The sources and targets of the differentials in F = burkeResolution(M,n), where M is an R = S/I-module, are direct sums whose summands are labeled, each by a List of ZZ corresponding to a tensor product of components of the S-free resolutions of R and M.
The maps in the AInfinity structures are similarly labeled (each one has a source that has just one summand.)
When applied to such a map, picture prints it as a table, with columns labeled with the symbols associated to the source and rows labeled with the symbols associated to the target. When applied to a complex, the output is a "netList" display of the pictures of each of the maps.
i1 : R = ZZ/101[a,b,c,d]/ideal"a3,a2b2,b4,c4,d2"
o1 = R
o1 : QuotientRing
|
i2 : F = burkeResolution(coker vars R, 4)
1 4 11 33 99
o2 = R <-- R <-- R <-- R <-- R
0 1 2 3 4
o2 : Complex
|
i3 : picture F.dd_3
+------+---+------+------+
o3 = | |{3}|{3, 0}|{2, 1}|
+------+---+------+------+
| {2} | * | * | * |
+------+---+------+------+
|{2, 0}| . | * | * |
+------+---+------+------+
|
i4 : picture F
+-------------------------------------------+
|+---+---+ |
o4 = || |{1}| |
|+---+---+ |
||{0}| * | |
|+---+---+ |
+-------------------------------------------+
|+---+---+------+ |
|| |{2}|{2, 0}| |
|+---+---+------+ |
||{1}| * | * | |
|+---+---+------+ |
+-------------------------------------------+
|+------+---+------+------+ |
|| |{3}|{3, 0}|{2, 1}| |
|+------+---+------+------+ |
|| {2} | * | * | * | |
|+------+---+------+------+ |
||{2, 0}| . | * | * | |
|+------+---+------+------+ |
+-------------------------------------------+
|+------+---+------+------+------+---------+|
|| |{4}|{4, 0}|{3, 1}|{2, 2}|{2, 2, 0}||
|+------+---+------+------+------+---------+|
|| {3} | * | * | * | * | * ||
|+------+---+------+------+------+---------+|
||{3, 0}| . | * | * | . | u ||
|+------+---+------+------+------+---------+|
||{2, 1}| . | . | * | * | * ||
|+------+---+------+------+------+---------+|
+-------------------------------------------+
|
The possible symbols in the table produced by picture are:
. if the corresponding matrix is zero * if the corresponding matrix is nonzero u if the entries of the corresponding matrix contain a unit.