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eliminationMatrices :: ciResDeg

ciResDeg -- compute a regularity index and partial degrees of the residual resultant over a complete intersection

Synopsis

Description

Given a system of polynomials f0,...,fn of degree d0,...,dn that are contained in a complete intersection g1,...,gm of degree k1,...,km, this function returns the regularity index used to form the matrix associated to the residual resultant over a complete intersection and then all the partial degrees of this resultant with respect to the coefficients of f0,f1,..,fn.

i1 : R=ZZ[d_0..d_3,k_1,k_2]

o1 = R

o1 : PolynomialRing
i2 : L=ciResDeg({d_0,d_1,d_2,d_3},{k_1,k_2})

                                                                         2  
o2 = {d  + d  + d  + d  - 3k  - 3, {d d d  - d k k  - d k k  - d k k  + k k 
       0    1    2    3     2        1 2 3    1 1 2    2 1 2    3 1 2    1 2
     ------------------------------------------------------------------------
          2                                       2        2                 
     + k k , d d d  - d k k  - d k k  - d k k  + k k  + k k , d d d  - d k k 
        1 2   0 2 3    0 1 2    2 1 2    3 1 2    1 2    1 2   0 1 3    0 1 2
     ------------------------------------------------------------------------
                          2        2                                     
     - d k k  - d k k  + k k  + k k , d d d  - d k k  - d k k  - d k k  +
        1 1 2    3 1 2    1 2    1 2   0 1 2    0 1 2    1 1 2    2 1 2  
     ------------------------------------------------------------------------
      2        2
     k k  + k k }}
      1 2    1 2

o2 : List

See also