detResDeg -- compute a regularity index and partial degrees of the determinantal resultant

Synopsis

• Usage:

  detResDeg(n, c, r, R)

• Inputs:

  • n, an integer, corresponding to the drop of rank used to form the determinantal resultant
  • c, a list, a list of degrees indexing the columns of a polynomial matrix
  • r, a list, a list of degrees indexing the rows of the same polynomial
  • R, a ring, an ambient ring where the computations take place
• Outputs:

  • a list, a list of element consisting of a regularity index and partial degree of homogeneity of the determinantal resultant

Description

i1 : R = ZZ[d1,d2,d3,k1,k2]

o1 = R

o1 : PolynomialRing

i2 : detResDeg(1,{d1,d2,d3},{k1,k2},R)

o2 = {d1 + d2 + d3 - k1 - 2k2 - 1, {d2 + d3 - k1 - k2, d1 + d3 - k1 - k2, d1
     ------------------------------------------------------------------------
     + d2 - k1 - k2}}

o2 : List

See also

• macaulayFormula -- returns two matrices such that the ratio of their determinants is the Macaulay resultant
• eliminationMatrix -- returns a matrix that represents the image of the map
• ciResDeg -- compute a regularity index and partial degrees of the residual resultant over a complete intersection
• bezoutianMatrix -- returns a matrix associated to generalized resultants