Division polynomials just a function of x ! [closed]

asked 2016-09-11 01:13:41 -0500

vishb gravatar image

I evaluated Divison polynomials using

R.<A,B>=PolynomialRing(ZZ)
E = EllipticCurve([A,B])
g = E.division_polynomial(k)

The results i noticed were just function of $x$ , In theory i saw that division polynomials for k even depends on y. In there something I am unable to notice.

For example : E.division_polynomial(k) returned 4*x^3 + 4*A*x + 4*B but theory says it is 2y. From this one can get a intuition that may be we are squaring them.

But E.division_polynomial(8) returned a degree $33$ polynomial which means that clearly we are not squaring things.

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Closed for the following reason question is not relevant or outdated by vishb
close date 2016-09-11 04:55:37.204704

Comments

Are we replacing $y$ by $x^2+ax+b$ everywhere ?

vishb gravatar imagevishb ( 2016-09-11 01:25:52 -0500 )edit
1

Could you just read the documentation: E.division_polynomial?

FrédéricC gravatar imageFrédéricC ( 2016-09-11 03:35:37 -0500 )edit