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Symbolic computation of of multiples of a point in elliptic curve.

Suppose we have an elliptic curve over the rational field E(Q). Let P=(s,t)E(Q) be a point with s,t being symbolic variables. Then we see that nP=(fn1/gn1,fn2/gn2), where fni,gni are polynomials in the variables s,t. In SageMath after defining the curve and the symbolic variables s and t if I write P=E(s,t), it is giving error. I am looking for method by which I can find all these polynomials in the variabls s,t using SageMath.

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updated 3 years ago

FrédéricC gravatar image

Symbolic computation of of multiples of a point in elliptic curve.

Suppose we have an elliptic curve over the rational field E(Q). Let P=(s,t)E(Q) be a point with s,t being symbolic variables. Then we see that nP=(fn1/gn1,fn2/gn2), where fni,gni are polynomials in the variables s,t. In SageMath after defining the curve and the symbolic variables s and t if I write P=E(s,t), it is giving error. I am looking for method by which I can find all these polynomials in the variabls s,t using SageMath.

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updated 3 years ago

FrédéricC gravatar image

Symbolic computation of of multiples of a point in elliptic curve.

Suppose we have an elliptic curve over the rational field E(Q). Let P=(s,t)E(Q) be a point with s,t being symbolic variables. Then we see that nP=(fn1/gn1,fn2/gn2), where fni,gni are polynomials in the variables s,t. In SageMath after defining the curve and the symbolic variables s and t if I write P=E(s,t), it is giving error. I am looking for method by which I can find all these polynomials in the variabls s,t using SageMath.