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 ], {t , t t , t t , t t , t })
0 1 0 4 0 0 1 0 1 0 1 1
o1 : RingMap QQ[t ..t ] <-- QQ[x ..x ]
0 1 0 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 })
0 1 0 4 0 0 1 0 1 0 1 1
o2 : RingMap QQ[y ..y ] <-- QQ[y ..y ]
0 1 0 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 ], {u , u u , u u , u u , u })
0 1 0 4 0 0 1 0 1 0 1 1
o3 : RingMap QQ[u ..u ] <-- QQ[z ..z ]
0 1 0 4
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i4 : veronese(2,2,ZZ/101)
ZZ ZZ 2 2 2
o4 = map (---[t ..t ], ---[x ..x ], {t , t t , t t , t , t t , t })
101 0 2 101 0 5 0 0 1 0 2 1 1 2 2
ZZ ZZ
o4 : RingMap ---[t ..t ] <-- ---[x ..x ]
101 0 2 101 0 5
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