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picture -- displays information about the blocks of a map or maps between direct sum modules

Synopsis

Description

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. If ShowRanks is true, then the rank of the corresponding summand is also displayed.

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}| . |   *  |   *  |   .  |    7    ||
     |+------+---+------+------+------+---------+|
     ||{2, 1}| . |   .  |   *  |   *  |    *    ||
     |+------+---+------+------+------+---------+|
     +-------------------------------------------+

The possible symbols in the table produced by picture are:

. if the corresponding matrix is zero * if the corresponding matrix is nonzero (number) if the entries of the corresponding matrix contain a unit, the rank of the matrix tensored with the residue field is displayed id if the corresponding matrix is the identity matrix

See also

Ways to use picture:

For the programmer

The object picture is a method function with options.