The maps produced by burkeResolution and aInfinity have direct sums of labeled modules as sources and targets; the label corresponds to the tensor factors.
displayBlocks M shows this data
i1 : R = ZZ/101[a,b,c]/(ideal(a,b,c^2))^2 o1 = R o1 : QuotientRing |
i2 : F = burkeResolution (coker vars R, 4) 1 3 9 27 81 o2 = R <-- R <-- R <-- R <-- R 0 1 2 3 4 o2 : Complex |
i3 : picture F +---------------------------------------+ |+---+---+ | o3 = || |{1}| | |+---+---+ | ||{0}| * | | |+---+---+ | +---------------------------------------+ |+---+---+------+ | || |{2}|{2, 0}| | |+---+---+------+ | ||{1}| * | * | | |+---+---+------+ | +---------------------------------------+ |+------+---+------+------+ | || |{3}|{3, 0}|{2, 1}| | |+------+---+------+------+ | || {2} | * | * | * | | |+------+---+------+------+ | ||{2, 0}| . | * | * | | |+------+---+------+------+ | +---------------------------------------+ |+------+------+------+------+---------+| || |{4, 0}|{3, 1}|{2, 2}|{2, 2, 0}|| |+------+------+------+------+---------+| || {3} | * | * | * | * || |+------+------+------+------+---------+| ||{3, 0}| * | * | . | * || |+------+------+------+------+---------+| ||{2, 1}| . | * | * | * || |+------+------+------+------+---------+| +---------------------------------------+ |
i4 : displayBlocks F.dd_3 +------+----------+-------------------------------+--------------------------------------------------------+ o4 = | | {3} | {3, 0} | {2, 1} | +------+----------+-------------------------------+--------------------------------------------------------+ | {2} |{2} | c || {2} | 0 b 0 0 0 0 0 0 | |{2} | 0 a 0 0 b c -b 0 0 0 c2 0 -c2 0 0 0 0 0 || | |{2} | -b || {2} | 0 0 ac bc 0 0 0 0 | |{2} | 0 0 a 0 0 0 0 0 0 -ac -bc 0 0 0 0 -c3 0 0 || | |{2} | a || {2} | 0 0 0 0 0 bc 0 0 | |{2} | 0 0 0 0 0 a 0 0 b 0 0 0 -ac -bc 0 0 -c3 0 || +------+----------+-------------------------------+--------------------------------------------------------+ |{2, 0}| . |{2} | b 0 c2 0 0 0 0 0 || {2} | a b c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | | | |{2} | -a b 0 c2 0 0 0 0 || {2} | 0 0 0 a b c 0 0 0 0 0 0 0 0 0 0 0 0 | | | | |{2} | 0 -a 0 0 0 c2 0 0 || {2} | 0 0 0 0 0 0 a b c 0 0 0 0 0 0 0 0 0 | | | | |{3} | 0 0 -a -b b 0 c2 0 || {3} | 0 0 0 0 0 0 0 0 0 a b c 0 0 0 0 0 0 | | | | |{3} | 0 0 0 0 -a -b 0 c2 || {3} | 0 0 0 0 0 0 0 0 0 0 0 0 a b c 0 0 0 | | | | |{4} | 0 0 0 0 0 0 -a -b || {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a b c | | +------+----------+-------------------------------+--------------------------------------------------------+ |
The object displayBlocks is a method function.