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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 ],{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

See also

Ways to use veronese :

For the programmer

The object veronese is a method function with options.