The terms of the burkeResolution resolution are direct sums of labeled modules. the function picture shows the symbols associated to the summands, while the function extractBlocks provides the submatrix associated with the summands specified.
i1 : R = ZZ/101[a,b,c,d]/ideal(a^2, b^2, c^3, d^4) o1 = R o1 : QuotientRing |
i2 : M = R^1/ideal(a*b,c*d) o2 = cokernel | ab cd | 1 o2 : R-module, quotient of R |
i3 : F = burkeResolution(M,5) 1 6 17 42 112 295 o3 = R <-- R <-- R <-- R <-- R <-- R 0 1 2 3 4 5 o3 : Complex |
i4 : picture F.dd_3 +------+---+------+------+ o4 = | |{3}|{3, 0}|{2, 1}| +------+---+------+------+ | {2} | * | u | u | +------+---+------+------+ |{2, 0}| . | . | * | +------+---+------+------+ |
i5 : extractBlocks(F.dd_3, {2,1}) o5 = {3} | 0 a b 0 0 0 -b 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 a 0 0 0 -a -b 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c 0 -d3 0 0 0 0 d3 0 | {5} | 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 | {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 | {5} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 | {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c2 0 0 0 -d -c2 0 | {6} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 | {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 | {6} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 | {2} | 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 | 17 24 o5 : Matrix R <--- R |
i6 : extractBlocks(F.dd_3,{2,0}, {2,1}) o6 = {2} | 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 | 4 24 o6 : Matrix R <--- R |
i7 : extractBlocks(F.dd_3,{2,0}, {{3,0},{2,1}}) o7 = {2} | 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 ------------------------------------------------------------------------ 0 | 0 | 0 | 0 | 4 30 o7 : Matrix R <--- R |
The object extractBlocks is a method function.