symmetryMap -- define the map to the base space with symmetric indices

Synopsis

Usage:
(Asym,phi)=symmetryMap(n,A)
Inputs:
- n, an integer, the number of variables of the homogeneous coordinate ring of P^n-1
- A, a polynomial ring, the base ring of the universal apolar unfolding
Outputs:
- Asym, a polynomial ring, in the symmetric variables
- phi, a ring map, A->Asym

Description

Construct the ring homomorhism A->Asym which induce the isomorphism A/lin = Asym, where lin denote the ideal of purely linear flattening relations.

The Example computation below shows that V(5) is smooth.

i1 : p=0,n=5

o1 = (0, 5)

o1 : Sequence

i2 : (R,A,I)=unfoldingEquations(p,n);

i3 : time (lin,J)=equationsInThePaper(n,A);betti J
     -- used 0.0351477 seconds

            0  1
o4 = total: 1 30
         0: 1  8
         1: . 15
         2: .  6
         3: .  1

o4 : BettiTally

i5 : (Asym,phi)=symmetryMap(n,A);

i6 : betti(J2= ideal mingens phi J)

            0  1
o6 = total: 1 10
         0: 1  .
         1: .  6
         2: .  3
         3: .  1

o6 : BettiTally

i7 : betti vars Asym

            0  1
o7 = total: 1 20
         0: 1 10
         1: .  6
         2: .  3
         3: .  1

o7 : BettiTally

i8 : lT=leadTerm gens J2

o8 = | 2a_(1,4,4) a_(1,3,4) 2a_(1,3,3) a_(1,2,4) a_(1,2,3) 2a_(1,2,2)
     ------------------------------------------------------------------------
     a_(1,1,4) a_(1,1,3) a_(1,1,2) 4a_(1,1,5) |

                1          10
o8 : Matrix Asym  <--- Asym

i9 : betti lT == betti J2

o9 = true

Ways to use `symmetryMap` :

symmetryMap(ZZ,Ring) (missing documentation)

symmetryMap -- define the map to the base space with symmetric indices

Synopsis

Description

Ways to use symmetryMap :

Ways to use `symmetryMap` :