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#176 2013-06-21 21:43:24

Herc11
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Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

Maybe its the same thing. I am not sure.

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#177 2013-06-21 22:43:31

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

I could also write the routines to generate a problem in Mathematica with exact arithmetic. Leaving Geogebra out. The error would diminish greatly.

Did you have a fixed n you needed to be solved or were you just seeing what could be done?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#178 2013-06-22 05:13:29

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

No, only I want to see...just being curious!

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#179 2013-06-22 05:22:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Hi;

Okay, I understand.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#180 2013-06-22 20:03:03

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

To be honest, I want to know if by having 2n equations

(of the previous form==leading coef.+ 1 point of the polynomial)

I can define the intersection point of the n degree polynomials.

You and  anomnimistefy prove that for the case of n=2, n=3 the previous case stands.

I think it stands for every n.

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#181 2013-06-22 21:25:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Each set of polynomials of n degree can only intersect at n points. Each point will have 2 variables x and y. You will need 2n equations to solve for them.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#182 2013-06-22 22:31:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Define the intersection points of polynomials

I thought we already got to this conclusion before.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#183 2013-06-23 00:13:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

The evidence supports this but there are practical considerations.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#184 2013-07-19 11:33:10

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

Hey bobby m,
Do you know if the set of equations that were talking about can be solved over Galois Fields?Or where to search?

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#185 2013-07-19 17:32:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

If you mean solved modulo 1...n, then Mathematica might be able to handle the job.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#186 2013-07-19 19:44:52

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

Yes I meant a Finite feild generated by a prime n or an irreducible polynomial.

I am not sure that is solvable if the equations of the set are nonlinear i.e. te polynomials are of 2-degree 3- etc...

Last edited by Herc11 (2013-07-19 19:55:22)

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#187 2013-07-19 21:27:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Hi;

Do you have a worked example?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#188 2013-07-19 21:52:46

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

No..It is not easy to test it. I have written in C a galois field multiplier and divider for an irreducilbe polynomial of degree 128.

The addition is simply an xor.

The equations are the same that I was posted in previous posts.

I google it and the results that wre obtained confused me. e.g. I tried to read the following thesis but with no result.

If i undersstood correctly the problem is not easily solvable but I am not sure that this thesis copes the same problem as mine


https://openaccess.leidenuniv.nl/bitstream/handle/1887/4392/Thesis.pdf?sequence=1

Last edited by Herc11 (2013-07-19 21:56:23)

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#189 2013-07-19 23:38:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Hi;

Reading the pdf now.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#190 2013-07-19 23:39:53

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

I think that when the set of equations is constituted by polynomials of degree-n, an unknown

will come up.

I dont know how

can be computed over GFs.

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#191 2013-07-19 23:46:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Isn't that covered in his "power extraction algorithm?" Of course, he has gone on and on with his existence proofs but I do not see an implementation so far.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#192 2013-07-19 23:51:36

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

Whats this?I ve never heard it. Can this solve the aforementioned problem?

You give me hope!

Last edited by Herc11 (2013-07-20 00:32:35)

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#193 2013-07-20 05:04:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

He mentions it in the pdf you provided.

You should not have hope yet. Highbrows like him rarely explain anything. The chance that he will provide an example that a lowbrow like me can follow is 1 in 10000.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#194 2013-07-20 19:31:07

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

If we try a different approach and instead replacing the

to the formula we write

then the formula will be  e.g for 3 degree polynomials

So If again we know

we need a ste of 2x3=6 such polynomials to solve the system and the system remains linear i.e. to get the
afterwards that we have defined

we can solve


and recover the missing intersection points.

So it seems that it can be solved over GF. I think...

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#195 2013-07-20 21:14:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Wouldn't a0, a1, a2,... all have to be members of the GF?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#196 2013-07-20 21:30:56

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

Yes all are members of the GF.

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#197 2013-07-20 21:47:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

Hi;

How can you be sure?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#198 2013-07-20 21:55:16

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

About what?

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#199 2013-07-20 22:35:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: Define the intersection points of polynomials

That the a0, a1, a2... will all be integers let alone mebers of that set?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#200 2013-07-20 22:43:27

Herc11
Member
Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

All the variables known and unknown will be elements of a Galois Field. Multiplication Division, addition(=substraction) will be defined over the GF. The result of the operations will be GFs too. They are not integers but elements of the GF. I mean that alla the problem will be defined and solved over the GF.

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