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In follow-up work on <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\text {GL}}_\\infty $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mtext>GL<\/mml:mtext>\n                    <mml:mi>\u221e<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-varieties, Bik\u2013Draisma\u2013Eggermont\u2013Snowden showed, among other things, that in characteristic zero every such closed subset is the image of a morphism whose domain is the product of a finite-dimensional affine variety and a polynomial functor. In this paper, we show that both results can be made algorithmic: there exists an algorithm <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textbf{implicitise}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>implicitise<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that takes as input a morphism into a polynomial functor and outputs finitely many equations defining the closure of the image; and an algorithm <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textbf{parameterise}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>parameterise<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that takes as input a finite set of equations defining a closed subset of a polynomial functor and outputs a morphism whose image is that closed subset.<\/jats:p>","DOI":"10.1007\/s10208-023-09619-6","type":"journal-article","created":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T17:06:01Z","timestamp":1693242361000},"page":"1567-1593","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implicitisation and Parameterisation in Polynomial Functors"],"prefix":"10.1007","volume":"24","author":[{"given":"Andreas","family":"Blatter","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Draisma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emanuele","family":"Ventura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"9619_CR1","unstructured":"Arthur Bik. 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