unfoldingEquations -- setup the unfolding equations

Synopsis

Usage:
(R,A,I)=unfoldingEquations(p,n)
Inputs:
- p, an integer, the characteristic of the desired ground field
- n, an integer, the number of variables of the homogeneous coordinate ring of P^n-1
Outputs:
- R, a polynomial ring, the homogeneous coordinate ring of P^n-1
- A, a polynomial ring, the base ring of the universal apolar unfolding
- I, an ideal, the ideal generated by the unfolding equations in A**R

Description

The grading of the variable is chosen carefully to make the ideal homogeneous.

i1 : p=0,n=5

o1 = (0, 5)

o1 : Sequence

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

i4 : isHomogeneous I

o4 = true

i5 : I

             2    2                                                          
o5 = ideal (x  - x a         - x x a         - x x a         - x x a        ,
             1    5 (1, 1),5    2 5 (1, 1),2    3 5 (1, 1),3    4 5 (1, 1),4 
     ------------------------------------------------------------------------
             2                                                               
     x x  - x a         - x x a         - x x a         - x x a        , x x 
      1 2    5 (1, 2),5    2 5 (1, 2),2    3 5 (1, 2),3    4 5 (1, 2),4   1 3
     ------------------------------------------------------------------------
        2                                                                 
     - x a         - x x a         - x x a         - x x a        , x x  -
        5 (1, 3),5    2 5 (1, 3),2    3 5 (1, 3),3    4 5 (1, 3),4   1 4  
     ------------------------------------------------------------------------
      2                                                            2         
     x a         - x x a         - x x a         - x x a        , x  - x x  -
      5 (1, 4),5    2 5 (1, 4),2    3 5 (1, 4),3    4 5 (1, 4),4   2    1 5  
     ------------------------------------------------------------------------
      2                                                                 
     x a         - x x a         - x x a         - x x a        , x x  -
      5 (2, 2),5    2 5 (2, 2),2    3 5 (2, 2),3    4 5 (2, 2),4   2 3  
     ------------------------------------------------------------------------
      2                                                                 
     x a         - x x a         - x x a         - x x a        , x x  -
      5 (2, 3),5    2 5 (2, 3),2    3 5 (2, 3),3    4 5 (2, 3),4   2 4  
     ------------------------------------------------------------------------
      2                                                            2         
     x a         - x x a         - x x a         - x x a        , x  - x x  -
      5 (2, 4),5    2 5 (2, 4),2    3 5 (2, 4),3    4 5 (2, 4),4   3    1 5  
     ------------------------------------------------------------------------
      2                                                                 
     x a         - x x a         - x x a         - x x a        , x x  -
      5 (3, 3),5    2 5 (3, 3),2    3 5 (3, 3),3    4 5 (3, 3),4   3 4  
     ------------------------------------------------------------------------
      2                                                            2         
     x a         - x x a         - x x a         - x x a        , x  - x x  -
      5 (3, 4),5    2 5 (3, 4),2    3 5 (3, 4),3    4 5 (3, 4),4   4    1 5  
     ------------------------------------------------------------------------
      2
     x a         - x x a         - x x a         - x x a        )
      5 (4, 4),5    2 5 (4, 4),2    3 5 (4, 4),3    4 5 (4, 4),4

o5 : Ideal of AR

Ways to use `unfoldingEquations` :

unfoldingEquations(ZZ,ZZ)

unfoldingEquations -- setup the unfolding equations

Synopsis

Description

Ways to use unfoldingEquations :

Ways to use `unfoldingEquations` :