i9 : describe Eta!
o9 = multi-rational map consisting of 3 rational maps
source variety: threefold in PP^3 x PP^2 x PP^2 x PP^3 cut out by 17 hypersurfaces of degrees ({1, 0, 0, 1},{0, 0, 1, 1},{0, 1, 0, 1},{1, 0, 0, 1},{1, 0, 0, 1},{0, 0, 1, 1},{0, 1, 0, 1},{1, 0, 0, 1},{1, 0, 0, 1},{1, 0, 0, 1},{0, 1, 1, 0},{0, 1, 1, 0},{0, 1, 1, 0},{1, 0, 1, 0},{1, 0, 1, 0},{1, 1, 0, 0},{1, 1, 0, 0})
target variety: threefold in PP^3 x PP^2 x PP^2 cut out by 7 hypersurfaces of degrees ({0, 1, 1},{0, 1, 1},{0, 1, 1},{1, 0, 1},{1, 0, 1},{1, 1, 0},{1, 1, 0})
base locus: empty subscheme of PP^3 x PP^2 x PP^2 x PP^3
dominance: true
birationality: true
--
rational map (1/3) defined by multiforms of degree {0, 0, 0, 1}
target variety: PP^3
dominance: true
birationality: true
projective degrees: {80, 24, 6, 1}
number of minimal representatives: 2, with degrees ({0, 0, 0, 1},{1, 0, 0, 0})
dimension base locus: -1
--
rational map (2/3) defined by multiforms of degree {0, 0, 1, 0}
target variety: PP^2
dominance: true
birationality: false
degree of map: 0
projective degrees: {80, 16, 2, 0}
number of minimal representatives: 5, with degrees ({0, 0, 1, 0},{0, 1, 0, 0},{0, 0, 0, 2},{1, 0, 0, 1},{2, 0, 0, 0})
dimension base locus: -1
--
rational map (3/3) defined by multiforms of degree {0, 0, 1, 0}
target variety: PP^2
dominance: true
birationality: false
degree of map: 0
projective degrees: {80, 16, 2, 0}
number of minimal representatives: 5, with degrees ({0, 0, 1, 0},{0, 1, 0, 0},{0, 0, 0, 2},{1, 0, 0, 1},{2, 0, 0, 0})
dimension base locus: -1
--
coefficient ring: ZZ/33331
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i10 : describe (inverse Eta)!
o10 = multi-rational map consisting of 4 rational maps
source variety: threefold in PP^3 x PP^2 x PP^2 cut out by 7 hypersurfaces of degrees ({0, 1, 1},{0, 1, 1},{0, 1, 1},{1, 0, 1},{1, 0, 1},{1, 1, 0},{1, 1, 0})
target variety: threefold in PP^3 x PP^2 x PP^2 x PP^3 cut out by 17 hypersurfaces of degrees ({1, 0, 0, 1},{0, 0, 1, 1},{0, 1, 0, 1},{1, 0, 0, 1},{1, 0, 0, 1},{0, 0, 1, 1},{0, 1, 0, 1},{1, 0, 0, 1},{1, 0, 0, 1},{1, 0, 0, 1},{0, 1, 1, 0},{0, 1, 1, 0},{0, 1, 1, 0},{1, 0, 1, 0},{1, 0, 1, 0},{1, 1, 0, 0},{1, 1, 0, 0})
base locus: empty subscheme of PP^3 x PP^2 x PP^2
dominance: true
birationality: true
--
rational map (1/4) defined by multiforms of degree {1, 0, 0}
target variety: PP^3
dominance: true
birationality: true
projective degrees: {25, 13, 5, 1}
number of minimal representatives: 1
dimension base locus: -1
--
rational map (2/4) defined by multiforms of degree {0, 0, 1}
target variety: PP^2
dominance: true
birationality: false
degree of map: 0
projective degrees: {25, 6, 1, 0}
number of minimal representatives: 3, with degrees ({0, 0, 1},{0, 1, 0},{2, 0, 0})
dimension base locus: -1
--
rational map (3/4) defined by multiforms of degree {0, 0, 1}
target variety: PP^2
dominance: true
birationality: false
degree of map: 0
projective degrees: {25, 6, 1, 0}
number of minimal representatives: 3, with degrees ({0, 0, 1},{0, 1, 0},{2, 0, 0})
dimension base locus: -1
--
rational map (4/4) defined by multiforms of degree {1, 0, 0}
target variety: PP^3
dominance: true
birationality: true
projective degrees: {25, 13, 5, 1}
number of minimal representatives: 1
dimension base locus: -1
--
coefficient ring: ZZ/33331
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