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 : genericPolynomials {1,2,3}
2 2 2 3 2 2 3 2
o1 = {a x + a x + a x , b x + b x x + b x + b x x + b x x + b x , c x + c x x + c x x + c x + c x x + c x x x +
0 0 1 1 2 2 0 0 1 0 1 3 1 2 0 2 4 1 2 5 2 0 0 1 0 1 3 0 1 6 1 2 0 2 4 0 1 2
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2 2 2 3
c x x + c x x + c x x + c x }
7 1 2 5 0 2 8 1 2 9 2
o1 : List
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i2 : first genericPolynomials({4,2,3},ZZ/101)
4 3 2 2 3 4 3 2 2 3 2 2 2 2 2 3
o2 = a x + a x x + a x x + a x x + a x + a x x + a x x x + a x x x + a x x + a x x + a x x x + a x x + a x x +
0 0 1 0 1 3 0 1 6 0 1 10 1 2 0 2 4 0 1 2 7 0 1 2 11 1 2 5 0 2 8 0 1 2 12 1 2 9 0 2
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3 4
a x x + a x
13 1 2 14 2
ZZ
o2 : ---[a ..a , b ..b , c ..c ][x ..x ]
101 0 14 0 5 0 9 0 2
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i3 : first genericPolynomials({4,-1,-1},ZZ/101)
4 3 2 2 3 4 3 2 2 3 2 2 2 2 2 3
o3 = a x + a x x + a x x + a x x + a x + a x x + a x x x + a x x x + a x x + a x x + a x x x + a x x + a x x +
0 0 1 0 1 3 0 1 6 0 1 10 1 2 0 2 4 0 1 2 7 0 1 2 11 1 2 5 0 2 8 0 1 2 12 1 2 9 0 2
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3 4
a x x + a x
13 1 2 14 2
ZZ
o3 : ---[a ..a ][x ..x ]
101 0 14 0 2
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The object genericPolynomials is a method function.