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

- Usage:
    `picture F`
    `picture m`
    `picture M`
- Inputs:
  - F, a complex,
  - F, a chain complex,
  - m, a matrix, of map between labeled direct sum modules
  - M, a module, a labeled directSum module
- Optional inputs:
  - ShowRanks => ..., default value false

## 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

- burkeResolution -- compute a resolution from A-infinity structures
- aInfinity -- aInfinity algebra and module structures on free resolutions

## Ways to use picture:

- `picture(ChainComplex)`
- `picture(Complex)`
- `picture(Matrix)`
- `picture(Module)`

## For the programmer

The object picture is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AInfinity.m2:1337:0.