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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 $E(\mathbb{Q}).$ Let $P = (s,t)\in E(\mathbb{Q})$ be a point with $s,t$ being symbolic variables. Then we see that $n*P = (f_{n1}/g_{n1}, f_{n2}/g_{n2})$, where $f_{ni}, g_{ni}$ 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.

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

Suppose we have an elliptic curve over the rational field $E(\mathbb{Q}).$ Let $P = (s,t)\in E(\mathbb{Q})$ be a point with $s,t$ being symbolic variables. Then we see that $n*P = (f_{n1}/g_{n1}, f_{n2}/g_{n2})$, where $f_{ni}, g_{ni}$ 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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Symbolic computation of of multiples of a point in elliptic curve.

Suppose we have an elliptic curve over the rational field $E(\mathbb{Q}).$ Let $P = (s,t)\in E(\mathbb{Q})$ be a point with $s,t$ being symbolic variables. Then we see that $n*P = (f_{n1}/g_{n1}, f_{n2}/g_{n2})$, where $f_{ni}, g_{ni}$ 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.