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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
Last edited by Herc11 (2013-06-21 08:34:00)
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Unless you eliminate the a0, a1 and a2 you will have more than 6 variables. You will have 9 variables. This means 9 cubics.
Fortunately I have a way around that.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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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
Last edited by Herc11 (2013-06-21 08:43:29)
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Aren't the a0, a1, a2, a3 the coefficients of the cubic?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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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=...
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Hi;
Yes, I see that. I am agreeing with you. They are replaced as you did in post #146, so did I. Eventually all of them are replaced and just the 6 variables we want remain.
I did not understand you were saying the same thing I was.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Ok:)
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Hi;
I am currently busy answering a question. I will need some sleep right after. I will work out the problem I posed and get the solution as soon as I wake up. I am really beat.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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ok ok.
I think that anonimnystefy can solve it as he solved the quadratics...
Last edited by Herc11 (2013-06-21 09:17:08)
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He is sleeping by now, I think. I need some rest. see you later and thanks for the problems.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Thans both of you!
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By the way are you students or college students?
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Hi guys
I haven't had time to post here. Have you got the interpolation thing to work?
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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Hi anonimnystefy,
See the posts #133,135 and 146,147.
The aim is to solve a set of 6 equations of a_3 with the information provided in post 133 and 135.
I thinh that you can with mathematica.
You have 6 equations, with 6 unknown variables. I cant see why this is not sovlable.
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Hi;
I have solved the problem given above using just 6 equations.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Thats nice!
So I think one can say that If you have n intesection points, and someone provides you with the lead coeficient and a point of 2n polynomials you can define the intersection point.
Scool student?
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Hi;
Yes, I would say so but the actually calculation becomes more and more difficult as n increases.
I am not a student.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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What do you mean "difficult"?
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Numerical difficulties. Although A,B and C in my problem are integers the equations have enough instability in them to run off to the complex plane. Already Geogebra cannot create the points accurately enough and it has 16 digits of precision.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Ok, if the operations were over a galois field will have any difference?
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You mean a set consisting of {1,2,3,4,...p} where p is primes? If so, that is what I did.
You noticed the ai's I provided for the problem? They are floating point numbers. Geogebra lost 4 digits in computing them. That suggests a condition number for the problem of around 10000.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Something like that...
The problem is that when you work over Finite fields,
addition multiplication and division are not equal to standard operations. operations are executed modulo the prime number etc..etc..
Last edited by Herc11 (2013-06-21 20:06:32)
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Yes, I know my grasp of theory is horrendous.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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I am familiar with Galois Fields and the operations executed over GFs but it is not ot easy to explain...
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A small thing to improve performance of solving that would be to have the coefficient of the constant term rather than the leading coefficient.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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