i1 : X = coincidentRootLocus {3,2,2}
o1 = CRL(3,2,2)
o1 : Coincident root locus
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i2 : f = map X
o2 = -- rational map --
source: Proj(QQ[t0 , t0 ]) x Proj(QQ[t1 , t1 ]) x Proj(QQ[t2 , t2 ])
0 1 0 1 0 1
target: Proj(QQ[t , t , t , t , t , t , t , t ])
0 1 2 3 4 5 6 7
defining forms: {
3 2 2
t0 t1 t2 ,
0 0 0
2 3 2 2 3 2 3 2 2 2
-t0 t1 t2 t2 + -t0 t1 t1 t2 + -t0 t0 t1 t2 ,
7 0 0 0 1 7 0 0 1 0 7 0 1 0 0
1 3 2 2 4 3 1 3 2 2 2 2 2 2 2 2 1 2 2 2
--t0 t1 t2 + --t0 t1 t1 t2 t2 + --t0 t1 t2 + -t0 t0 t1 t2 t2 + -t0 t0 t1 t1 t2 + -t0 t0 t1 t2 ,
21 0 0 1 21 0 0 1 0 1 21 0 1 0 7 0 1 0 0 1 7 0 1 0 1 0 7 0 1 0 0
2 3 2 2 3 2 3 2 2 2 12 2 3 2 2 2 6 2 2 6 2 2 1 3 2 2
--t0 t1 t1 t2 + --t0 t1 t2 t2 + --t0 t0 t1 t2 + --t0 t0 t1 t1 t2 t2 + --t0 t0 t1 t2 + --t0 t0 t1 t2 t2 + --t0 t0 t1 t1 t2 + --t0 t1 t2 ,
35 0 0 1 1 35 0 1 0 1 35 0 1 0 1 35 0 1 0 1 0 1 35 0 1 1 0 35 0 1 0 0 1 35 0 1 0 1 0 35 1 0 0
1 3 2 2 6 2 2 6 2 2 3 2 2 2 12 2 3 2 2 2 2 3 2 2 3 2
--t0 t1 t2 + --t0 t0 t1 t1 t2 + --t0 t0 t1 t2 t2 + --t0 t0 t1 t2 + --t0 t0 t1 t1 t2 t2 + --t0 t0 t1 t2 + --t0 t1 t2 t2 + --t0 t1 t1 t2 ,
35 0 1 1 35 0 1 0 1 1 35 0 1 1 0 1 35 0 1 0 1 35 0 1 0 1 0 1 35 0 1 1 0 35 1 0 0 1 35 1 0 1 0
1 2 2 2 2 2 2 2 2 2 1 3 2 2 4 3 1 3 2 2
-t0 t0 t1 t2 + -t0 t0 t1 t1 t2 + -t0 t0 t1 t2 t2 + --t0 t1 t2 + --t0 t1 t1 t2 t2 + --t0 t1 t2 ,
7 0 1 1 1 7 0 1 0 1 1 7 0 1 1 0 1 21 1 0 1 21 1 0 1 0 1 21 1 1 0
3 2 2 2 2 3 2 2 3 2
-t0 t0 t1 t2 + -t0 t1 t1 t2 + -t0 t1 t2 t2 ,
7 0 1 1 1 7 1 0 1 1 7 1 1 0 1
3 2 2
t0 t1 t2
1 1 1
}
o2 : MultihomogeneousRationalMap (rational map from PP^1 x PP^1 x PP^1 to PP^7)
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i3 : describe f
o3 = rational map defined by multiforms of degree {3, 2, 2}
source variety: PP^1 x PP^1 x PP^1
target variety: PP^7
image: 3-dimensional variety of degree 36 in PP^7 cut out by 364 hypersurfaces of degree 6
dominance: false
birationality: false
coefficient ring: QQ
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