The map from monic complex polynomials to the unordered tuples of their roots (each appearing according to its multiplicity) is computable. This seems to have been known for a long time, and with modern technology is quick and easy to prove.

What I am interested in is whether there is a canonical reference for this (and if so, whom to credit).

The weaker observation that if the coefficients are computable numbers, then the roots are computable numbers, too, doesn't count here. The uniformity is important.

There is a paper from 2002 proving the result I mentioned (Lester, Chambers, and Lu - A constructive algorithm for finding the exact roots of polynomials with computable real coefficients), but there are older references to the result being well-known. In fact, I vaguely remember having read a pre-LaTeX paper containing a proof — unfortunately, I don't remember where I may have come across it. Weihrauch's Computable Analysis on the other hand does not seem to mention the result.

The map from monic complex polynomials to the unordered tuples of their roots (each appearing according to its multiplicity) is computable. This seems to have been known for a long time, and with modern technology is quick and easy to prove.

What I am interested in is whether there is a canonical reference for this (and if so, whom to credit).

The weaker observation that if the coefficients are computable numbers, then the roots are computable numbers, too, doesn't count here. The uniformity is important.

There is a paper from 2002 proving the result I mentioned (Lester, Chambers, and Lu - A constructive algorithm for finding the exact roots of polynomials with computable real coefficients), but there are older references to the result being well-known. In fact, I vaguely remember having read a pre-LaTeX paper containing a proof — unfortunately, I don't remember where I may have come across it. Weihrauch's Computable Analysis has this as Exercise 6.3.11.

The map from monic complex polynomials to the unordered tuples of their roots (each appearing according to its multiplicty) is computable. This seems to have been known for a long time, and with modern technology is quick and easy to prove.

What I am interested in is whether there is canonic reference for this (and if so, who to credit).

The weaker observation that if the coefficients are computable numbers, then the roots are computable numbers, too, doesn't count here. The uniformity is important.

There is a paper from 2002 proving the result I mentioned (https://doi.org/10.1016/S0304-3975(00)00426-6), but there are older references to the result being well-known. In fact, I vaguely remember having read a pre-LaTeX paper containing a proof - unfortunately, I don't remember where I may have come across it. Weihrauch's Computable Analysis on the other hand does not seem to mention the result.

The map from monic complex polynomials to the unordered tuples of their roots (each appearing according to its multiplicity) is computable. This seems to have been known for a long time, and with modern technology is quick and easy to prove.

What I am interested in is whether there is a canonical reference for this (and if so, whom to credit).

The weaker observation that if the coefficients are computable numbers, then the roots are computable numbers, too, doesn't count here. The uniformity is important.

There is a paper from 2002 proving the result I mentioned (Lester, Chambers, and Lu - A constructive algorithm for finding the exact roots of polynomials with computable real coefficients), but there are older references to the result being well-known. In fact, I vaguely remember having read a pre-LaTeX paper containing a proof — unfortunately, I don't remember where I may have come across it. Weihrauch's Computable Analysis on the other hand does not seem to mention the result.