detRes -- returns a matrix corresponding to the residual resultant over a Cohen-Macaulay codimension 2 base locus

Synopsis

• Usage:

  detRes(aSingleRowMatrix, Matrix, varList)

• Inputs:

  • Matrix, a matrix, a polynomial matrix M
  • Integer, an integer, an integer r corresponding to the regularity index used to form the determinantal resultant
  • varList, a list, a list of homogeneous variables that are to be eliminated
• Outputs:

  • aMatrix, a matrix, a matrix corresponding to the determinantal resultant

Description

i1 : R=QQ[a_0..a_5,b_0..b_5,x,y]

o1 = R

o1 : PolynomialRing

i2 : M:=matrix{{a_0*x+a_1*y,a_2*x+a_3*y,a_4*x+a_5*y},{b_0*x+b_1*y,b_2*x+b_3*y,b_4*x+b_5*y}}

o2 = | a_0x+a_1y a_2x+a_3y a_4x+a_5y |
     | b_0x+b_1y b_2x+b_3y b_4x+b_5y |

             2       3
o2 : Matrix R  <--- R

i3 : detRes(M,1,{x,y})

o3 = {2} | -a_2b_0+a_0b_2               -a_4b_0+a_0b_4              
     {2} | -a_3b_0-a_2b_1+a_1b_2+a_0b_3 -a_5b_0-a_4b_1+a_1b_4+a_0b_5
     {2} | -a_3b_1+a_1b_3               -a_5b_1+a_1b_5              
     ------------------------------------------------------------------------
     -a_4b_2+a_2b_4               |
     -a_5b_2-a_4b_3+a_3b_4+a_2b_5 |
     -a_5b_3+a_3b_5               |

             3       3
o3 : Matrix R  <--- R

See also

• macaulayFormula -- returns two matrices such that the ratio of their determinants is the Macaulay resultant
• macRes -- returns a matrix associated to the Macaulay resultant
• ciRes -- returns a matrix corresponding to the residual resultant over a complete intersection
• cm2Res -- returns a matrix corresponding to the residual resultant over a Cohen-Macaulay codimension 2 base locus
• bezoutianMatrix -- returns a matrix associated to generalized resultants