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Resultants :: veronese

veronese -- Veronese embedding

Synopsis

Description

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

See also

Ways to use veronese :