permute(MultiprojectiveVariety,List) -- permute the factors of the ambient multi-projective space

Synopsis

Function: permute
Usage:

permute(X,s)
Inputs:
- X, a multi-projective variety, a subvariety of $\mathbb{P}^{k_0}\times\mathbb{P}^{k_1}\times\cdots\times\mathbb{P}^{k_{n}}$
- s, a list, a permutation of the set $\{0,1,\ldots,n\}$
Outputs:
- a multi-rational map, an isomorphism from $X$ to a subvariety of $\mathbb{P}^{k_{s(0)}}\times\mathbb{P}^{k_{s(1)}}\times\cdots\times\mathbb{P}^{k_{s(n)}}$

i1 : X = PP_(ZZ/33331)^{2,3,1};

o1 : ProjectiveVariety, PP^2 x PP^3 x PP^1

i2 : f = permute(X,{1,0,2});

o2 : MultirationalMap (rational map from X to PP^3 x PP^2 x PP^1)

i3 : assert isIsomorphism f

i4 : Y = random({0,1,1},0_X);

o4 : ProjectiveVariety, hypersurface in PP^2 x PP^3 x PP^1

i5 : g = permute(Y,{2,0,1});

o5 : MultirationalMap (rational map from Y to hypersurface in PP^1 x PP^2 x PP^3)

i6 : assert isIsomorphism g