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Let $\cal C$ be a space curve defined as the common zeros of $n-1$ polynomials. Assuming that $\cal C$ admits a rational parametrisation, there is an algorithm generating a point on the curve through algebraic operations, given a value $\tau$ on the base field. This mapping covers all the curve apart from a finite number of points. The input of the algorithm is given by the polynomials defining $\cal C$ and the parameter $\tau$.

What is the minimal number of required algebraic operations in terms of $n$ and the degree of the polynomials? Let me assume that this number does not depend on $\tau$.

Let $\cal C$ be a space curve defined as the common zeros of $n-1$ polynomials. Assuming that $\cal C$ admits a rational parametrisation, there is an algorithm generating a point on the curve through algebraic operations, given a value $\tau$ on the base field. This mapping covers all the curve apart from a finite number of points. The input of the algorithm is given by the polynomials defining $\cal C$ and the parameter $\tau$. Let me also assume that one point of $\cal C$ is known.

What is the minimal number of required algebraic operations in terms of $n$ and the degree of the polynomials? Let me assume that this number does not depend on $\tau$.

Let $\cal C$ be a space curve defined as the common zeros of $n-1$ polynomials. If $\cal C$ admits a rational parametrisation, then there is an algorithm generating a point on the curve through algebraic operations, given a value $\tau$ on the base field. This mapping covers all the curve apart from a finite number of points. The input of the algorithm is given by the polynomials defining $\cal C$ and the parameter $\tau$.

What is the minimal number of required algebraic operations in terms of $n$ and the degree of the polynomials? Let me assume that this number does not depend on $\tau$.

Let $\cal C$ be a space curve defined as the common zeros of $n-1$ polynomials. Assuming that $\cal C$ admits a rational parametrisation, there is an algorithm generating a point on the curve through algebraic operations, given a value $\tau$ on the base field. This mapping covers all the curve apart from a finite number of points. The input of the algorithm is given by the polynomials defining $\cal C$ and the parameter $\tau$.

What is the minimal number of required algebraic operations in terms of $n$ and the degree of the polynomials? Let me assume that this number does not depend on $\tau$.

Let $\cal C$ be a space curve defined as the common zeros of $n-1$ polynomials. If $\cal C$ admits a rational parametrisation, then there is an algorithm generating a point on the curve through algebraic operations, given a value $\tau$ on the base field. This mapping covers all the curve apart from a finite number of points. The input of the algorithm is given by the polynomials and the parameter $\tau$.

What is the minimal number of required algebraic operations in terms of $n$ and the degree of the polynomials? Let me assume that this number does not depend on $\tau$.

Let $\cal C$ be a space curve defined as the common zeros of $n-1$ polynomials. If $\cal C$ admits a rational parametrisation, then there is an algorithm generating a point on the curve through algebraic operations, given a value $\tau$ on the base field. This mapping covers all the curve apart from a finite number of points. The input of the algorithm is given by the polynomials defining $\cal C$ and the parameter $\tau$.

What is the minimal number of required algebraic operations in terms of $n$ and the degree of the polynomials? Let me assume that this number does not depend on $\tau$.