Suppose given a homogeneous ideal l.c.i. CM codim 2 J=(g1,..,gn), such that I=(f1,..,fm) is included in J and (I:J) is a residual intersection. Let H be the matrix that I=J.H. Let R be the matrixof the first syzygies of J. This function computes an elimination matrix corresponding to the residual resultant over V(I) over V(J).
i1 : R = QQ[X,Y,Z,x,y,z]
o1 = R
o1 : PolynomialRing
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i2 : F = matrix{{x*y^2,y^3,x*z^2,y^3+z^3}}
o2 = | xy2 y3 xz2 y3+z3 |
1 4
o2 : Matrix R <--- R
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i3 : G = matrix{{y^2,z^2}}
o3 = | y2 z2 |
1 2
o3 : Matrix R <--- R
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i4 : M = matrix{{1,0,0},{0,1,0},{0,0,1},{-X,-Y,-Z}}
o4 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
| -X -Y -Z |
4 3
o4 : Matrix R <--- R
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i5 : H = (F//G)*M
o5 = {2} | -Xy+x -Yy+y -Zy |
{2} | -Xz -Yz -Zz+x |
2 3
o5 : Matrix R <--- R
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i6 : l = {x,y,z}
o6 = {x, y, z}
o6 : List
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i7 : L=cm2Res (G,H,l)
o7 = {3} | 0 0 0 0 0 0 1 0 0 0 0 0 |
{3} | 0 0 0 0 0 0 -X 1 0 -Y+1 0 0 |
{3} | 0 0 -Y 0 0 0 -Z 0 1 0 0 0 |
{3} | -1 0 0 0 0 0 0 -X 0 0 -Y+1 0 |
{3} | 0 0 X -Y 0 0 0 -Z -X -Z 0 -Y+1 |
{3} | 0 0 0 0 -Y -1 0 0 -Z 0 0 0 |
{3} | X Y-1 0 0 0 Z 0 0 0 0 0 0 |
{3} | 0 0 0 X 0 0 0 0 0 0 -Z 0 |
{3} | 0 0 0 0 X 0 0 0 0 0 0 -Z |
{3} | X Y 0 0 0 Z 0 0 0 0 0 0 |
10 12
o7 : Matrix R <--- R
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i8 : maxCol L
o8 = {{3} | 0 0 0 0 0 0 1 0 0 0 |, {0, 1, 2, 3, 4, 5, 6, 7, 8,
{3} | 0 0 0 0 0 0 -X 1 0 -Y+1 |
{3} | 0 0 -Y 0 0 0 -Z 0 1 0 |
{3} | -1 0 0 0 0 0 0 -X 0 0 |
{3} | 0 0 X -Y 0 0 0 -Z -X -Z |
{3} | 0 0 0 0 -Y -1 0 0 -Z 0 |
{3} | X Y-1 0 0 0 Z 0 0 0 0 |
{3} | 0 0 0 X 0 0 0 0 0 0 |
{3} | 0 0 0 0 X 0 0 0 0 0 |
{3} | X Y 0 0 0 Z 0 0 0 0 |
------------------------------------------------------------------------
9}}
o8 : List
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