the best option I guess.
>
> Bruno
So the plan is to create a t_vector from which I can pull values for t to plug into the polynomial. so with each t value I'll get a specific set of roots R=roots(P) where P is the vector of the coefficients of the polynomial. The problem is that I only want to plot specific roots against t. From this plot of x vs t, i want matlab to compute the equation (the same way in excel, one can plot a graph from raw data and get excel to compute the equation)

On 22 Nov, 10:24, "dineo " <ngwdin...@uct.ac.za> wrote:
> "Bruno Luong" <b.lu...@fogale.findmycountry> wrote in message <jafonr$9u...@newscl01ah.mathworks.com>...
> > "Nasser M. Abbasi" <n...@12000.org> wrote in message <jafn85$bj...@speranza.aioe.org>...
> > > On 11/22/2011 2:12 AM, dineo wrote:
> > > > I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function
> > > >of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic
> > > >math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.
>
> > > I did not think there is a solution for roots of 6th degree poly in terms of its coefficients?
>
> > Yes and no; actually the solution can be expressed as hypergeometric functions:
> >http://library.wolfram.com/examples/quintic/main.html
>
> > Problem: to my knowledge, there is no *efficient* implementation of hypergeometric function in Matlab.
>
> > > I think Someone called Gaolis or is it Abel? said so if I remember.
>
> > Abel is the first, but Galois's theory go straight into the heart of the problem and explains "why".
>
> > > May be you have to use numerics? (plug in a value for 't').
>
> > That's the best option I guess.
>
> > Bruno
>
> So the plan is to create a t_vector from which I can pull values for t to plug into the polynomial. so with each t value I'll get a specific set of roots R=roots(P) where P is the vector of the coefficients of the polynomial.

That's straight-forward numerical work.

> The problem is that I only want to plot specific roots against t.

This one might be harder - impossible? - to have a computer do,
depending on how you decide what roots to keep. If the criteria
are strictly numerical, then it can be done algorithmically.
If the criteria are related to some analytical expression, as
roots of differential eqations associated with certain
physical phenomena, you might be in for a hard task.

> From this plot of x vs t, i want matlab to compute the equation (the same way in excel, one can plot a graph from raw data and get excel to compute the equation)

I wouldn't be surprised if Excel actually has a function
that pretends to do that kind of thing, but trust me:
That's humbug. Never trust anything that pops out of
such a function.

Rune

Rune Allnor <allnor@tele.ntnu.no> wrote in message <9e8e7564-6ad5-43d9-98ca-dfb523b61086@y42g2000yqh.googlegroups.com>...
> On 22 Nov, 10:24, "dineo " <ngwdin...@uct.ac.za> wrote:
> > "Bruno Luong" <b.lu...@fogale.findmycountry> wrote in message <jafonr$9u...@newscl01ah.mathworks.com>...
> > > "Nasser M. Abbasi" <n...@12000.org> wrote in message <jafn85$bj...@speranza.aioe.org>...
> > > > On 11/22/2011 2:12 AM, dineo wrote:
> > > > > I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function
> > > > >of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic
> > > > >math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.
> >
> > > > I did not think there is a solution for roots of 6th degree poly in terms of its coefficients?
> >
> > > Yes and no; actually the solution can be expressed as hypergeometric functions:
> > >http://library.wolfram.com/examples/quintic/main.html
> >
> > > Problem: to my knowledge, there is no *efficient* implementation of hypergeometric function in Matlab.
> >
> > > > I think Someone called Gaolis or is it Abel? said so if I remember.
> >
> > > Abel is the first, but Galois's theory go straight into the heart of the problem and explains "why".
> >
> > > > May be you have to use numerics? (plug in a value for 't').
> >
> > > That's the best option I guess.
> >
> > > Bruno
> >
> > So the plan is to create a t_vector from which I can pull values for t to plug into the polynomial. so with each t value I'll get a specific set of roots R=roots(P) where P is the vector of the coefficients of the polynomial.
>
> That's straight-forward numerical work.
>
> > The problem is that I only want to plot specific roots against t.
>
> This one might be harder - impossible? - to have a computer do,
> depending on how you decide what roots to keep. If the criteria
> are strictly numerical, then it can be done algorithmically.
> If the criteria are related to some analytical expression, as
> roots of differential eqations associated with certain
> physical phenomena, you might be in for a hard task.

> I want to keep the positive and real roots

> > From this plot of x vs t, i want matlab to compute the equation (the same way in excel, one can plot a graph from raw data and get excel to compute the equation)
>
> I wouldn't be surprised if Excel actually has a function
> that pretends to do that kind of thing, but trust me:
> That's humbug. Never trust anything that pops out of
> such a function.
>
> Rune
I want to keep the positive and real roots

On 22 Nov, 11:37, "dineo " <ngwdin...@uct.ac.za> wrote:
> Rune Allnor <all...@tele.ntnu.no> wrote in message <9e8e7564-6ad5-43d9-98ca-dfb523b61...@y42g2000yqh.googlegroups.com>...
> > On 22 Nov, 10:24, "dineo " <ngwdin...@uct.ac.za> wrote:
> > > "Bruno Luong" <b.lu...@fogale.findmycountry> wrote in message <jafonr$9u...@newscl01ah.mathworks.com>...
> > > > "Nasser M. Abbasi" <n...@12000.org> wrote in message <jafn85$bj...@speranza.aioe.org>...
> > > > > On 11/22/2011 2:12 AM, dineo wrote:
> > > > > > I have a 6th degree polynomial (e.g: c1tx^6 + c2/t*x^5 + x^4/t....=0 )whose roots are a function
> > > > > >of a variable 't'. I want to eventually obtain solve for x in terms of t. I don't have symbolic
> > > > > >math toolbox so can someone please advice on how to write a code that will find help me see how x changes with 't'.
>
> > > > > I did not think there is a solution for roots of 6th degree poly in terms of its coefficients?
>
> > > > Yes and no; actually the solution can be expressed as hypergeometric functions:
> > > >http://library.wolfram.com/examples/quintic/main.html
>
> > > > Problem: to my knowledge, there is no *efficient* implementation of hypergeometric function in Matlab.
>
> > > > > I think Someone called Gaolis or is it Abel? said so if I remember.
>
> > > > Abel is the first, but Galois's theory go straight into the heart of the problem and explains "why".
>
> > > > > May be you have to use numerics? (plug in a value for 't').
>
> > > > That's the best option I guess.
>
> > > > Bruno
>
> > > So the plan is to create a t_vector from which I can pull values for t to plug into the polynomial. so with each t value I'll get a specific set of roots R=roots(P) where P is the vector of the coefficients of the polynomial.
>
> > That's straight-forward numerical work.
>
> > > The problem is that I only want to plot specific roots against t.
>
> > This one might be harder - impossible? - to have a computer do,
> > depending on how you decide what roots to keep. If the criteria
> > are strictly numerical, then it can be done algorithmically.
> > If the criteria are related to some analytical expression, as
> > roots of differential eqations associated with certain
> > physical phenomena, you might be in for a hard task.
> > I want to keep the positive and real roots
> > > From this plot of x vs t, i want matlab to compute the equation (the same way in excel, one can plot a graph from raw data and get excel to compute the equation)
>
> > I wouldn't be surprised if Excel actually has a function
> > that pretends to do that kind of thing, but trust me:
> > That's humbug. Never trust anything that pops out of
> > such a function.
>
> > Rune
>
> I want to keep the positive and real roots– Skjul sitert tekst –

Straight-forward, as long as you are aware
of the usual numerical pitfalls.

Rune