If only one degree (as integer, or list of integers) is given for targetBox or sourceBox, then only rows or columns that match that exact degree are used.
i1 : R = QQ[a..d]; |
i2 : I = ideal"a2b-c3,abc-d3,ac2-bd2-cd2,abcd-c4"
2 3 3 2 2 2 4
o2 = ideal (a b - c , a*b*c - d , a*c - b*d - c*d , - c + a*b*c*d)
o2 : Ideal of R
|
i3 : C = res I; |
i4 : m = C.dd_2
o4 = {3} | ac2-bd2-cd2 0 -abc+d3 0 -a3c+a2cd
{3} | 0 ac2-bd2-cd2 a2b-c3 -acd+cd2 a4-a3d-acd2+cd3
{3} | -a2b+c3 -abc+d3 0 abd-bd2 -a2c2+ac2d-acd2+cd3
{4} | 0 0 0 b2+bc-cd a3-bcd-c2d-cd2
------------------------------------------------------------------------
-a3c+a2cd
a4-a3d+a2cd-3acd2-ad3+2cd3+d4
-a2c2-a2bd+ac2d+2abd2-acd2-bd3+cd3
a3-ab2+b2d+acd-c2d-2cd2-d3
------------------------------------------------------------------------
-a3c+a2cd
a4-a3d+a2cd-3acd2-ad3+2cd3+d4
-a2c2-a2bd+ac2d+2abd2-acd2-ad3-bd3+cd3+d4
a3-ab2+ac2+b2d+acd-c2d-bd2-3cd2-d3
------------------------------------------------------------------------
-a2bc+a2cd-acd2+d4 a2cd-acd2 |
a3b-a3d+abcd+ac2d+a2d2-2bcd2-c2d2-bd3-cd3 -a3d+ac2d+a2d2-c2d2 |
-abc2-ab2d-abcd+ac2d+b2d2-c2d2+cd3+d4 -abcd+ac2d+bcd2-c2d2 |
a2b-b3-b2c+bc2-a2d+bcd -b2c+c3-a2d+c2d |
4 9
o4 : Matrix R <--- R
|
i5 : submatrixByDegrees(m, 3, 6)
o5 = {3} | ac2-bd2-cd2 0 -abc+d3 0 |
{3} | 0 ac2-bd2-cd2 a2b-c3 -acd+cd2 |
{3} | -a2b+c3 -abc+d3 0 abd-bd2 |
3 4
o5 : Matrix R <--- R
|
i6 : submatrixByDegrees(m, (3,3), (6,7))
o6 = {3} | ac2-bd2-cd2 0 -abc+d3 0 -a3c+a2cd
{3} | 0 ac2-bd2-cd2 a2b-c3 -acd+cd2 a4-a3d-acd2+cd3
{3} | -a2b+c3 -abc+d3 0 abd-bd2 -a2c2+ac2d-acd2+cd3
------------------------------------------------------------------------
-a3c+a2cd
a4-a3d+a2cd-3acd2-ad3+2cd3+d4
-a2c2-a2bd+ac2d+2abd2-acd2-bd3+cd3
------------------------------------------------------------------------
-a3c+a2cd
a4-a3d+a2cd-3acd2-ad3+2cd3+d4
-a2c2-a2bd+ac2d+2abd2-acd2-ad3-bd3+cd3+d4
------------------------------------------------------------------------
-a2bc+a2cd-acd2+d4 a2cd-acd2 |
a3b-a3d+abcd+ac2d+a2d2-2bcd2-c2d2-bd3-cd3 -a3d+ac2d+a2d2-c2d2 |
-abc2-ab2d-abcd+ac2d+b2d2-c2d2+cd3+d4 -abcd+ac2d+bcd2-c2d2 |
3 9
o6 : Matrix R <--- R
|
i7 : submatrixByDegrees(m, (4,4), (7,7))
o7 = {4} | a3-bcd-c2d-cd2 a3-ab2+b2d+acd-c2d-2cd2-d3
------------------------------------------------------------------------
a3-ab2+ac2+b2d+acd-c2d-bd2-3cd2-d3 a2b-b3-b2c+bc2-a2d+bcd
------------------------------------------------------------------------
-b2c+c3-a2d+c2d |
1 5
o7 : Matrix R <--- R
|
For multidegrees, the interval is a box.
i8 : S = QQ[a..d, Degrees=>{2:{1,0},2:{0,1}}];
|
i9 : I = ideal(a*d^4, b^3, a^2*d^2, a*b*c*d^3)
4 3 2 2 3
o9 = ideal (a*d , b , a d , a*b*c*d )
o9 : Ideal of S
|
i10 : C = res I
1 4 6 4 1
o10 = S <-- S <-- S <-- S <-- S <-- 0
0 1 2 3 4 5
o10 : ChainComplex
|
i11 : m = C.dd_2
o11 = {3, 0} | 0 -a2d2 0 0 -acd3 -ad4 |
{2, 2} | -d2 b3 -bcd 0 0 0 |
{1, 4} | a 0 0 -bc 0 b3 |
{2, 4} | 0 0 a d b2 0 |
4 6
o11 : Matrix S <--- S
|
i12 : degrees target m
o12 = {{3, 0}, {2, 2}, {1, 4}, {2, 4}}
o12 : List
|
i13 : degrees source m
o13 = {{2, 4}, {5, 2}, {3, 4}, {2, 5}, {4, 4}, {4, 4}}
o13 : List
|
i14 : submatrixByDegrees(C.dd_2, ({2,2},{2,4}), ({2,2},{5,4}))
o14 = {2, 2} | -d2 b3 -bcd 0 0 |
{2, 4} | 0 0 a b2 0 |
2 5
o14 : Matrix S <--- S
|
The degrees are taken from the target and source free modules, not from the matrix entries themselves.
The object submatrixByDegrees is a method function.