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 |
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 |
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 |
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 |