$N$ random points make a random polynomial?
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Let's say I have a finite field $A$, and I choose $N$ (distinct) points uniformly at random from $A times A$. Then using Lagrange interpolation I can find a polynomial $f(x)$ of degree $N-1$ that goes through all my points. Is $f$ a random polynomial? That is, are its coefficients also uniform at random?
polynomials finite-fields lagrange-interpolation
asked Nov 14 at 20:58
eternalmothra
83
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Let's say I have a finite field $A$, and I choose $N$ (distinct) points uniformly at random from $A times A$. Then using Lagrange interpolation I can find a polynomial $f(x)$ of degree $N-1$ that goes through all my points. Is $f$ a random polynomial? That is, are its coefficients also uniform at random?
polynomials finite-fields lagrange-interpolation
asked Nov 14 at 20:58
eternalmothra
83
Is $f$ a function from $A$ to $A$?
– Paul
Nov 14 at 22:35
Yes. That should be so because I said I was picking points from $A times A$, right?
– eternalmothra
Nov 15 at 2:41
Yeah I thought so, but when picking random points, you could pick two points with the same $x$ and a different $y$. I guess you want to exclude those situations, but that should be made clear.
– Paul
Nov 15 at 12:25
Is it possible to ask you to tell about background of your question. Thanks.
– user0410
Nov 19 at 21:57
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let's say I have a finite field $A$, and I choose $N$ (distinct) points uniformly at random from $A times A$. Then using Lagrange interpolation I can find a polynomial $f(x)$ of degree $N-1$ that goes through all my points. Is $f$ a random polynomial? That is, are its coefficients also uniform at random?
polynomials finite-fields lagrange-interpolation
asked Nov 14 at 20:58
eternalmothra
83
Let's say I have a finite field $A$, and I choose $N$ (distinct) points uniformly at random from $A times A$. Then using Lagrange interpolation I can find a polynomial $f(x)$ of degree $N-1$ that goes through all my points. Is $f$ a random polynomial? That is, are its coefficients also uniform at random?
polynomials finite-fields lagrange-interpolation
polynomials finite-fields lagrange-interpolation
asked Nov 14 at 20:58
eternalmothra
83
asked Nov 14 at 20:58
eternalmothra
83
asked Nov 14 at 20:58
eternalmothra
83
asked Nov 14 at 20:58
eternalmothra
83
asked Nov 14 at 20:58
eternalmothra
83
83
Is $f$ a function from $A$ to $A$?
– Paul
Nov 14 at 22:35
Yes. That should be so because I said I was picking points from $A times A$, right?
– eternalmothra
Nov 15 at 2:41
Yeah I thought so, but when picking random points, you could pick two points with the same $x$ and a different $y$. I guess you want to exclude those situations, but that should be made clear.
– Paul
Nov 15 at 12:25
Is it possible to ask you to tell about background of your question. Thanks.
– user0410
Nov 19 at 21:57
add a comment |
Is $f$ a function from $A$ to $A$?
– Paul
Nov 14 at 22:35
Yes. That should be so because I said I was picking points from $A times A$, right?
– eternalmothra
Nov 15 at 2:41
Yeah I thought so, but when picking random points, you could pick two points with the same $x$ and a different $y$. I guess you want to exclude those situations, but that should be made clear.
– Paul
Nov 15 at 12:25
Is it possible to ask you to tell about background of your question. Thanks.
– user0410
Nov 19 at 21:57
Is $f$ a function from $A$ to $A$?
– Paul
Nov 14 at 22:35
Is $f$ a function from $A$ to $A$?
– Paul
Nov 14 at 22:35
Yes. That should be so because I said I was picking points from $A times A$, right?
– eternalmothra
Nov 15 at 2:41
Yes. That should be so because I said I was picking points from $A times A$, right?
– eternalmothra
Nov 15 at 2:41
Yeah I thought so, but when picking random points, you could pick two points with the same $x$ and a different $y$. I guess you want to exclude those situations, but that should be made clear.
– Paul
Nov 15 at 12:25
Yeah I thought so, but when picking random points, you could pick two points with the same $x$ and a different $y$. I guess you want to exclude those situations, but that should be made clear.
– Paul
Nov 15 at 12:25
Is it possible to ask you to tell about background of your question. Thanks.
– user0410
Nov 19 at 21:57
Is it possible to ask you to tell about background of your question. Thanks.
– user0410
Nov 19 at 21:57
add a comment |
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Is $f$ a function from $A$ to $A$?
– Paul
Nov 14 at 22:35
Yes. That should be so because I said I was picking points from $A times A$, right?
– eternalmothra
Nov 15 at 2:41
Yeah I thought so, but when picking random points, you could pick two points with the same $x$ and a different $y$. I guess you want to exclude those situations, but that should be made clear.
– Paul
Nov 15 at 12:25
Is it possible to ask you to tell about background of your question. Thanks.
– user0410
Nov 19 at 21:57