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displayBlocks -- prints a matrix showing the source and target decomposition

Synopsis

Description

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 |      |
     +------+----------+-------------------------------+--------------------------------------------------------+

See also

Ways to use displayBlocks:

For the programmer

The object displayBlocks is a method function.