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makePureBettiDiagram -- makes a pure Betti diagram given a list of degrees

Synopsis

Description

See pureBetti for a description of the Herzog-Kuhl equations.
i1 : makePureBettiDiagram{0,2,4,5}

            0  1  2 3
o1 = total: 3 10 15 8
         0: 3  .  . .
         1: . 10  . .
         2: .  . 15 8

o1 : BettiTally
i2 : makePureBettiDiagram({0,2,4,5}, TableEntries => HerzogKuhl)

             0  1 2  3
             1  1 1  1
o2 = total: -- -- - --
            40 12 8 15
             1      
         0: --  . .  .
            40      
                1   
         1:  . -- .  .
               12   
                  1  1
         2:  .  . - --
                  8 15

o2 : BettiTally
i3 : makePureBettiDiagram{0,3,4,5,6,7,10}

            0  1   2   3   4  5 6
o3 = total: 1 50 175 252 175 50 1
         0: 1  .   .   .   .  . .
         1: .  .   .   .   .  . .
         2: . 50 175 252 175 50 .
         3: .  .   .   .   .  . .
         4: .  .   .   .   .  . 1

o3 : BettiTally
i4 : makePureBettiDiagram({0,3,4,5,6,7,10}, TableEntries => RealizationModules)

             0    1    2    3    4    5  6
o4 = total: 36 1800 6300 9072 6300 1800 36
         0: 36    .    .    .    .    .  .
         1:  .    .    .    .    .    .  .
         2:  . 1800 6300 9072 6300 1800  .
         3:  .    .    .    .    .    .  .
         4:  .    .    .    .    .    . 36

o4 : BettiTally
i5 : makePureBettiDiagram{0,3,4,5,6,7,8,11}

            0  1   2   3   4   5  6 7
o5 = total: 1 77 330 616 616 330 77 1
         0: 1  .   .   .   .   .  . .
         1: .  .   .   .   .   .  . .
         2: . 77 330 616 616 330 77 .
         3: .  .   .   .   .   .  . .
         4: .  .   .   .   .   .  . 1

o5 : BettiTally
i6 : makePureBettiDiagram({0,3,4,5,6,7,8,11}, TableEntries => HerzogKuhl)

                 0    1   2   3   4   5    6      7
               1     1   1   1   1   1    1     1
o6 = total: ------ ---- --- --- --- --- ---- ------
            221760 2880 672 360 360 672 2880 221760
               1                             
         0: ------    .   .   .   .   .    .      .
            221760                           
         1:      .    .   .   .   .   .    .      .
                     1   1   1   1   1    1  
         2:      . ---- --- --- --- --- ----      .
                   2880 672 360 360 672 2880 
         3:      .    .   .   .   .   .    .      .
                                                1
         4:      .    .   .   .   .   .    . ------
                                             221760

o6 : BettiTally
i7 : makePureBettiDiagram({0,3,4,5,6,7,8,11}, TableEntries => RealizationModules)

             0    1     2     3     4     5    6  7
o7 = total: 45 3465 14850 27720 27720 14850 3465 45
         0: 45    .     .     .     .     .    .  .
         1:  .    .     .     .     .     .    .  .
         2:  . 3465 14850 27720 27720 14850 3465  .
         3:  .    .     .     .     .     .    .  .
         4:  .    .     .     .     .     .    . 45

o7 : BettiTally

See also

Ways to use makePureBettiDiagram :

For the programmer

The object makePureBettiDiagram is a method function with options.