ciResDegGH -- compute a regularity index used for the residual resultant over a complete intersection

• Usage:

  ciResDegGH(r, m, v)

• Inputs:
  • v, a list, list 'var' of variables with respect to which the polynomials are homogeneous and from which one wants to remove these variables
  • r, a matrix, a single row matrix describing the base locus
  • m, a matrix, a matrix corresponding to the decomposition of a polynomial system over the base locus
• Outputs:
  • an integer, a regularity index to form the residual resultant-

i1 : R=QQ[a_0,a_1,a_2,a_3,a_4,b_0,b_1,b_2,b_3,b_4,c_0,c_1,c_2,c_3,c_4,x,y,z]

o1 = R

o1 : PolynomialRing

i2 : G=matrix{{z,x^2+y^2}}

o2 = | z x2+y2 |

             1      2
o2 : Matrix R  <-- R

i3 : H=matrix{{a_0*z+a_1*x+a_2*y,b_0*z+b_1*x+b_2*y,c_0*z+c_1*x+c_2*y},{a_3,b_3,c_3}}

o3 = | a_1x+a_2y+a_0z b_1x+b_2y+b_0z c_1x+c_2y+c_0z |
     | a_3            b_3            c_3            |

             2      3
o3 : Matrix R  <-- R

i4 : ciResDegGH({x,y,z},G,H)

o4 = 2