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 |
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 |
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 |
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 |
The object veronese is a method function with options.