Some special GM fourfolds are known to be rational. In this case, the function tries to obtain a birational map from $\mathbb{P}^4$ (or, e.g., from a quadric hypersurface in $\mathbb{P}^5$) to the fourfold.
i1 : X = specialGushelMukaiFourfold "tau-quadric";
o1 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0
i2 : time phi = parametrize X;
-- used 0.147833 seconds
o2 : MultirationalMap (birational map from PP^4 to X)
i3 : time describe phi
-- used 0.9553 seconds
o3 = multi-rational map consisting of one single rational map
source variety: PP^4
target variety: 4-dimensional subvariety of PP^8 cut out by 6 hypersurfaces of degree 2
base locus: surface in PP^4 cut out by 5 hypersurfaces of degrees 3^1 4^4
dominance: true
multidegree: {1, 4, 8, 10, 10}
degree: 1
degree sequence (map 1/1): [4]
coefficient ring: ZZ/65521