This is an auxiliary method to build tests and examples. For instance, the two following codes have to produce the same polynomial up to a renaming of variables: 1) resultant genericPolynomials((n+1):d,K) and 2) fromPluckerToStiefel dualize chowForm veronese(n,d,K).
i1 : veronese(1,4)
4 3 2 2 3 4
o1 = map(QQ[t , t ],QQ[x , x , x , x , x ],{t , t t , t t , t t , t })
0 1 0 1 2 3 4 0 0 1 0 1 0 1 1
o1 : RingMap QQ[t , t ] <--- QQ[x , x , x , x , x ]
0 1 0 1 2 3 4
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i2 : veronese(1,4,Variable=>y)
4 3 2 2 3 4
o2 = map(QQ[y , y ],QQ[y , y , y , y , y ],{y , y y , y y , y y , y })
0 1 0 1 2 3 4 0 0 1 0 1 0 1 1
o2 : RingMap QQ[y , y ] <--- QQ[y , y , y , y , y ]
0 1 0 1 2 3 4
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i3 : veronese(1,4,Variable=>(u,z))
4 3 2 2 3 4
o3 = map(QQ[u , u ],QQ[z , z , z , z , z ],{u , u u , u u , u u , u })
0 1 0 1 2 3 4 0 0 1 0 1 0 1 1
o3 : RingMap QQ[u , u ] <--- QQ[z , z , z , z , z ]
0 1 0 1 2 3 4
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i4 : veronese(2,2,ZZ/101)
ZZ ZZ 2 2 2
o4 = map(---[t , t , t ],---[x , x , x , x , x , x ],{t , t t , t t , t , t t , t })
101 0 1 2 101 0 1 2 3 4 5 0 0 1 0 2 1 1 2 2
ZZ ZZ
o4 : RingMap ---[t , t , t ] <--- ---[x , x , x , x , x , x ]
101 0 1 2 101 0 1 2 3 4 5
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