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#101 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 09:10:19

ok ok.

I think that anonimnystefy can solve it as he solved the quadratics...

#103 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 08:46:48

Yes they are coeffients.

But see equation in #146.

Then suppose you have 6 equations like #146.

You know a3 y3 x3, and you dont know x0x1x2 y0y1y2.

By a set of 6 equations isn t the set of equations solvable?

Our aim is to define the intersection points i.e.  x0x1x2 y0y1y2.

Once you solve the set of the 6 equations you will have discovered the  x0x1x2 y0y1y2.

If you d like you can then define a0=y0 a1=... and  a2=...

#104 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 08:35:38

Why to eliminate?

Simply substitute the a0 a1 and a2 with x0-y2.

See post #146.

Dont use a0..etc if it confuses you...

You have only to solve for x0..y2.

And six equations like that in #146 are enough

#105 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 08:31:23

I think it has not to do with interpolation. See in #146 post

the formula for computing a_3

if the unknowns are x0 y0 x1 y1 x2 y2

and known the x3 y3 and a3

I think that by having a set of 6 equations you can define x0-y2.

Also, bobbym

posted another one problem

#106 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 08:21:41

What do you mean?

It is the same thing. You have only to solve the set of equations of a3. \

Afterwards, you know the x0-y3. If you wish you can compute a0-a2, but there is no need.

Of course you can substitute. Either you solve for a0 to a2 or for x0-y3 its the same.

#107 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 08:06:38

So, if you now look a_3 you have six unknows. Using 6 cubics I think can leed to a soultion.

#108 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 07:58:44

Yes


So you have only to replace the coefficients with the are equals

#110 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 06:46:33

I think that it will be solved as you have 6 equations and 6 unknowns..x0---y3

#111 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 06:35:40

Yes I think what you write in #139 is correct.

#115 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-21 00:29:34

Ok, and for solving the system you use Mathematica or the afore mentioned tool?

#116 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 23:24:33

How do you construct the polynomials?

MAthematica? I am not familiar with it..

#118 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 22:02:54

Yes. this is true. So the unknown variables will be six (the 3 intersection points)
So we need 6 cubics etc etc....

#121 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 21:40:40

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...

#122 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 21:29:56

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

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

#123 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 19:56:43

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

It would be helpful if you could post the algorithm.

#124 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 19:48:50

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

#125 Re: Help Me ! » Define the intersection points of polynomials » 2013-06-20 19:31:36

Ok. I correct the denom..

Hi anonimnystefy,
Did you see my post #105?

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