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#101 2013-06-20 18:20:24

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

Re: Define the intersection points of polynomials

Maybe it is easier  to understand what I was saying...

I was saying that in Eq. of post 98 there are 4 unknowns i.e. x0...y1.

If I knew 3 more eq. like post #98, I think that the problem has a solution and the intersection points can be spotted.

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#102 2013-06-20 18:23:30

Herc11
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Registered: 2013-06-19
Posts: 169

Re: Define the intersection points of polynomials

So, you think that for quadratics you can determine the intersection point  If you know the leading coef of 4 quads and one point from each of them.

Now I am wondering, If I did not know the lead coef. and I had 8 quad. could I find again the intersection points?

I am confused.

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#103 2013-06-20 18:25:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Define the intersection points of polynomials

Herc11 wrote:

24??? Can you explain please?

When I count the unknowns, I count only the missing intersection points.

It is considered that the cubics intercept at 3 points. Each intersction point has two coordinates which are unknown i.e six unknowns.

From each cubic I know one point and its leading coefficient. (****Now I am confused and I m starting thinking that I dont even need

the lead. coef.)

So, in order to find the 6 unkowns I need 6 cubics and the respective lead. coefs and one point from each cubic.

*** It is possible if I do not know the leading coefficient to finde the interscetion points only by using more cubics??

I am confused...

How easy or not is to specify the n-1 intersection points of all the degree n polynomials which pass from the intersection points?

The coordinates of intersection points aren't the only unknowns. What about the 2nd, the 3rd and the 4th coefficients of each polynomial?


“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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#104 2013-06-20 18:25:46

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

I am still working with your divided difference - Newton formula.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#105 2013-06-20 18:30:52

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

Re: Define the intersection points of polynomials

If I use the Eq. of post #98 or 99,

only the intersection points are the unknowns?

Last edited by Herc11 (2013-06-20 18:31:35)

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#106 2013-06-20 18:32:09

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

Formula in post #98 checks out.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#107 2013-06-20 18:33:41

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

Re: Define the intersection points of polynomials

bobbym,
What do you mean exactly?

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#108 2013-06-20 18:37:22

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

I just found the intersection points of a new problem using it and it worked fine. You wrote that you were worried you made a mistake in writing it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#109 2013-06-20 18:40:41

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

Re: Define the intersection points of polynomials

Ok.
So, from 4 quads that the only known info is a point of each of them and their leading coefficient we can find their intersection points?
Is that right?

I am  thinking that the same will stand for cubics but we will need 6 cubics to solve the previous problem.

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#110 2013-06-20 18:48:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

Hold on please we have the time to go slow. I am having trouble with post #99's formula. Please check it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#111 2013-06-20 18:57:37

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

Re: Define the intersection points of polynomials

bobbym, I think that i correct it #99. At Π i-1 and not i...I think

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#112 2013-06-20 19:06:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

That was not the problem. The denominator is always 0. The upper limit on the product can not be k.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#113 2013-06-20 19:31:36

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

Re: Define the intersection points of polynomials

Ok. I correct the denom..

Hi anonimnystefy,
Did you see my post #105?

Last edited by Herc11 (2013-06-20 19:33:00)

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#114 2013-06-20 19:47:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Define the intersection points of polynomials

Hm, I am not sure. maybe it could work. I am not sure at all, now.


“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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#115 2013-06-20 19:48:50

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

Re: Define the intersection points of polynomials

When you solved the problem of bobbym what Equations did you use?

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#116 2013-06-20 19:54:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Define the intersection points of polynomials

I used a set of 12 equations. Each one was basically each point's coordinates inserted into the appropriate polynomial.


“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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#117 2013-06-20 19:56:43

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

Re: Define the intersection points of polynomials

12? you had only the lead coefficient, and a point..

It would be helpful if you could post the algorithm.

Last edited by Herc11 (2013-06-20 20:16:07)

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#118 2013-06-20 21:27:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

Only 4 equations for my problem are necessary.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#119 2013-06-20 21:29:56

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

Re: Define the intersection points of polynomials

Ok. That is what I am thinking too. Did you find the solution?

We can suppose that for a cubic 6 equations are demanded?

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#120 2013-06-20 21:33:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

The formula in post #99 is now working.

We can suppose that for a cubic 6 equations are demanded?

To test that would require a model problem. I do not have one yet.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#121 2013-06-20 21:40:40

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

Re: Define the intersection points of polynomials

But it seems that at the formula #, when a3, there will be six unknown variables x0y0...x2y2. There fore, 6 equations will be needed

so 6 cubics plus their leading coefficient and one point of each...

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#122 2013-06-20 21:44:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

It seems that is correct but a test always helps.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#123 2013-06-20 21:50:27

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

Re: Define the intersection points of polynomials

Yes.
Thats the only fact!:)

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#124 2013-06-20 21:51:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,607

Re: Define the intersection points of polynomials

If we have cubics there is another difference.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#125 2013-06-20 21:57:14

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

Re: Define the intersection points of polynomials

what difference?

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